CN101676744B - A high-precision tracking method for weak and small targets under complex background and low signal-to-noise ratio - Google Patents

Abstract

Translated fromChinese

本发明提供一种复杂背景低信噪比下弱小目标高精度跟踪方法，该方法通过对复杂背景低信噪比下的图像进行预处理、基于二项分布判断准则的目标自适应门限分割提取目标后，再采用基于Kalman滤波器思想改进的曲线拟合算法进行目标的运动预测，并通过红外与可见光传感器的数据融合提高目标的检测概率、降低虚警概率；当目标形状发生改变时，利用边缘特征归一化的形状识别寻找特征不变量以达到目标的精确跟踪。

The invention provides a high-precision tracking method for weak and small targets under complex background and low signal-to-noise ratio. The method preprocesses images under complex background and low signal-to-noise ratio, and extracts targets based on target adaptive threshold segmentation based on the binomial distribution judgment criterion. Finally, the improved curve fitting algorithm based on the Kalman filter idea is used to predict the motion of the target, and the detection probability of the target is improved and the probability of false alarm is reduced through the data fusion of infrared and visible light sensors; when the shape of the target changes, the edge is used to Feature-normalized shape recognition looks for feature invariants to achieve precise object tracking.

Description

Translated fromChinese

一种复杂背景低信噪比下弱小目标高精度跟踪方法A high-precision tracking method for weak and small targets under complex background and low signal-to-noise ratio

(一)技术领域：(1) Technical field:

本发明涉及一种复杂背景低信噪比下弱小目标高精度跟踪方法，尤其指一种模式识别与智能控制、复杂背景下目标自动检测与识别技术、图像处理与数据融合方法，通过对可见光和红外信息的融合，实现了对复杂背景下弱小目标的检测与跟踪，属于信息处理技术领域。The invention relates to a high-precision tracking method for weak and small targets under complex backgrounds and low signal-to-noise ratios, in particular to a pattern recognition and intelligent control, target automatic detection and recognition technology under complex backgrounds, image processing and data fusion methods, through visible light and The fusion of infrared information realizes the detection and tracking of weak and small targets in complex backgrounds, and belongs to the field of information processing technology.

(二)背景技术：(two) background technology:

在现代战争中，各种精确制导武器的大量使用使防空作战变得越来越困难，巡航导弹、隐形飞机、武装直升机、反辐射导弹、侦察和攻击无人机的应用使防空形势变得越来越严峻，如何在保存自己的情况下探测到来袭目标并对其实施有效的攻击是现代防空急需解决的问题。而目前我国的防空体系主要是对抗常规飞机而建立的，所以对上述目标的对抗能力是较弱的，其主要原因是对上述目标的探测存在困难。特别是反辐射导弹的威胁使得防空雷达的应用受到很大的限制。据报道，在2003年发生的伊拉克战争前，伊方80％以上的防空体系是完好无损的，但是在战争打响后，伊方的防空武器几乎毫无建树，其主要原因就是制电磁权完全掌握在美军手中，伊拉克军队的防空雷达只要一开机，几分钟内就遭到美军反辐射导弹的攻击，美军摧毁伊军防空体系的同时更摧毁了伊军的战斗意志，所以伊军虽然大部分防空武器完好无损，但是却不敢使用，成了无用的一堆废铁。伊军防空作战未能有效发挥作用的主要原因是缺乏有效的针对美军空中威胁的探测手段。In modern warfare, the extensive use of various precision-guided weapons has made air defense operations more and more difficult. The application of cruise missiles, stealth aircraft, armed helicopters, anti-radiation missiles, reconnaissance and attack drones has made the air defense situation more and more difficult. How to detect the incoming target and carry out an effective attack on it while saving oneself is an urgent problem to be solved by modern air defense. At present, my country's air defense system is mainly established to fight against conventional aircraft, so the ability to fight against the above-mentioned targets is relatively weak. The main reason is that there are difficulties in detecting the above-mentioned targets. In particular, the threat of anti-radiation missiles has greatly restricted the application of air defense radars. According to reports, before the Iraq War in 2003, more than 80% of Iraq's air defense system was intact, but after the war broke out, Iraq's air defense weapons were almost useless. In his hands, as long as the Iraqi army's air defense radar is turned on, it will be attacked by the US anti-radiation missile within a few minutes. While destroying the Iraqi air defense system, the US army also destroyed the Iraqi army's will to fight. Therefore, although most of the Iraqi army's air defense weapons are intact It is non-destructive, but dare not use it, and has become a pile of useless scrap iron. The main reason why the Iraqi air defense operations failed to function effectively is the lack of effective means of detection against US air threats.

光电探测系统对抗上述目标威胁具有独特的优点，光电探测系统和雷达配合使用，具有很强的互补性。光电空中目标探测系统有如下雷达所不具备的优点：The photoelectric detection system has unique advantages in combating the above-mentioned target threats, and the photoelectric detection system and radar are used together and are highly complementary. The photoelectric air target detection system has the following advantages that radar does not have:

1)被动式工作方式，不辐射电磁波，隐蔽性好；1) Passive working mode, does not radiate electromagnetic waves, and has good concealment;

2)工作在光波范围，不受电子干扰；2) Work in the light wave range, free from electronic interference;

3)目标不易隐身；3) The target is not easy to stealth;

4)低角跟踪时，不受地物杂波的影响，无低空盲区；4) When tracking at low angles, it is not affected by ground clutter and has no low-altitude blind spots;

5)跟踪精度和测距精度高；5) High tracking accuracy and ranging accuracy;

6)目标图像直观清晰，易于目标识别。6) The target image is intuitive and clear, easy to identify the target.

光电探测跟踪系统需要解决的关键问题是研制具有智能化的视频目标识别跟踪器和高精度的伺服跟踪转台。光电探测系统的设计应尽可能地在远距离时发现和识别目标，由于空中目标在远距离时通常十分弱小，因此复杂背景下弱小目标检测识别和跟踪是需要解决的关键技术问题。The key problem to be solved in the photoelectric detection and tracking system is to develop an intelligent video target recognition tracker and a high-precision servo tracking turntable. The design of the photoelectric detection system should detect and identify targets at a long distance as much as possible. Since air targets are usually very weak at long distances, the detection, identification and tracking of weak targets in complex backgrounds is a key technical problem that needs to be solved.

(三)发明内容：(3) Contents of the invention:

本发明的目的在于提供一种复杂背景低信噪比下弱小目标高精度跟踪方法，以实现在极低信噪比下，及时检测、识别弱小目标，检测出目标后，在复杂背景(诱饵、目标抖动、成像噪声、多目标、交叉等)情况下稳定的跟踪目标，不丢失目标。The purpose of the present invention is to provide a high-precision tracking method for weak and small targets under a complex background and low SNR, so as to detect and identify weak and small targets in time under an extremely low SNR. Target jitter, imaging noise, multi-target, intersection, etc.) to track the target stably without losing the target.

本发明是一种复杂背景低信噪比下弱小目标高精度跟踪方法，其采用的复杂背景下多模数据融合可提高目标的检测概率和精确跟踪精度，同时充分考虑系统化和工程化应用的要求，在设计上考虑多种通用需求，多种信息接口，集成强大的软、硬件资源，在不改变硬件情况下只需改变软件即可实现对海上、空中等不同目标的处理。The present invention is a high-precision tracking method for weak and small targets under a complex background and low signal-to-noise ratio. The multi-mode data fusion under the complex background adopted by it can improve the detection probability and precise tracking accuracy of the target, and at the same time fully consider the system and engineering application Requirements, in the design, consider a variety of general requirements, a variety of information interfaces, integrate powerful software and hardware resources, and only need to change the software without changing the hardware to realize the processing of different targets such as sea and air.

本发明的技术方案为：Technical scheme of the present invention is:

将本发明复杂背景低信噪比下弱小目标高精度跟踪方法应用在自主研制的多模多目标精密跟踪装置上，以验证系统的性能指标。该多模多目标精密跟踪装置，由以下三部分构成：数字伺服平台、综合信息处理平台、压缩及传输设备；本发明的复杂背景低信噪比下弱小目标高精度跟踪方法主要在综合信息处理平台中得以实现。该装置中：The high-precision tracking method for weak and small targets under the complex background and low signal-to-noise ratio of the present invention is applied to the self-developed multi-mode and multi-target precision tracking device to verify the performance indicators of the system. The multi-mode multi-target precision tracking device is composed of the following three parts: digital servo platform, comprehensive information processing platform, compression and transmission equipment; the high-precision tracking method for weak and small targets under complex background and low signal-to-noise ratio of the present invention is mainly in the comprehensive information processing realized in the platform. In this device:

1)数字伺服平台：1) Digital servo platform:

该数字伺服平台是由CCD(Charge Coupled Device，即电荷藕合器件图像传感器)摄像机、红外传感器、高精度数字伺服转台、手柄和监视器组成，也可根据需要选用两个CCD摄像机或两个红外传感器。该数字伺服平台中的CCD摄像机可以是模拟信号输入或数字信号输入，采用的红外传感器其分辨率为768×576。The digital servo platform is composed of a CCD (Charge Coupled Device, that is, a charge-coupled device image sensor) camera, an infrared sensor, a high-precision digital servo turntable, a handle and a monitor. Two CCD cameras or two infrared cameras can also be selected according to needs. sensor. The CCD camera in this digital servo platform can be an analog signal input or a digital signal input, and the infrared sensor adopted has a resolution of 768×576.

该数字伺服平台是图像获取装置的支撑平台，其中的CCD摄像机和红外传感器分别安装在高精度数字伺服转台两端，可随高精度数字伺服转台一起运动。同时该高精度数字伺服转台可根据接收的控制命令进行转动，对目标进行精确跟踪，使目标保持在图像获取装置的视场中心。The digital servo platform is the supporting platform of the image acquisition device, in which the CCD camera and infrared sensor are respectively installed at both ends of the high-precision digital servo turntable, and can move together with the high-precision digital servo turntable. At the same time, the high-precision digital servo turntable can be rotated according to the received control command, and the target can be precisely tracked, so that the target can be kept at the center of the field of view of the image acquisition device.

将CCD摄像机同红外传感器组合使用，同时获取可见光和红外的目标图像信息，综合两种信息中的目标特征，从而提高目标的检测概率和精确跟踪精度。The CCD camera is used in combination with the infrared sensor to obtain visible light and infrared target image information at the same time, and integrate the target features in the two kinds of information, thereby improving the detection probability and precise tracking accuracy of the target.

2)综合信息处理平台：2) Comprehensive information processing platform:

该综合信息处理平台是由信息接口、高速数字信号处理器、伺服控制处理器组成。其高速数字信号处理器采用基于DSP(数字信号处理器)的信号处理系统。高速数字信号处理器接收从CCD摄像机和红外传感器传入的图像信息，完成对复杂背景低信噪比条件下可见光和红外图像中的目标特征提取、特征匹配、目标运动预测与估计、精确跟踪方法的实现。伺服控制处理器根据目标预测与跟踪的结果，确定高精度数字伺服转台的运动方向，并向高精度数字伺服转台发出控制命令，使高精度数字伺服转台根据预测与跟踪的结果对目标进行跟踪。The integrated information processing platform is composed of an information interface, a high-speed digital signal processor, and a servo control processor. Its high-speed digital signal processor adopts a signal processing system based on DSP (Digital Signal Processor). The high-speed digital signal processor receives the image information from the CCD camera and infrared sensor, and completes the target feature extraction, feature matching, target motion prediction and estimation, and precise tracking methods in the visible light and infrared images under the condition of complex background and low signal-to-noise ratio realization. The servo control processor determines the movement direction of the high-precision digital servo turntable based on the results of target prediction and tracking, and sends control commands to the high-precision digital servo turntable, so that the high-precision digital servo turntable can track the target according to the results of prediction and tracking.

这里采用两个独立的信号处理器，即高速数字信号处理器和伺服控制处理器，即高速数字信号处理器和伺服控制处理器，分别对图像信息和伺服平台的控制信息进行处理，在图像预处理、目标识别与跟踪关键算法中，针对复杂背景下弱小目标的特点，采取多种算法改进与创新实现对弱小目标的识别与跟踪。Two independent signal processors are used here, that is, a high-speed digital signal processor and a servo control processor, that is, a high-speed digital signal processor and a servo control processor, to process the image information and the control information of the servo platform respectively. In the key algorithms of processing, target recognition and tracking, according to the characteristics of weak and small targets in complex backgrounds, various algorithm improvements and innovations are adopted to realize the identification and tracking of weak and small targets.

3)压缩及传输设备：3) Compression and transmission equipment:

压缩及传输设备使该多模多目标精密跟踪装置具有“人在回路”功能，将自动识别检测出的目标的所有信息和图像传回指挥中心，并接受指挥中心的指令对跟踪的目标进行调整以提高自动识别的精度。该压缩及传输设备由视频压缩处理器、GPRS传输模块组成。视频压缩处理器的图像输入可以是数字视频或模拟视频，可根据不同的输出要求选择不同的接口协议，采用MEPG-4的视频压缩算法，后端GPRS传输模块采用基于GPRS无线信道进行传输。The compression and transmission equipment make the multi-mode multi-target precision tracking device have the function of "human in the loop", and send all the information and images of the automatically identified and detected targets back to the command center, and accept the commands of the command center to adjust the tracked targets In order to improve the accuracy of automatic identification. The compression and transmission equipment is composed of a video compression processor and a GPRS transmission module. The image input of the video compression processor can be digital video or analog video, and different interface protocols can be selected according to different output requirements. The video compression algorithm of MEPG-4 is adopted, and the back-end GPRS transmission module uses GPRS wireless channel for transmission.

该装置突破了目标识别跟踪器单一的目标检测识别处理模式，还可以与其它探测系统联网进行数据交互、图像传输，并具有伺服组网控制、人在回路控制功能。The device breaks through the single target detection and recognition processing mode of the target recognition tracker, and can also be networked with other detection systems for data interaction and image transmission, and has the functions of servo network control and human-in-the-loop control.

该多模多目标精密跟踪装置各组成部分之间的关系详述如下：The relationship between the various components of the multi-mode multi-target precision tracking device is described in detail as follows:

该装置的连接关系为该数字伺服平台包括CCD摄像机、红外传感器、高精度数字伺服转台、手柄和监视器五部分。其中CCD摄像机和红外传感器分别安装在高精度数字伺服转台上部的两端，两者通过电缆同信息接口相连进行图像数据的传输，手柄和监视器分别放置在高精度数字伺服转台下部的两侧。该综合信息处理平台，包括信息接口、高速数字信号处理器和伺服控制处理器三部分，三部分均集成于信息处理板并置于控制箱中，放置在高精度数字伺服转台一侧。其中数字伺服平台中的手柄同信息接口相连进行控制信号的传输，数字伺服平台中的监视器同信息接口相连用于显示获取的图像数据信息，高速数字信号处理器与信息接口相连，用于获取CCD摄像机和红外传感器传输的图像数据，伺服控制处理器与信息接口相连，用于获取高速数字信号处理器的目标检测识别信息和高精度数字伺服转台反馈的位置信息，并向高精度数字伺服转台传输控制命令。该压缩及传输设备，包括视频压缩处理器和GPRS传输模块两部分，两者分别集成于信息处理板上，视频压缩处理器后端同GPRS传输模块相连，视频压缩处理器前端同综合信息处理平台中的高速数字信号处理器相连。就多模多目标精密跟踪装置整体而言，数字伺服平台处于多模多目标精密跟踪装置的前端，综合信息处理平台处于多模多目标精密跟踪装置的中端，压缩及传输设备处于多模多目标精密跟踪装置的后端。The connection relationship of the device is that the digital servo platform includes five parts: a CCD camera, an infrared sensor, a high-precision digital servo turntable, a handle and a monitor. The CCD camera and the infrared sensor are respectively installed at both ends of the upper part of the high-precision digital servo turntable, and the two are connected with the information interface through a cable to transmit image data. The handle and the monitor are respectively placed on both sides of the lower part of the high-precision digital servo turntable. The comprehensive information processing platform includes three parts: information interface, high-speed digital signal processor and servo control processor. The three parts are integrated on the information processing board and placed in the control box, which is placed on the side of the high-precision digital servo turntable. Among them, the handle in the digital servo platform is connected with the information interface to transmit the control signal, the monitor in the digital servo platform is connected with the information interface for displaying the acquired image data information, and the high-speed digital signal processor is connected with the information interface for obtaining The image data transmitted by the CCD camera and infrared sensor, the servo control processor is connected with the information interface, used to obtain the target detection and identification information of the high-speed digital signal processor and the position information fed back by the high-precision digital servo turntable, and send it to the high-precision digital servo turntable Transmission control commands. The compression and transmission equipment includes two parts, a video compression processor and a GPRS transmission module, which are respectively integrated on the information processing board. The back end of the video compression processor is connected to the GPRS transmission module, and the front end of the video compression processor is connected to the comprehensive information processing platform. connected to the high-speed digital signal processor. As far as the multi-mode and multi-target precision tracking device is concerned, the digital servo platform is at the front end of the multi-mode and multi-target precision tracking device, the comprehensive information processing platform is at the middle end of the multi-mode and multi-target precision tracking device, and the compression and transmission equipment is at the multi-mode and multi-target precision tracking device. The back end of the target precision tracker.

本发明一种复杂背景低信噪比下弱小目标高精度跟踪方法，是在高速数字信号处理器中完成，其在整个多模多目标精密跟踪装置中的工作流程为，首先通过CCD摄像机和红外传感器获取目标的可见光和红外图像，然后将复杂背景低信噪比下的图像信号通过信息接口传送给高速数字信号处理器，经处理器对图像进行预处理、检测后，完成对目标的自动识别与高精度跟踪，同时将跟踪的目标信息传送给伺服控制处理器，由伺服控制处理器产生控制命令给高精度数字伺服转台；在将图像信号通过监视器进行显示的同时把原图像信息和叠加了跟踪目标信息的图像传送给视频压缩处理器进行视频压缩，然后通过GPRS传输模块进行无线传输，使指挥中心通过解码处理器在控制中心的监视器中观察到目标跟踪情况。本发明一种复杂背景低信噪比下弱小目标高精度跟踪方法，其步骤是：A high-precision tracking method for weak and small targets under a complex background and low signal-to-noise ratio of the present invention is completed in a high-speed digital signal processor, and its workflow in the entire multi-mode and multi-target precision tracking device is as follows: The sensor acquires the visible light and infrared images of the target, and then transmits the image signal under the complex background and low signal-to-noise ratio to the high-speed digital signal processor through the information interface. After the processor preprocesses and detects the image, the automatic recognition of the target is completed. With high-precision tracking, the tracked target information is sent to the servo control processor at the same time, and the servo control processor generates control commands to the high-precision digital servo turntable; while displaying the image signal through the monitor, the original image information and superimposed The image of the tracking target information is sent to the video compression processor for video compression, and then wirelessly transmitted through the GPRS transmission module, so that the command center can observe the target tracking situation on the monitor of the control center through the decoding processor. The present invention provides a high-precision tracking method for weak and small targets under complex backgrounds and low signal-to-noise ratios, the steps of which are as follows:

(1)、复杂背景、低信噪比条件下的图像预处理：采用基于改进的离散平稳小波变换和非线性增强算子的弱小目标图像增强算法，通过在小波变换的每个尺度上分别选取不同的阈值来对图像进行去噪；(1) Image preprocessing under the condition of complex background and low signal-to-noise ratio: using the weak and small target image enhancement algorithm based on improved discrete stationary wavelet transform and nonlinear enhancement operator, by selecting Different thresholds to denoise the image;

(2)、基于二项分布判断准则的目标自适应门限分割：对单帧检测概率、单帧虚警概率与总检测概率和总虚警概率之间的关系建立基于概率论二项分布准则的模型，解决了序列图像检测中相关帧数和门限的确定问题；(2) Target adaptive threshold segmentation based on binomial distribution criterion: establish the relationship between single frame detection probability, single frame false alarm probability, total detection probability and total false alarm probability based on probability theory binomial distribution criterion The model solves the problem of determining the number of relevant frames and the threshold in sequence image detection;

(3)、红外与可见光数据进行多模融合：对可见光和红外图像进行匹配后，对图像中的目标特征采用多传感器概率数据互联滤波器将两种图像中的目标特征对应起来，获得融合数据，从而提高目标检测识别的置信度，并剔除虚假目标；(3) Multi-mode fusion of infrared and visible light data: After matching the visible light and infrared images, the target features in the image are connected using a multi-sensor probability data interconnection filter to match the target features in the two images to obtain fusion data , so as to improve the confidence of target detection and recognition, and eliminate false targets;

(4)、目标运动预测与估计：采用基于Kalman滤波器思想改进的曲线拟合算法进行运动预测，解决没有规律的抖动、目标交叠、记忆跟踪情况下的运动预测问题；(4) Target motion prediction and estimation: The improved curve fitting algorithm based on the Kalman filter idea is used for motion prediction to solve the problem of motion prediction in the case of irregular jitter, target overlap, and memory tracking;

(5)目标形状发生改变时的目标特征提取：当目标形状发生改变时，采用利用边缘特征归一化的形状识别寻找从电场角度引出的特征不变量的方法达到对目标精确跟踪。(5) Target feature extraction when the target shape changes: when the target shape changes, the method of using edge feature normalization shape recognition to find the feature invariant derived from the electric field angle is used to achieve accurate tracking of the target.

其中：所述步骤(4)中基于Kalman滤波器思想改进的曲线拟合预测算法，是采用指数窗函数来截取轨迹点数据，并通过设置权系数来来控制轨迹点对拟合的作用；并通过设置机动性系数，通过权机动性系数的大小来选取截取轨迹点的长度；当处于多目标交叉的状态时，多个跟踪链竞争一个候选目标，采用将候选目标舍弃，竞争的链各自进行记忆跟踪，直到没有竞争为止的方法处理多目标交叉时的目标跟踪问题。Wherein: in the described step (4), based on the improved curve fitting prediction algorithm of the Kalman filter idea, the exponential window function is adopted to intercept the track point data, and the effect of the control track point on fitting is controlled by setting the weight coefficient; and By setting the mobility coefficient, the length of the intercepted trajectory point is selected by the size of the weighted mobility coefficient; when it is in the state of multi-target crossing, multiple tracking chains compete for a candidate target, and the candidate target is discarded, and the competing chains are respectively carried out. Memory Tracking until No Competition Approach handles the problem of object tracking when multiple objects intersect.

其中，所述步骤(5)中目标形状发生改变时的目标特征提取方法，是把像素点赋予电荷点的含义，从电场角度找出一个不随形状改变而变化的特征量来对不规则图形进行有效的识别。Wherein, the target feature extraction method when the target shape changes in the step (5) is to assign the pixel point to the meaning of the charge point, and find out a feature quantity that does not change with the shape change from the electric field angle to carry out the irregular figure. effective identification.

下面，对每一步骤进行详细说明：Below, each step is described in detail:

1)复杂背景、低信噪比条件下的图像预处理1) Image preprocessing under conditions of complex background and low signal-to-noise ratio

对复杂背景下的弱小目标检测必须选择有效的预处理方法，这对后续的目标检测识别过程中具有很重要的意义。在我们以往的研究中，对很多预处理方法都进行过仿真与工程应用。经过大量实验和分析，本系统的图像预处理采用基于改进的离散平稳小波变换(DSWT)和非线性增强算子的弱小目标图像增强算法。For weak and small target detection in complex backgrounds, an effective preprocessing method must be selected, which is of great significance to the subsequent target detection and recognition process. In our previous research, many preprocessing methods have been simulated and applied in engineering. After a lot of experiments and analysis, the image preprocessing of this system adopts the weak and small target image enhancement algorithm based on the improved Discrete Stationary Wavelet Transform (DSWT) and nonlinear enhancement operator.

小波变换具有完善的重建能力；在时域和频域同时具有局部化特性(伸缩性)，可以聚焦到对象任意细节；多尺度、多分辨率特性；方向选择性，与人类视觉系统的方向性吻合。小波分析的多尺度特性，使得它适合于在信噪比低的环境下进行目标检测。其伸缩特性可使部分图像特征在某个尺度下被有效地抑制，而某些感兴趣的目标(如小目标)可以被突显出来。小波分析不仅可以用在图像预处理中，也可以用在图像分割和目标运动估计上。Wavelet transform has perfect reconstruction ability; it has localization characteristics (scalability) in both time domain and frequency domain, and can focus on any details of objects; multi-scale and multi-resolution characteristics; direction selectivity, and the directionality of the human visual system match. The multi-scale characteristic of wavelet analysis makes it suitable for target detection in the environment with low signal-to-noise ratio. Its stretching properties can effectively suppress some image features at a certain scale, while some interesting objects (such as small objects) can be highlighted. Wavelet analysis can be used not only in image preprocessing, but also in image segmentation and target motion estimation.

从大量国内外文献分析，在复杂背景下，弱小目标识别跟踪这个领域，传统的基于小波变换的图像预处理基本上都是进行如下操作的：From the analysis of a large number of domestic and foreign literature, in the field of weak and small target recognition and tracking under complex backgrounds, the traditional image preprocessing based on wavelet transform basically performs the following operations:

(1)选择合适的小波基，并对图像进行N层小波分解；(1) Select an appropriate wavelet base, and perform N-level wavelet decomposition on the image;

(2)高频系数的阈值选择。对于第一层到第N层的每一层，选择一个阈值进行处理。(2) Threshold selection of high frequency coefficients. For each layer from the first layer to the Nth layer, a threshold is selected for processing.

(3)根据第N层的低频系数和从第一层到第N层经过修改的高频系数，计算出图像的小波重建。(3) Calculate the wavelet reconstruction of the image according to the low-frequency coefficients of the Nth layer and the modified high-frequency coefficients from the first layer to the Nth layer.

传统的基于小波变换的预处理尽管可以得到不错的处理结果，但是在对高频系数进行处理的时候，大部分采用了线性的统一阈值，图像的边缘等细节遭到了不同程度的削弱。本系统在总结传统的基于小波变换图像预处理的基础上，利用基于离散平稳小波变换(DSWT)和非线性增强算子对弱小目标的图像进行增强。在进行DSWT的基础上，得到的高频子带具有较差的分辨率，对这些高频子带进行非线性算子运算来改善和增强高频子带，从而达到了滤波增强的作用。实验结果表明，这种算法可以有效消除1/f噪声，加性高斯白噪声和乘性噪声，提高图像的信噪比。本算法主要包括以下三个部分：Although the traditional preprocessing based on wavelet transform can get good processing results, most of them use a linear unified threshold when processing high-frequency coefficients, and the details such as the edges of the image are weakened to varying degrees. On the basis of summarizing the traditional image preprocessing based on wavelet transform, this system uses discrete stationary wavelet transform (DSWT) and nonlinear enhancement operator to enhance the image of weak and small targets. On the basis of DSWT, the obtained high-frequency sub-bands have poor resolution. Non-linear operator operations are performed on these high-frequency sub-bands to improve and enhance the high-frequency sub-bands, thereby achieving the effect of filter enhancement. Experimental results show that this algorithm can effectively eliminate 1/f noise, additive Gaussian white noise and multiplicative noise, and improve the signal-to-noise ratio of the image. This algorithm mainly includes the following three parts:

(1)抑制噪声(1) Noise suppression

(2)阈值选取(2) Threshold selection

(3)非线性增强算子(3) Nonlinear enhancement operator

下面就这三部分进行详细说明These three parts are described in detail below

(1)抑制噪声(1) Noise suppression

采用传统的“全局阈值”对图像来去噪，效果不理想。I.M.Johnston证明了相关噪声的小波变换在所有的尺度上都是平稳的，我们可以在每个尺度上分别用不同的阈值来对图像进行去噪。Using the traditional "global threshold" to denoise the image, the effect is not ideal. I.M.Johnston proved that the wavelet transform of correlated noise is stable on all scales, and we can use different thresholds on each scale to denoise the image.

假设离散图像的模型如下：Assume the model of the discrete image as follows:

g[i，j]＝f[i，j]+ε[i，j](4.1)g[i,j]=f[i,j]+ε[i,j] (4.1)

上面的公式可以写成矩阵的格式：The above formula can be written in matrix format:

g＝f+ε     (4.2)g=f+ε (4.2)

其中，g＝{g[i，j]}_i，j是观测到的信号。f＝{f[i，j]}_i，j表示没有噪声污染的原始信号，ε＝{ε[i，j]}_i，j，i＝1，...，M；j＝1，...，N是平稳信号。where g={g[i, j]}_{i, j} is the observed signal. f={f[i, j]}_{i, j} represents the original signal without noise pollution, ε={ε[i, j]}_{i, j} , i=1,...,M; j=1,. . . , N is a stationary signal.

对(4.2)进行DSWT，得：Perform DSWT on (4.2), get:

X＝Sf    (4.3)X＝Sf (4.3)

V＝Sε   (4.4)V＝Sε (4.4)

Y＝Sg    (4.5)Y＝Sg (4.5)

Y＝X+V   (4.6)Y=X+V (4.6)

其中S表示二维平稳小波变换算子，在图像中引用Donoho提出的“软阈值”函数对图像进行去噪处理：Among them, S represents the two-dimensional stationary wavelet transform operator, and the "soft threshold" function proposed by Donoho is used in the image to denoise the image:

Y_δ＝T_δοY(4.7)Y_δ ＝T_δ οY(4.7)

T_δ＝diag{t[m，m]}T_δ =diag{t[m,m]}

$\mathrm{<span><span>t</span>t</span>}<span><span>[</span>[</span>\mathrm{<span><span>m</span>m</span>}<span><span>,</span>,</span>\mathrm{<span><span>m</span>m</span>}<span><span>]</span>]</span><span><span>=</span>=</span>\left\{\begin{array}{cc}\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>& <span><span>|</span>|</span>\mathrm{<span><span>Y</span>Y</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>|</span>|</span><span><span><</span><</span>\mathrm{<span><span>\&delta;</span>\&delta;</span>}\\ \mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\frac{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}{<span><span>|</span>|</span>\mathrm{<span><span>Y</span>Y</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>|</span>|</span>}& <span><span>|</span>|</span>\mathrm{<span><span>Y</span>Y</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>|</span>|</span><span><span>\&GreaterEqual;</span>\&Greater\; Equal;</span>\mathrm{<span><span>\&delta;</span>\&delta;</span>}\end{array}\right.$

其中，i＝1，...，M，j＝1，...，N，m＝1，...，MNAmong them, i=1,..., M, j=1,..., N, m=1,..., MN

根据式(4.5)和(4.7)，输入信号的反变换为：According to equations (4.5) and (4.7), the inverse transformation of the input signal is:

g_δ＝S^-1οY_δ(4.8)g_δ = S^-1 οY_δ (4.8)

其中T_δ与阈值δ和信号g相关。where T_δ is related to threshold δ and signal g.

(2)阈值选取(2) Threshold selection

假设原始信号f(x，y)可以用其邻域像素线性表示。若令是g[k，l]的线性表示，用邻域均值对图像进行平滑，可以去除一部分噪声。Assume that the original signal f(x, y) can be linearly represented by its neighboring pixels. Ruoling It is a linear representation of g[k, l]. Smoothing the image with the neighborhood mean can remove part of the noise.

平滑后的

可以用来计算去除噪声的阈值。g[i，j]表示g中的[i，j]元素，它被替代：smoothed

Can be used to calculate the threshold for removing noise. g[i, j] represents the [i, j] element in g, which is Alternate:

$\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>g</span>g</span>}}<span><span>=</span>=</span>\mathrm{<span><span>Z</span>Z</span>}{<span><span>(</span>(</span>\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>1,1</span>1,1</span>}<span><span>]</span>]</span><span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span>\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>M</span>m</span>}<span><span>,</span>,</span>\mathrm{<span><span>N</span>N</span>}<span><span>]</span>]</span><span><span>)</span>)</span>}^{\mathrm{<span><span>T</span>T</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.9</span>4.9</span>}<span><span>)</span>)</span>$

我们认为

比g[i，j]能更好的得到优化阈值。We believe

It is better than g[i, j] to get the optimized threshold.

如果阈值δ太小，

中主要表现为噪声；如果阈值δ太大，会滤掉很多有用的信号。If the threshold δ is too small,

Mainly manifested as noise; if the threshold δ is too large, many useful signals will be filtered out.

对所有的像素实施同样的操作，最佳的阈值可以通过如下运算来得到：Perform the same operation on all pixels, and the optimal threshold can be obtained by the following operations:

$\mathrm{<span><span>OCV</span>OCV</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>MN</span>MN</span>}}\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{<span><span>(</span>(</span>\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>-</span>-</span>{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>g</span>g</span>}}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.10</span>4.10</span>}<span><span>)</span>)</span>$

的形式有很多种，在这里，令${\tilde{g}}_{\mathrm{\&delta;}}[i,j]=\tilde{g}[i,j],$则：

There are many forms, here, let${\tilde{g}}_{\mathrm{\&delta;}}[i,j]=\tilde{g}[i,j],$ but:

$\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>-</span>-</span>{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>g</span>g</span>}}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>-</span>-</span>{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span>}{\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>z</span>z</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.11</span>4.11</span>}<span><span>)</span>)</span>$

其中：in:

$\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>z</span>z</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>=</span>=</span>\frac{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>-</span>-</span>{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>g</span>g</span>}}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span>}{\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>-</span>-</span>{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>g</span>g</span>}}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span>}<span><span>\&ap;</span>\&ap;</span>{\mathrm{<span><span>z</span>z</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>[</span>[</span>\mathrm{<span><span>m</span>m</span>}<span><span>,</span>,</span>\mathrm{<span><span>n</span>no</span>}<span><span>]</span>]</span><span><span>=</span>=</span>\frac{{<span><span>\&PartialD;</span>\&PartialD;</span>\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span>}{<span><span>\&PartialD;</span>\&PartialD;</span>{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>k</span>k</span>}<span><span>,</span>,</span>\mathrm{<span><span>l</span>l</span>}<span><span>]</span>]</span>}$

其中，i，k＝1，...，M，j，l＝1，...，N，m，n＝1，...，MNAmong them, i, k=1,..., M, j, l=1,..., N, m, n=1,..., MN

然而，在(4.11)中，z′[m，m]为1或者是0，在实际计算中不可用。因此给出如下公式来替代(4.10)：However, in (4.11), z'[m, m] is 1 or 0, which is not available in actual calculation. So give the following formula to replace (4.10):

$\mathrm{<span><span>SGCV</span>SGCV</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>MN</span>MN</span>}}{<span><span>|</span>|</span><span><span>|</span>|</span>\mathrm{<span><span>Y</span>Y</span>}<span><span>-</span>-</span>{\mathrm{<span><span>Y</span>Y</span>}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>|</span>|</span><span><span>|</span>|</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{<span><span>[</span>[</span>\frac{\mathrm{<span><span>trace</span>trace</span>}<span><span>(</span>(</span>\mathrm{<span><span>I</span>I</span>}<span><span>-</span>-</span>{\mathrm{<span><span>Z</span>Z</span>}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>MN</span>MN</span>}}<span><span>]</span>]</span>}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.12</span>4.12</span>}<span><span>)</span>)</span>$

其中，trace表示矩阵的迹，||·||表示欧几里德范数。I是M×N的单位矩阵。令δ^*＝argminMSE(δ)，$\widetilde{\mathrm{\&delta;}}=\arg \min \mathrm{SGCV}\left(\mathrm{\&delta;}\right),$M.Jansen证明了

是渐进最优阈值。Among them, trace represents the trace of the matrix, and ||·|| represents the Euclidean norm. I is an M×N identity matrix. Let δ^* = argminMSE(δ),$\widetilde{\mathrm{\&delta;}}=\arg \min \mathrm{SGCV}\left(\mathrm{\&delta;}\right),$ M. Jansen proved

is the asymptotically optimal threshold.

(3)非线性增强算子(3) Nonlinear enhancement operator

1994年，A.Laine曾给出了基于DSWT的非线性增强算子，来增强图像的局部对比度。为了方便起见，在每个尺度上分别定义每个高频子带图像的变换函数：In 1994, A.Laine gave a nonlinear enhancement operator based on DSWT to enhance the local contrast of the image. For convenience, the transformation function of each high-frequency subband image is defined separately at each scale:

g[i，j]＝MAG{f[i，j]}(4.13)g[i,j]=MAG{f[i,j]} (4.13)

其中，g[i，j]是增强的子带，f[i，j]是原始的子带图像，MAG是非线性增强算子。where g[i,j] is the enhanced subband, f[i,j] is the original subband image, and MAG is the non-linear enhancement operator.

令f_s^r[i，j]是s分解尺度上第r个高频子带系数，其中s＝1，2，…，L；r＝1，2，3.max f_s^r是所有像素f_s^r[i，j]中的最大灰度值。f_s^r[i，j]可以从[-max f_s^r，max f_s^r]映射到[-1，1]。Let_fsr [i,j] be the rth high-frequency subband coefficient on the decomposition scale of s, where s = 1, 2, ..., L;^{r = 1, 2, 3. max fsr}_is^all pixels f The maximum gray value^{in sr}_[ i,j]. f_s^r [i, j] can be mapped from [-max f_s^r , max f_s^r ] to [-1, 1].

因此，a、b和c的范围可以分别来设定。对比增强方法可以描述如下：Therefore, the ranges of a, b, and c can be set separately. The contrast enhancement method can be described as follows:

${\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>=</span>=</span>\left\{\begin{array}{cc}{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>,</span>,</span>& <span><span>|</span>|</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>|</span>|</span><span><span><</span><</span>{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}\\ \mathrm{<span><span>a</span>a</span>}<span><span>\&CenterDot;</span>\&CenterDot;</span>\mathrm{<span><span>max</span>max</span>}{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>\{</span>\{</span>\mathrm{<span><span>sigm</span>sigm</span>}<span><span>[</span>[</span>\mathrm{<span><span>c</span>c</span>}<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>-</span>-</span>\mathrm{<span><span>b</span>b</span>}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>-</span>-</span>\mathrm{<span><span>sigm</span>sigm</span>}<span><span>[</span>[</span><span><span>-</span>-</span>\mathrm{<span><span>c</span>c</span>}<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>\}</span>\}</span><span><span>,</span>,</span>& <span><span>|</span>|</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>|</span>|</span><span><span>\&GreaterEqual;</span>\&Greater\; Equal;</span>{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}\end{array}\right.<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.14</span>4.14</span>}<span><span>)</span>)</span>$

其中，in,

${\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>=</span>=</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>/</span>/</span>\mathrm{<span><span>max</span>max</span>}{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}$

最后进行小波反变换，即得到预处理后的图像。Finally, inverse wavelet transform is performed to obtain the preprocessed image.

本系统在充分分析研究红外弱小目标的特征与背景模型基础上，采用离散平稳小波变换(DSWT)和非线性增强算子的算法对红外弱小目标进行图像增强的预处理。实验结果表明该算法不仅对弱小目标的背景抑制、目标增强有较好的效果，对大目标的噪声、背景抑制同样有较好的效果。On the basis of fully analyzing and researching the characteristics and background model of small infrared targets, the system uses the algorithm of discrete stationary wavelet transform (DSWT) and nonlinear enhancement operator to preprocess the image enhancement of small infrared targets. Experimental results show that the algorithm not only has a good effect on the background suppression and target enhancement of weak and small targets, but also has a good effect on the noise and background suppression of large targets.

2)基于二项分布判断准则的目标自适应门限分割2) Target adaptive threshold segmentation based on binomial distribution judgment criterion

基于弱小目标的特点(低SNR、复杂背景)，对它的检测依靠单帧是不可能达到的，必须依靠图像序列。在目前所做的弱小目标检测中，给出的检测识别概率一般大于等于98％，虚警概率小于等于10^-6，若这两个参数体现在检测中，就是用它们选取噪声门限。一方面，若按照虚警率小于等于10^-6选取噪声门限，则门限很高，很多目标将会丢失；另一方面，若按照检测识别概率大于等于98％选取噪声门限，则门限的选取应很低，以保证取出所有的目标点，这样会导致很大的虚警率。在这种低信噪比条件下的弱小目标检测，是无法单帧实现的，必须利用多帧图像的相关信息，将目标的运动特征和运动轨迹的连续性、一致性结合起来进行考虑。从总的检测概率与虚警概率计算出单帧的检测概率和虚警概率，从而选取合理的噪声门限为要解决的关键问题。Based on the characteristics of weak and small targets (low SNR, complex background), it is impossible to rely on a single frame to detect it, and must rely on image sequences. In the weak target detection done so far, the given detection and recognition probability is generally greater than or equal to 98%, and the false alarm probability is less than or equal to 10^-6 . If these two parameters are reflected in the detection, they are used to select the noise threshold. On the one hand, if the noise threshold is selected according to the false alarm rate being less than or equal to 10^-6 , the threshold is very high, and many targets will be lost; on the other hand, if the noise threshold is selected according to the detection and recognition probability being greater than or equal to 98%, the selection of the threshold should be It is very low to ensure that all target points are taken out, which will lead to a large false alarm rate. Weak target detection under such low signal-to-noise ratio conditions cannot be realized in a single frame, and the relevant information of multiple frames of images must be used to consider the motion characteristics of the target and the continuity and consistency of the motion trajectory. The detection probability and false alarm probability of a single frame are calculated from the total detection probability and false alarm probability, and a reasonable noise threshold is selected as the key problem to be solved.

以概率论为基础，我们在整个图像检测中，根据单帧检测概率、单帧虚警概率与总检测概率和总虚警概率的关系，解决序列图像检测中相关帧数和门限的确定问题，为低虚警率、高检测率提供了理论保证。Based on probability theory, we solve the problem of determining the number of relevant frames and the threshold in sequence image detection according to the relationship between single frame detection probability, single frame false alarm probability and total detection probability and total false alarm probability in the whole image detection, It provides a theoretical guarantee for low false alarm rate and high detection rate.

将每帧图像中的目标检测看作是独立的重复实验，根据概率论中的原理，检测概率应该服从二项分布，据此建立数学模型，假定预处理后图像噪声为高斯分布的白噪声，根据统计理论，图像进行单帧门限检测时[推导过程参见发表文章]：The target detection in each frame image is regarded as an independent repeated experiment. According to the principle of probability theory, the detection probability should obey the binomial distribution. Based on this, a mathematical model is established, and the image noise after preprocessing is assumed to be white noise of Gaussian distribution. According to statistical theory, when an image is subjected to single-frame threshold detection [see published articles for the derivation process]:

${\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>=</span>=</span>{<span><span>\&Integral;</span>\&Integral;</span>}_{\mathrm{<span><span>v</span>v</span>}}^{<span><span>+</span>+</span><span><span>\&infin;</span>\&infin;</span>}\mathrm{<span><span>p</span>p</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>)</span>)</span>\mathrm{<span><span>dx</span>dx</span>}<span><span>=</span>=</span>{<span><span>\&Integral;</span>\&Integral;</span>}_{\mathrm{<span><span>v</span>v</span>}}^{<span><span>+</span>+</span><span><span>\&infin;</span>\&infin;</span>}\frac{\mathrm{<span><span>1</span>1</span>}}{\sqrt{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}}\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}\mathrm{<span><span>exp</span>exp</span>}<span><span>(</span>(</span><span><span>-</span>-</span>\frac{{<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&sigma;S</span>\&sigma;S</span>}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>)</span>)</span>\mathrm{<span><span>dx</span>dx</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>v</span>v</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&sigma;S</span>\&sigma;S</span>}}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}<span><span>)</span>)</span>$

$<span><span>=</span>=</span>\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>+</span>+</span>\mathrm{<span><span>\&sigma;S</span>\&sigma;S</span>}<span><span>-</span>-</span>\mathrm{<span><span>v</span>v</span>}}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.15</span>4.15</span>}<span><span>)</span>)</span>$

${\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>f</span>f</span>}}<span><span>=</span>=</span>{<span><span>\&Integral;</span>\&Integral;</span>}_{\mathrm{<span><span>v</span>v</span>}}^{<span><span>+</span>+</span><span><span>\&infin;</span>\&infin;</span>}\frac{\mathrm{<span><span>1</span>1</span>}}{\sqrt{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}}\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}\mathrm{<span><span>exp</span>exp</span>}<span><span>(</span>(</span><span><span>-</span>-</span>\frac{{<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>)</span>)</span>\mathrm{<span><span>dx</span>dx</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>v</span>v</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>-</span>-</span>\mathrm{<span><span>v</span>v</span>}}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}<span><span>)</span>)</span>$

$\frac{\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>+</span>+</span>\mathrm{<span><span>\&sigma;S</span>\&sigma;S</span>}<span><span>-</span>-</span>\mathrm{<span><span>v</span>v</span>}}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.16</span>4.16</span>}<span><span>)</span>)</span>$

其中ν＝μ+σS-σΦ^-1(p_d)或ν＝μ-σΦ^-1(p_f)where ν=μ+σS-σΦ^-1 (p_d ) or ν=μ-σΦ^-1 (p_f )

可推出单帧检测概率和单帧虚警概率的关系：The relationship between single frame detection probability and single frame false alarm probability can be deduced:

Φ^-1(P_f)-Φ^-1(P_d)＝S    (4.17)Φ^-1 (P_f )-Φ^-1 (P_d )＝S (4.17)

式中：ν——检测门限，σ²——噪声均方差In the formula: ν——detection threshold, σ² ——noise mean square error

      μ——为第K帧背景对消后的噪声均值μ——the mean value of the noise after the background cancellation of the Kth frame

       S——信噪比SNR定义为信号的幅值与噪声的均方差之比S——Signal-to-noise ratio SNR is defined as the ratio of the amplitude of the signal to the mean square error of the noise

总检测概率与单帧检测概率的关系：The relationship between the total detection probability and the single frame detection probability:

${\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>D</span>D.</span>}}<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>\&GreaterEqual;</span>\&Greater\; Equal;</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>D</span>D.</span>}}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>i</span>i</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>n</span>no</span>}}^{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>d</span>d</span>}}^{\mathrm{<span><span>k</span>k</span>}}{<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>n</span>no</span>}<span><span>-</span>-</span>\mathrm{<span><span>k</span>k</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.18</span>4.18</span>}<span><span>)</span>)</span>$

在上述实验中，假定单帧检测概率是P_d＝0.90，要求总的检测概率P_D＝0.98。那么当在n幅图像中，目标出现了k次时，可以达到要求。例如，当每次采集16帧图像做判断时，如果目标出现11次，则总检测概率能够达到要求。In the above experiments, it is assumed that the detection probability of a single frame is P_d =0.90, and the total detection probability P_D =0.98 is required. Then when the target appears k times in n images, the requirement can be met. For example, when 16 frames of images are collected each time for judgment, if the target appears 11 times, the total detection probability can meet the requirements.

因此可由单帧检测概率、单帧虚警概率与总检测概率和总虚警概率的关系，解决序列图像检测中相关帧数和门限的确定问题。Therefore, the problem of determining the number of relevant frames and the threshold in sequence image detection can be solved by the relationship between single frame detection probability, single frame false alarm probability, total detection probability and total false alarm probability.

3)红外与可见光数据进行多模融合3) Multi-mode fusion of infrared and visible light data

基于红外与可见光传感器融合的目标检测，可以提高目标的检测概率、降低虚警概率。Target detection based on the fusion of infrared and visible light sensors can improve the detection probability of targets and reduce the probability of false alarms.

对可见光和红外图像融合需要进行图像匹配，首先对不同传感器的目标进行特征提取，然后通过目标匹配结果可以得出可见光和红外图像之间的变换关系，如平移、旋转、缩放等。具体使用的配准方法是基于最小二乘的控制点匹配，相位相关法，模板匹配法等。The fusion of visible light and infrared images requires image matching. First, feature extraction is performed on the targets of different sensors, and then the transformation relationship between visible light and infrared images can be obtained through the target matching results, such as translation, rotation, scaling, etc. The specific registration methods used are control point matching based on least squares, phase correlation method, template matching method and so on.

在图像配准后，根据最近邻原则，同一目标在配准后图像中的坐标应该是重合、或者是非常接近的，通过临近性或相似性测度能够把两种图像中的目标特征对应起来。After image registration, according to the nearest neighbor principle, the coordinates of the same target in the registered image should be coincident or very close, and the target features in the two images can be matched by the proximity or similarity measure.

我们将多传感器概率数据互联滤波器用于可见光和红外图像的融合，来降低虚警率。概率数据互联的基本思想是：只要是有效检测信息，都可能源于目标，只是每个信息源于目标的概率有所不同。这种方法利用了跟踪窗内的所有信息以获得可能的后验信息，并根据大量的相关计算给出各概率加权系数及其加权和，然后用它更新目标状态。本研究采用此方法进行目标特征融合。We use the multi-sensor probabilistic data interconnection filter for the fusion of visible light and infrared images to reduce the false alarm rate. The basic idea of probabilistic data interconnection is: as long as it is effective detection information, it may come from the target, but the probability that each information comes from the target is different. This method uses all the information in the tracking window to obtain possible posterior information, and gives each probability weighting coefficient and its weighted sum according to a large number of correlation calculations, and then uses it to update the target state. This study adopts this method for target feature fusion.

经过目标融合处理后，丰富了目标的特征信息，提高了目标检测概率，降低了虚警率。After target fusion processing, the feature information of the target is enriched, the target detection probability is improved, and the false alarm rate is reduced.

红外与可见光数据的融合采用的处理步骤如下：The processing steps adopted for the fusion of infrared and visible light data are as follows:

a)对可见光和红外图像分别进行目标特征提取；a) Target feature extraction is performed on visible light and infrared images respectively;

b)对提取的特征进行不同传感器的特征匹配，确定可见光和红外图像之间的变换关系；b) Perform feature matching of different sensors on the extracted features, and determine the transformation relationship between visible light and infrared images;

对匹配后图像中的目标特征，使用概率互联滤波器处理获得融合数据，从而提高目标检测识别的置信度，并剔除虚假目标。For the target features in the matched image, the probabilistic interconnection filter is used to process the fused data, so as to improve the confidence of target detection and recognition, and eliminate false targets.

4)目标运动预测与估计4) Target motion prediction and estimation

目标跟踪过程中的多目标、交叉、抖动、记忆跟踪等都涉及目标的运动估计预测问题弱小目标的运动轨迹，帧与帧之间存在抖动，并不具有方向一致性，而其它目标如小鸟的面积比目标稍大，它的运动轨迹比弱小目标更具有方向性。这是由于成像系统、空间光干扰、空气振动等原因造成了图像的抖动，抖动的同时还使目标的几何中心在相邻像素之间发生变化，如果数据不经过处理，连续帧之间的目标位置由于抖动的存在，并不按方向的一致性变化，这就给用方向性进行约束(如常规的滤波器预测)的目标精确跟踪带来误差。In the process of target tracking, multi-target, intersection, jitter, memory tracking, etc. all involve the motion estimation and prediction of the target. The trajectory of the weak target, there is jitter between frames, and there is no direction consistency, while other targets such as birds The area is slightly larger than the target, and its trajectory is more directional than the weak target. This is due to the image shaking caused by the imaging system, spatial light interference, air vibration, etc. The shaking also causes the geometric center of the target to change between adjacent pixels. If the data is not processed, the target between consecutive frames Due to the existence of jitter, the position does not change according to the consistency of the direction, which brings errors to the precise tracking of the target constrained by the directionality (such as conventional filter prediction).

怎样消除抖动现象产生的影响是实际跟踪要解决的一个重要问题。在项目中解决这类方法采用了两种方法：How to eliminate the influence of jitter phenomenon is an important problem to be solved in actual tracking. There are two ways to solve this kind of method in the project:

●基于Kalman滤波器思想改进的曲线拟合的运动预测。解决没有规律的抖动、目标交叠、记忆跟踪等情况下的运动预测问题。●Motion prediction based on improved curve fitting based on Kalman filter idea. Solve the problem of motion prediction in the case of irregular jitter, overlapping targets, memory tracking, etc.

●在识别为目标后，将粗跟踪转为精确跟踪，将形心位置转换为质心位置，减小跟踪时的抖动现象，提高跟踪精度。●After the target is identified, the rough tracking is converted to precise tracking, and the centroid position is converted to the centroid position to reduce the jitter phenomenon during tracking and improve tracking accuracy.

由于Kalman滤波器不能即时反映出目标的运动变化，所以当目标机动性强时，Kalman跟踪的误差会较大。我们从Kalman动力学方程出发，定义了机动性参数，同时对拟合方式进行了改进，增强其跟踪预测的性能。Since the Kalman filter cannot reflect the movement changes of the target in real time, the Kalman tracking error will be larger when the target is highly maneuverable. Starting from the Kalman kinetic equation, we defined the maneuverability parameters, and improved the fitting method to enhance its performance of tracking prediction.

图7所示为基于轨迹预测的目标检测、识别跟踪流程图。目标运动预测与估计的过程为图像经过预处理，进行目标的特征提取，获得潜在的目标，通过二项分布的判断准则来判断是否是新目标，通过kalman理论建立轨迹方程，若轨迹方程已建立，则需要对轨迹方程进行更新，同时预测目标在下一帧的轨迹，得到预测位置，并用拟合修正Kalman跟踪滤波器修正预测位置。Figure 7 shows the flow chart of target detection, recognition and tracking based on trajectory prediction. The process of target motion prediction and estimation is that the image is preprocessed, the feature extraction of the target is carried out, and the potential target is obtained, and whether it is a new target is judged by the judgment criterion of the binomial distribution, and the trajectory equation is established by the Kalman theory. If the trajectory equation has been established , it is necessary to update the trajectory equation, and at the same time predict the trajectory of the target in the next frame to obtain the predicted position, and use the fitting correction Kalman tracking filter to correct the predicted position.

以下为基于Kalman理论改进的曲线拟合预测目标运行轨迹研究的几点讨论和改进：The following are some discussions and improvements based on the improved Kalman theory of curve fitting to predict the target trajectory research:

(1)改进的最小二乘直线拟合方法(1) Improved least squares straight line fitting method

经典最小二乘拟合中的准则函数是各数据点沿纵坐标y到拟合曲线的距离的平方和。假设数据点(x_i，y_i)，其中y＝f(x)。做最小二乘拟合得到的曲线是基于如下准则：The criterion function in classical least squares fitting is the sum of the squares of the distances of each data point along the ordinate y to the fitting curve. Assume a data point (x_i , y_i ), where y=f(x). The curve obtained by least squares fitting is based on the following criteria:

$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{{\mathrm{\&delta;}}^2}_i=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\left(x_i\right){[s^{*}\left(x\right)-f\left(x_i\right)]}^2=\underset{s\left(x\right)\&Element;\mathrm{\&Phi;}}{\min }\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\left(x_i\right){[s\left(x\right)-f\left(x_i\right)]}^2,$但用距离的平方和$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_i^2=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\left(x_i\right){\left(\frac{|y-a_{i}x-b_i|}{\sqrt{1+a_i^2}}\right)}^2=\min$做准则函数更合适，后者是力学中的最小惯性矩。$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{{\mathrm{\&delta;}}^2}_i=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\left(x_i\right){[{\mathrm{the\; s}}^{*}\left(x\right)-f\left(x_i\right)]}^2=\underset{\mathrm{the\; s}\left(x\right)\&Element;\mathrm{\&Phi;}}{\min }\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\left(x_i\right){[\mathrm{the\; s}\left(x\right)-f\left(x_i\right)]}^2,$ But using the sum of the squares of the distances$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_i^2=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\left(x_i\right){\left(\frac{|\mathrm{the\; y}-a_{i}x-b_i|}{\sqrt{1+a_i^2}}\right)}^2=\min$ It is more appropriate to be a criterion function, which is the minimum moment of inertia in mechanics.

(2)截取轨迹点做拟合(2) Intercept trajectory points for fitting

在应用中，只考虑临近几个或几十个轨迹点，如果取权系数ω(x_i)≡1，相当于用矩形窗截取轨迹获得近期的轨迹点。矩形窗不能反映重要性的变化，并且不能平滑截断；指数函数可以反映数据点重要性随时间的变化，而且指数函数是光滑的，所以采用指数窗函数来截取数据。In the application, only a few or dozens of nearby trajectory points are considered. If the weight coefficient ω(xi₎ ≡1 is used, it is equivalent to intercepting the trajectory with a rectangular window to obtain the recent trajectory points. The rectangular window cannot reflect the change of importance, and cannot be truncated smoothly; the exponential function can reflect the change of the importance of data points over time, and the exponential function is smooth, so the exponential window function is used to intercept the data.

考虑到目标运动的连续性和一致性，每帧即时速度的大小、方向和整体运动趋势相比较不应该有大的跳变，当这种变动较大时，其中应该包含了较大的误差，应该给这个数据点较小的权值抑制这种误差。Considering the continuity and consistency of the target motion, the size and direction of the instant speed of each frame should not have a large jump compared with the overall motion trend. When the change is large, it should contain a large error. This data point should be given a smaller weight to suppress this error.

根据以上准则，通过实验和理论推导，定义权系数的取值：According to the above criteria, through experiments and theoretical derivation, the value of the weight coefficient is defined:

$\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>q</span>q</span>}}^{\mathrm{<span><span>n</span>no</span>}}<span><span>\&CenterDot;</span>\&CenterDot;</span>{\mathrm{<span><span>p</span>p</span>}}^{{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>i</span>i</span>}}}$

其中|q|＜1，|p|＜1，d_i为数据点到拟合直线Ax+By+C＝0的距离，$d_i=\frac{|{\mathrm{Ax}}_i+{\mathrm{By}}_i+C|}{\sqrt{A^2+B^2}};$n＝N-i，N是当前的帧数，N-M≤i＜N，M是拟合数据点的个数。q和p的值可以通过实验获得，一般取0.7～0.8之间。Where |q|<1, |p|<1, d_i is the distance from the data point to the fitting line Ax+By+C=0,$d_i=\frac{|{\mathrm{Ax}}_i+{\mathrm{By}}_i+C|}{\sqrt{A^2+{\mathrm{<figure-callout\; label="B"\; filenames="H2009101807801E00011.png,H2009101807801E00022.png"\; state="\{\{state\}\}">B</figure-callout>}}^2}};$ n=Ni, N is the current frame number, NM≤i<N, M is the number of fitting data points. The values of q and p can be obtained through experiments, generally between 0.7 and 0.8.

轨迹点个数M可以选择固定，通过调整权系数大小来控制轨迹点对拟合的作用，例如选小的衰减系数，相当于截取较短的轨迹，选择较大的衰减系数，相当于截取较长的轨迹。The number M of trajectory points can be fixed, and the effect of trajectory points on the fitting can be controlled by adjusting the weight coefficient. long track.

(3)机动性系数(3) Mobility coefficient

前面定义了权系数$\mathrm{\&omega;}\left(x_i\right)=q^n\&CenterDot;p^{d_i},$其中q大小的选取和截取轨迹点长度有关，并且要求机动性强时，截取轨迹短一些，机动性低时，截取轨迹长一些。The weight coefficient was defined earlier$\mathrm{\&omega;}\left(x_i\right)=q^{\mathrm{no}}\&Center\; Dot;p^{d_i},$ The selection of the size of q is related to the length of the intercepted trajectory point, and when the maneuverability is required, the intercepted trajectory is shorter, and when the maneuverability is low, the intercepted trajectory is longer.

设系统方程为：X(k+1)＝F(k)X(k)+w(k)(4.19)Let the system equation be: X(k+1)=F(k)X(k)+w(k)(4.19)

观测方程：z(k)＝H(k)X(k)+u(k)      (4.20)Observation equation: z(k)=H(k)X(k)+u(k) (4.20)

机动系数定义为：$\mathrm{\&lambda;}=\frac{{\mathrm{\&sigma;}}_w{T}^2}{{\mathrm{\&sigma;}}_u}---\left(4.21\right)$The mobility coefficient is defined as:$\mathrm{\&lambda;}=\frac{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; label="w\; T"\; filenames="H2009101807801E00011.png,H2009101807801E00022.png"\; state="\{\{state\}\}">w</figure-callout>}}{T}^{}{}^2}{{\mathrm{\&sigma;}}_u}---\left(4.21\right)$

其中σ_u是观测噪声方差，σ_w是系统噪声方差，T是采样周期。在实际应用中σ_u和σ_w无法获得，可以用相关参量代替。因为跟踪中目标坐标有三种：预测值、实际观测值和当前估计值。预测值是指在上一帧处理过程中得到的对当前帧目标位置的预测，用

表示；观测值表示当前图像分割得到的目标位置，用z(k)表示；当前估计值是指根据当前观测值估计出的目标在空间中的实际坐标，用X(k)表示。where_σu is the observation noise variance,_σw is the system noise variance, and T is the sampling period. In practical applications,_σu and_σw cannot be obtained and can be replaced by related parameters. Because there are three kinds of target coordinates in tracking: predicted value, actual observed value and current estimated value. The prediction value refers to the prediction of the target position of the current frame obtained during the processing of the previous frame.

Represents; the observed value represents the target position obtained by the current image segmentation, represented by z(k); the current estimated value refers to the actual coordinate of the target in space estimated according to the current observed value, represented by X(k).

在Kalman滤波中$\stackrel{\&OverBar;}{X}\left(k\right)=\hat{X}\left(k\right|k);$而在拟合跟踪中，X(k)是z(k)在拟合直线上的投影。因为可以把X(k)当作目标的真实坐标，则观测值噪声可以表示为u(k)＝z(k)-X(k)，而预测值和真实值的差

体现了系统的不确定性，或者说代表了跟踪系统中不可预测的因素，所以可以认为系统噪声为$w\left(n\right)=\hat{X}(k-1)-\stackrel{\&OverBar;}{X}\left(k\right).$这样σ_u和σ_w可以用以下参量代替：In Kalman filtering$\stackrel{\&OverBar;}{x}\left(k\right)=\hat{x}\left(k\right|k);$ In the fitting tracking, X(k) is the projection of z(k) on the fitting line. Because X(k) can be regarded as the real coordinates of the target, the observed value noise can be expressed as u(k)=z(k)-X(k), and the difference between the predicted value and the real value

reflects the uncertainty of the system, or represents the unpredictable factors in the tracking system, so the system noise can be considered as$w\left(\mathrm{no}\right)=\hat{x}(k-1)-\stackrel{\&OverBar;}{x}\left(k\right).$ Thus σ_u and σ_w can be replaced by the following parameters:

${\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>u</span>u</span>}}<span><span>\&ap;</span>\&ap;</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}}\sqrt{\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>\mathrm{<span><span>z</span>z</span>}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>-</span>-</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>)</span>)</span>{<span><span>(</span>(</span>\mathrm{<span><span>z</span>z</span>}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>-</span>-</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>)</span>)</span>}^{\mathrm{<span><span>T</span>T</span>}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.22</span>4.22</span>}<span><span>)</span>)</span>$

${\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>w</span>w</span>}}<span><span>\&ap;</span>\&ap;</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}}\sqrt{\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span><span><span>-</span>-</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>)</span>)</span>{<span><span>(</span>(</span>\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span><span><span>-</span>-</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>)</span>)</span>}^{\mathrm{<span><span>T</span>T</span>}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.23</span>4.23</span>}<span><span>)</span>)</span>$

T就是红外图像采集的间隔周期，是已知参数，可以计算出机动系数λ。通过试验可以发现σ_w取值大小和目标机动性吻合，就是说σ_w越大，目标运动变化剧烈；相反，σ_w小，则目标运动变化平缓。T is the interval period of infrared image acquisition, which is a known parameter, and the maneuver coefficient λ can be calculated. Through experiments, it can be found that the value_{of σw} is consistent with the maneuverability of the target, that is to say, the larger the_σw , the sharper the change of the target movement; on the contrary, the smaller the_σw , the smoother the change of the target movement.

(4)拟合后的数据关联(4) Data association after fitting

如果多个跟踪链竞争一个候选目标，通常是处于多目标交叉的状态。拟采取这样处理方法：将候选目标舍弃，竞争的链各自进行记忆跟踪，直到没有竞争为止。If multiple tracking chains compete for a candidate target, it is usually in the state of multi-target intersection. It is proposed to take the following approach: the candidate target is discarded, and the competing chains perform memory tracking on their own until there is no competition.

也可以将候选目标看作是可疑新目标，对它进行跟踪，由连续性判断是否为新目标；当轨迹链找不到匹配的候选目标时，应该记忆跟踪，直到重新找回目标；如果超过一定时间仍无法找回目标，则认为跟踪目标丢失，此时数据关联的关系变得简单。The candidate target can also be regarded as a suspicious new target, track it, and judge whether it is a new target by the continuity; when the trajectory chain cannot find a matching candidate target, it should remember to track until the target is found again; if more than If the target cannot be retrieved within a certain period of time, it is considered that the tracking target is lost, and the relationship of data association becomes simple at this time.

在跟踪预测中，一阶多项式拟合即直线拟合最能反映出运动趋势。经典最小二乘的误差函数是y坐标距离曲线的距离函数，对于直线而言用点到直线距离平方作误差函数更为合适；另外在拟合中引入时间加权因子，解决时效性的问题；通过调整权系数，使拟合的迭代运算量固定，从而整个跟踪的运算量可以控制，便于系统设计和实现。In tracking prediction, the first-order polynomial fitting, that is, straight line fitting, can best reflect the motion trend. The error function of the classical least squares is the distance function of the y-coordinate distance curve. For a straight line, it is more appropriate to use the square of the point-to-line distance as the error function; in addition, a time weighting factor is introduced in the fitting to solve the problem of timeliness; through By adjusting the weight coefficients, the iterative calculation amount of fitting is fixed, so the calculation amount of the whole tracking can be controlled, which is convenient for system design and implementation.

5)不同情况下的目标特征提取5) Target feature extraction in different situations

当目标形状发生改变时，利用边缘特征归一化的形状识别寻找从电场角度引出的特征不变量达到目标精确跟踪。When the shape of the target changes, the feature invariant derived from the electric field angle is found by using the shape recognition normalized by the edge feature to achieve accurate target tracking.

当目标由远距离几个像素点变大时，由于探测器成像角度不同，同一目标的形状会发生改变，这时如何保证跟踪点不变，继续精确跟踪是关键问题。在图像目标的匹配识别中，人们希望的是要找到一个能表征目标图形特征的量，然后通过该特征量来表征两图形是否为同一目标。传统的匹配，对不规则图形的识别常用以下几种方法：傅里叶描叙子的匹配识别、基于不变矩特征方法的匹配识别及近些年来的通过神经网络学习方法的匹配识别等。傅里叶描叙子的识别方法是从频率域的角度进行匹配识别；不变矩特征方法是用矩表征一幅图像，并通过提取与统计学和力学中相似特征这一途径来进行匹配识别；神经网络学习方法是通过样本特征学习来进行识别；该申请项目的研究方法是把像素点赋予电荷点的含义，从电场这个全新角度来对不规则图形进行有效的识别，经过理论推导、研究和实验，找出一个不随形状改变而变化的特征量。以下详细介绍电场强度与电势识别形状算法When the target becomes larger from a few pixels at a distance, the shape of the same target will change due to the different imaging angles of the detectors. At this time, how to ensure that the tracking point remains unchanged and continue to accurately track is the key issue. In the matching and recognition of image targets, people hope to find a quantity that can characterize the characteristics of the target figure, and then use this feature quantity to characterize whether the two figures are the same target. In traditional matching, the following methods are commonly used for the recognition of irregular graphics: matching recognition of Fourier descriptors, matching recognition based on invariant moment feature methods, and matching recognition through neural network learning methods in recent years. The recognition method of the Fourier descriptor is to perform matching and recognition from the perspective of the frequency domain; the invariant moment feature method is to use moments to characterize an image, and to perform matching and recognition by extracting similar features in statistics and mechanics ; The neural network learning method is to identify through sample feature learning; the research method of this application is to assign the meaning of the charge point to the pixel point, and effectively identify the irregular figure from the new perspective of the electric field. After theoretical derivation and research And experiment to find a feature quantity that does not change with the shape change. The following is a detailed introduction to the electric field strength and potential recognition shape algorithm

在电学中，电荷均匀分布的任意带电体在自身周围空间中所产生静电场的分布是唯一的，而且该带电体与它在三维空间所产生的静电场是一一对应的。静电场只与该导体的大小、电荷密度大小及形状有关。以上概念得到一个结论：形状不同的均匀带电体在三维空间产生的电场分布是不相同的。In electricity, the distribution of electrostatic field generated by any charged object with uniform charge distribution in its surrounding space is unique, and the charged object corresponds to the electrostatic field generated by it in three-dimensional space. The electrostatic field is only related to the size, charge density and shape of the conductor. The above concept leads to a conclusion: the electric field distribution generated by uniform charged bodies with different shapes in three-dimensional space is different.

利用这个结论，推导出识别形状的特征不变量。在推导方法时，不过多考虑带电体的表面电荷密度的分布，着重考虑带电体的大小和形状对电场分布产生的影响。Using this conclusion, feature invariants for recognizing shapes are derived. When deriving the method, the distribution of the surface charge density of the charged body is not considered too much, and the influence of the size and shape of the charged body on the electric field distribution is emphasized.

由于图形的形状信息主要在边缘，因此通过图像处理的边缘检测方法，二值化后能够得到图形的边缘信息，如果把这些边缘像素点看作带电体，那么就可以计算出该图形在三维空间的电势与电场强度分布，也就可以将电场和电势的分布作为判别两个图形是否相同或相似的依据。Since the shape information of the graph is mainly at the edge, the edge information of the graph can be obtained after binarization through the edge detection method of image processing. The distribution of electric potential and electric field intensity can be used as the basis for judging whether two figures are the same or similar.

如图8所示，本研究采用多边形逼近的方法，以“直”代“曲”，来将图形边缘用近似多边形表示。As shown in Figure 8, this study adopts the method of polygonal approximation, replacing "curved" with "straight" to represent the edges of graphics with approximate polygons.

由于电势是个标量，因此各条边在空间任意一点产生的电势是可以直接代数相加的。电场强度虽然是矢量，但投影到z方向上，各条边的电场强度也可以代数相加。这样通过多边形逼近后，Since the electric potential is a scalar quantity, the electric potential generated by each edge at any point in space can be directly algebraically added. Although the electric field strength is a vector, but projected in the z direction, the electric field strength of each edge can also be added algebraically. After this approximation by polygons,

任意图形的边缘是由线段组成，那么图形边缘对空间任意一点(以下称这种点为观测点)所产生的电势与电场强度大小公式为The edge of any graph is composed of line segments, then the electric potential and electric field intensity generated by the edge of the graph to any point in space (hereinafter referred to as the observation point) are as follows:

电势大小公式：Potential size formula:

$\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>|</span>|</span>\mathrm{<span><span>ln</span>ln</span>}<span><span>|</span>|</span>\frac{\mathrm{<span><span>tan</span>the\; tan</span>}\frac{{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}}{\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>tan</span>the\; tan</span>}\frac{{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>2</span>2</span>}}}<span><span>|</span>|</span><span><span>|</span>|</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.24</span>4.24</span>}<span><span>)</span>)</span>$

电场强度大小公式：The electric field strength formula:

$\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{<span><span>|</span>|</span>{\mathrm{<span><span>PO</span><figure-callout\; label="PO"\; filenames="H2009101807801E00022.png"\; state="\{\{state\}\}">PO</figure-callout></span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>|</span>|</span>}{{<span><span>|</span>|</span>\mathrm{<span><span>OP</span>OP</span>}<span><span>|</span>|</span>}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>|</span>|</span><span><span>(</span>(</span>\mathrm{<span><span>cos</span>cos</span>}{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>cos</span>cos</span>}\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span><span><span>|</span>|</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.25</span>4.25</span>}<span><span>)</span>)</span>$

其中θ_i，1，θ_i，2分别表示组成图形边缘的第i条线段的θ₁与θ₂。Among them, θ_i,1 and θ_i,2 respectively denote θ₁ and θ₂ of the ith line segment forming the edge of the graph.

观测点的归一化如下：The normalization of observation points is as follows:

各个图形的观测点选取要求“一致”，其目的是由于要保证相同形状图形在各自对应的观测点所产生的电势与电场强度相同，所以先要对图形的观测点进行“一致”化，称之为观测点的归一化。The selection of observation points of each graph requires "consistency", the purpose is to ensure that the electric potential and electric field intensity generated by the same shape graph at their corresponding observation points are the same, so the observation points of the graph must be "consistent", called It is the normalization of observation points.

为寻找归一化观测点，在本研究中对原来公式做了一定的修改，对应的归一化观测点应满足：从各图形的中心到各个观测点做射线，各条射线应与图形平面相垂直或在图形平面上的投影与以各需识别图形的主方向的偏角一致，且射线与图形平面的夹角相同，则此时对应观测点到各图形中心的距离之比等于各图形面积开方之比[证明见所发表文章]。In order to find the normalized observation points, the original formula has been modified in this study, and the corresponding normalized observation points should meet the following requirements: a ray is drawn from the center of each graph to each observation point, and each ray should be consistent with the graph plane The projections perpendicular to or on the graphics plane are consistent with the declination angles of the main directions of the graphics to be identified, and the angle between the ray and the graphics plane is the same, then the ratio of the distance from the corresponding observation point to the center of each graphics is equal to that of each graphics Ratio of square root of area [see published article for proof].

这样如图9所示，公式(4.24)(4.25)改进为如下In this way, as shown in Figure 9, the formula (4.24) (4.25) is improved as follows

电势大小变换公式：The electric potential size transformation formula:

$\mathrm{<span><span>U</span>u</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>|</span>|</span>\mathrm{<span><span>ln</span>ln</span>}<span><span>|</span>|</span>\frac{\mathrm{<span><span>tan</span>the\; tan</span>}\frac{{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}}{\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>tan</span>the\; tan</span>}\frac{{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>2</span>2</span>}}}<span><span>|</span>|</span><span><span>|</span>|</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.26</span>4.26</span>}<span><span>)</span>)</span>$

电场强度大小变换公式：The electric field strength magnitude transformation formula:

$\mathrm{<span><span>E</span>E.</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>z</span>z</span>}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}}\sqrt{\mathrm{<span><span>S</span>S</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{<span><span>|</span>|</span>{\mathrm{<span><span>PO</span><figure-callout\; label="PO"\; filenames="H2009101807801E00022.png"\; state="\{\{state\}\}">PO</figure-callout></span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>|</span>|</span>}{{<span><span>|</span>|</span>\mathrm{<span><span>OP</span>OP</span>}<span><span>|</span>|</span>}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>|</span>|</span><span><span>(</span>(</span>\mathrm{<span><span>cos</span>cos</span>}{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>\mathrm{<span><span>cos</span>cos</span>}{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span><span><span>|</span>|</span>\sqrt{\mathrm{<span><span>S</span>S</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.27</span>4.27</span>}<span><span>)</span>)</span>$

其中θ_i，1，θ_i，2分别表示组成图形边缘的第i条线段的(如图8所示)θ₁与θ₂。Among them, θ_i,1 and θ_i,2 denote respectively θ₁ and θ₂ of the i-th line segment (as shown in Fig. 8 ) forming the edge of the graph.

虽然修改了以上公式，但电场强度仍然保留了需要的物理意义。这样通过对应观测点的归一化，就解决了大小不同形状相同图形的可比性问题。Although the above formula is modified, the electric field strength still retains the required physical meaning. In this way, through the normalization of the corresponding observation points, the comparability problem of the same graphics with different sizes and shapes is solved.

采用本发明中的技术和装置，整个系统对复杂背景下的弱小目标的检测识别与精确跟踪可达到如下的技术指标：By adopting the technology and device of the present invention, the whole system can achieve the following technical indicators for the detection, recognition and precise tracking of weak and small targets in complex backgrounds:

1)输入信号：红外、电视视频信号(GPS信号、激光测距仪信号输入接口及处理能力)；1) Input signal: infrared, TV video signal (GPS signal, laser rangefinder signal input interface and processing capacity);

2)输出误差信号：目标相对于视场中心的角位置偏移值；2) Output error signal: the angular position offset value of the target relative to the center of the field of view;

3)最小跟踪对比度：≤3％；3) Minimum tracking contrast: ≤3%;

4)捕获能力：能同时自动捕获和跟踪视场内4个目标；4) Acquisition capability: it can automatically capture and track 4 targets in the field of view at the same time;

5)记忆跟踪：当目标暂时被遮挡，跟踪器应能自动转入记忆跟踪状态，输出保持目标丢失时刻的值不变；目标再出现时，能重新自动捕获；5) Memory tracking: When the target is temporarily blocked, the tracker should be able to automatically switch to the memory tracking state, and the output value remains unchanged at the time when the target is lost; when the target reappears, it can be automatically captured again;

6)误差输出延迟：≤20ms；接口：并口、RS232、PCI6) Error output delay: ≤20ms; interface: parallel port, RS232, PCI

7)ATR(自动检测系统参数)：全屏(768×576)实时检测，误差信息可按场、帧输出。目标特性：天空、地面目标。7) ATR (automatic detection system parameters): full-screen (768×576) real-time detection, error information can be output by field and frame. Target characteristics: sky, ground targets.

8)环境条件：工作温度：-35℃～+55℃，相对湿度：95％。8) Environmental conditions: Working temperature: -35℃～+55℃, relative humidity: 95%.

本发明是一种多模多目标精密跟踪装置和方法，其优点在于：本发明检测的是复杂背景下弱小、斑点和大目标，具有很好的复杂战场环境下的自适应跟踪和抗干扰能力，其主要体现在：The present invention is a multi-mode and multi-target precision tracking device and method, and its advantages are: the present invention detects weak, speckle and large targets in complex backgrounds, and has good self-adaptive tracking and anti-jamming capabilities in complex battlefield environments , which is mainly reflected in:

1)预处理部分：1) Preprocessing part:

(1)解决了由于运动或平台抖动造成模糊的图像复原问题；(1) Solve the problem of blurred image restoration caused by motion or platform shake;

(2)完成了图像恢复过程中的振铃效应抑制；(2) The ringing effect suppression in the image restoration process has been completed;

(3)采用了改进的基于离散平稳小波变换和非线性增强算子的弱小目标图像增强算法，解决了实际工程应用中复杂背景低信噪比条件下，弱小目标的信噪比增强问题。(3) An improved weak target image enhancement algorithm based on discrete stationary wavelet transform and nonlinear enhancement operator is adopted to solve the problem of SNR enhancement of weak and small targets under the condition of complex background and low SNR in practical engineering applications.

2)基于运动补偿的弱小目标的检测及精确跟踪技术：2) Detection and precise tracking technology of weak and small targets based on motion compensation:

(1)基于轨迹预测的跟踪方法，提出了结合Kalman滤波思想改进的曲线拟合方法预测目标运动方向和速度，降低了数据关联的复杂性，选择了合适的判断模型和判决准则。(1) Based on the trajectory prediction tracking method, an improved curve fitting method combined with the Kalman filtering idea is proposed to predict the direction and speed of the target's movement, which reduces the complexity of data association and selects an appropriate judgment model and judgment criterion.

(2)研究了复杂背景下针对不同目标的运动预测和补偿算法，解决了目标交叠、抖动、多目标等复杂情况下的精确跟踪问题。(2) The motion prediction and compensation algorithms for different targets in complex backgrounds are studied, and the precise tracking problems in complex situations such as target overlapping, shaking, and multiple targets are solved.

(3)精确跟踪过程中，特征不变量的寻找。当目标形状发生改变时，如何找到一种特征不变量去表征目标一直是图像处理领域的一个难点与关键技术。在本项目中，利用边缘特征归一化的形状识别寻找了从电场角度引出的特征不变量它不随目标旋转、位移、变形而发生改变，进而有效的达到了目标精确跟踪的目的。(3) In the process of precise tracking, the search for feature invariants. When the shape of the target changes, how to find a feature invariant to represent the target has always been a difficult and key technology in the field of image processing. In this project, the shape recognition using edge feature normalization finds the characteristic invariant derived from the electric field angle, which does not change with the target's rotation, displacement, and deformation, and thus effectively achieves the goal of accurate target tracking.

3)建立了可见光、红外目标融合检测模型：3) A visible light and infrared target fusion detection model is established:

单传感器目标检测概率较低，虚警概率高，建立适合的融合结构至关重要。本项目中：The probability of single-sensor target detection is low, and the probability of false alarm is high. It is very important to establish a suitable fusion structure. In this project:

(1)完成了多传感器融合结构体系选择；(1) Completed the selection of multi-sensor fusion structure system;

(2)解决了多传感器时间对准、空间对准、目标特征匹配问题；(2) Solve the problems of multi-sensor time alignment, space alignment, and target feature matching;

4)系统化和工程化应用：4) Systematic and engineering application:

充分考虑系统化和工程化应用的要求，在设计上考虑多种通用需求，多种信息接口，集成强大的软、硬件资源，在不改变硬件情况下只需改变软件即可实现对海上、空中等不同目标的处理。Fully consider the requirements of systematic and engineering applications, consider various general requirements in design, multiple information interfaces, integrate powerful software and hardware resources, and only need to change the software without changing the hardware. and other processing of different objectives.

(四)附图说明：(4) Description of drawings:

图1所示为多模多目标精密跟踪装置的构成框图Figure 1 shows the block diagram of the multi-mode multi-target precision tracking device

图2所示为数字伺服平台的构成框图Figure 2 shows the block diagram of the digital servo platform

图3所示为综合信息处理平台的构成框图Figure 3 shows the block diagram of the integrated information processing platform

图4所示为压缩及传输设备的构成框图Figure 4 shows the block diagram of the compression and transmission equipment

图5所示为多模多目标精密跟踪装置连接图Figure 5 shows the connection diagram of the multi-mode multi-target precision tracking device

图6所示为复杂背景低信噪比下弱小目标高精度跟踪方法流程图Figure 6 shows the flow chart of the high-precision tracking method for weak and small targets under complex background and low SNR

图7所示为基于轨迹预测的目标检测、识别跟踪流程图Figure 7 shows the flow chart of target detection, recognition and tracking based on trajectory prediction

图8(a)所示为多边形逼近示意图之原图Figure 8(a) shows the original image of the polygon approximation schematic

图8(b)所示为多边形逼近示意图之直线段逼近效果图Figure 8(b) shows the approximation effect of the straight line segment of the polygonal approximation schematic diagram

图9所示为归一化观测点关系示意图Figure 9 is a schematic diagram of the relationship between normalized observation points

图中标号说明如下：The symbols in the figure are explained as follows:

1、数字伺服平台        11、CCD摄像机 12、红外传感器1.Digital servo platform 11.CCD camera 12. Infrared sensor

13、高精度数字伺服转台 14、手柄      15、监视器13. High-precisiondigital servo turntable 14.Handle 15. Monitor

2、综合信息处理平台  21、信息接口        22、高速数字信号处理器2. Comprehensiveinformation processing platform 21.Information interface 22. High-speed digital signal processor

23、伺服控制处理器23. Servo control processor

3、压缩及传输设备    31、视频压缩处理器  32、GPRS传输模块3. Compression and transmission equipment 31. Video compression processor 32. GPRS transmission module

(五)具体实施方式：(5) Specific implementation methods:

将本发明复杂背景低信噪比下弱小目标高精度跟踪方法，应用在自主研制的多模多目标精密跟踪装置上，以验证系统的性能指标。该多模多目标精密跟踪装置，如图1所示：由以下三部分构成：数字伺服平台1、综合信息处理平台2、压缩及传输设备3；本发明的复杂背景低信噪比下弱小目标高精度跟踪方法主要在综合信息处理平台中得以实现。该装置中：The high-precision tracking method for weak and small targets under the complex background and low signal-to-noise ratio of the present invention is applied to the self-developed multi-mode and multi-target precision tracking device to verify the performance indicators of the system. The multi-mode multi-target precision tracking device, as shown in Figure 1, consists of the following three parts:digital servo platform 1, comprehensiveinformation processing platform 2, compression andtransmission equipment 3; weak and small targets under complex background and low signal-to-noise ratio of the present invention The high-precision tracking method is mainly realized in the comprehensive information processing platform. In this device:

1)数字伺服平台1) Digital servo platform

如图2所示，数字伺服平台1由CCD(Charge Coupled Device，即电荷藕合器件图像传感器)摄像机11、红外传感器12、高精度数字伺服转台13、手柄14和监视器15组成，也可根据需要选用两个CCD摄像机11或两个红外传感器12。本发明采用的CCD摄像机11可以是模拟信号输入或数字信号输入，采用的红外传感器是分辨率为768×576。As shown in Figure 2, thedigital servo platform 1 is composed of a CCD (Charge Coupled Device, i.e. a charge-coupled device image sensor)camera 11, aninfrared sensor 12, a high-precisiondigital servo turntable 13, ahandle 14 and amonitor 15. TwoCCD cameras 11 or twoinfrared sensors 12 need to be selected. TheCCD camera 11 adopted by the present invention can be an analog signal input or a digital signal input, and the infrared sensor adopted has a resolution of 768×576.

该数字伺服平台1是图像获取装置的支撑平台，上述装置中的CCD摄像机11和红外传感器12分别安装在高精度数字伺服转台13两端，可随高精度数字伺服转台13一起运动。同时高精度数字伺服转台13可根据接收的控制命令进行转动，对目标进行精确跟踪，使目标保持在图像获取装置的视场中心。Thedigital servo platform 1 is the support platform of the image acquisition device. TheCCD camera 11 and theinfrared sensor 12 in the above device are respectively installed at the two ends of the high-precisiondigital servo turntable 13, and can move together with the high-precisiondigital servo turntable 13. At the same time, the high-precisiondigital servo turntable 13 can be rotated according to the received control command to accurately track the target, so that the target can be kept at the center of the field of view of the image acquisition device.

将CCD摄像机11同红外传感器12组合使用，同时获取可见光和红外的目标图像信息，综合两种信息中的目标特征，从而提高目标的检测概率和精确跟踪精度。TheCCD camera 11 is used in combination with theinfrared sensor 12 to obtain visible light and infrared target image information at the same time, and integrate target features in the two types of information, thereby improving target detection probability and precise tracking accuracy.

2)综合信息处理平台2) Comprehensive information processing platform

如图3所示，该综合信息处理平台2由信息接口21、高速数字信号处理器22、伺服控制处理器23组成。该高速数字信号处理器22采用基于DSP(数字信号处理器)的信号处理系统。高速数字信号处理器22接收从CCD摄像机11或红外传感器12传入的图像信息，完成对复杂背景低信噪比下可见光和红外图像中的目标特征提取、特征匹配、目标运动预测与估计、精确跟踪方法的实现。伺服控制处理器23根据目标预测与跟踪的结果，确定高精度数字伺服转台13的运动方向，并向高精度数字伺服转台13发出控制命令，使高精度数字伺服转台13根据预测与跟踪的结果对目标进行跟踪。As shown in FIG. 3 , the integratedinformation processing platform 2 is composed of aninformation interface 21 , a high-speeddigital signal processor 22 and aservo control processor 23 . The high-speeddigital signal processor 22 employs a signal processing system based on a DSP (Digital Signal Processor). The high-speeddigital signal processor 22 receives the image information from theCCD camera 11 or theinfrared sensor 12, and completes the target feature extraction, feature matching, target motion prediction and estimation, and accurate Implementation of the trace method. Theservo control processor 23 determines the motion direction of the high-precisiondigital servo turntable 13 according to the results of target prediction and tracking, and sends a control command to the high-precisiondigital servo turntable 13, so that the high-precisiondigital servo turntable 13 can control the target according to the results of prediction and tracking. target to track.

该信息处理平台采用两个独立的信号处理器，即高速数字信号处理器22和伺服控制处理器23，分别对图像信息和高精度数字伺服转台13的控制信息进行处理，在图像预处理、目标识别与跟踪关键算法中，针对复杂背景下弱小目标的特点，采取多种算法改进与创新实现对弱小目标的识别与跟踪。The information processing platform adopts two independent signal processors, that is, a high-speeddigital signal processor 22 and aservo control processor 23, which respectively process the image information and the control information of the high-precisiondigital servo turntable 13. In the identification and tracking key algorithm, according to the characteristics of weak and small targets in complex backgrounds, a variety of algorithm improvements and innovations are adopted to realize the identification and tracking of weak and small targets.

3)压缩及传输设备3) Compression and transmission equipment

该压缩及传输设备3使该多模多目标精密跟踪装置具有“人在回路”功能，将自动识别检测出的目标的所有信息和图像传回指挥中心，并接受指挥中心的指令对跟踪的目标进行调整以提高自动识别的精度。如图4所示，压缩及传输设备3由视频压缩处理器31、GPRS传输模块32组成。该视频压缩处理器31的图像输入可以是数字视频或模拟视频，可根据不同的输出要求选择不同的接口协议，采用MEPG-4的视频压缩算法，后端GPRS传输模块采用基于GPRS无线信道进行传输。The compression andtransmission equipment 3 enables the multi-mode multi-target precision tracking device to have the function of "human-in-the-loop", and transmits all the information and images of the detected targets automatically to the command center, and accepts the commands of the command center to track the target Make adjustments to improve the accuracy of automatic recognition. As shown in FIG. 4 , the compression andtransmission device 3 is composed of a video compression processor 31 and a GPRS transmission module 32 . The image input of the video compression processor 31 can be digital video or analog video, and different interface protocols can be selected according to different output requirements. The video compression algorithm of MEPG-4 is adopted, and the back-end GPRS transmission module adopts GPRS wireless channel for transmission .

该装置突破了目标识别跟踪器单一的目标检测识别处理模式，还可以与其它探测系统联网进行数据交互、图像传输，并具有伺服组网控制、人在回路控制等功能。The device breaks through the single target detection and recognition processing mode of the target recognition tracker, and can also be networked with other detection systems for data interaction and image transmission, and has functions such as servo networking control and human-in-the-loop control.

多模多目标精密跟踪装置各部分之间的关系如图5所示多模多目标精密跟踪装置的连接关系，该数字伺服平台1，包括CCD摄像机11、红外传感器12、高精度数字伺服转台13、手柄14和监视器15五部分。其中CCD摄像机11和红外传感器12分别安装在高精度数字伺服转台13上部的两端，两者通过电缆同信息接口21相连进行图像数据的传输，手柄14和监视器15分别放置在高精度数字伺服转台13下部的两侧。该综合信息处理平台2，包括信息接口21、高速数字信号处理器22和伺服控制处理器23三部分，三部分均集成于信息处理板并置于控制箱中，放置在高精度数字伺服转台13一侧。其中该数字伺服平台1中的手柄14同信息接口21相连进行控制信号的传输，该数字伺服平台1中的监视器15同信息接口21相连用于显示获取的图像数据信息，高速数字信号处理器22与信息接口21相连，用于获取CCD摄像机11和红外传感器12传输的图像数据，伺服控制处理器23与信息接口21相连，用于获取高速数字信号处理器的目标检测识别信息和高精度数字伺服转台13反馈的位置信息，并向高精度数字伺服转台13传输控制命令。该压缩及传输设备3，包括视频压缩处理器31和GPRS传输模块32两部分，两者分别集成于信息处理板上，视频压缩处理器31后端同GPRS传输模块32相连，视频压缩处理器31前端同综合信息处理平台2中的高速数字信号处理器22相连。就多模多目标精密跟踪装置整体而言，数字伺服平台1处于多模多目标精密跟踪装置的前端，综合信息处理平台2处于多模多目标精密跟踪装置的中端，压缩及传输设备3处于多模多目标精密跟踪装置的后端。如图5所示，本发明一种复杂背景低信噪比下弱小目标高精度跟踪方法，是在高速数字信号处理器中完成，其在整个多模多目标精密跟踪装置中的工作流程为，首先通过CCD摄像机11和红外传感器12获取目标的可见光和红外图像，然后将复杂背景低信噪比下的图像信号通过信息接口21传送给高速数字信号处理器22，经处理器对图像进行预处理、检测后，完成对目标的自动识别与跟踪，同时将跟踪的目标信息传送给伺服控制处理器23，由伺服控制处理器23产生控制命令给高精度数字伺服转台13；在将图像信号通过监视器15进行显示的同时把原图像信息和叠加了跟踪目标信息的图像传送给视频压缩处理器31进行视频压缩，然后通过GPRS传输模块32进行无线传输，使指挥中心通过解码处理器在控制中心的监视器15中观察到目标跟踪情况。The relationship between the various parts of the multi-mode multi-target precision tracking device is shown in Figure 5. The connection relationship of the multi-mode multi-target precision tracking device, thedigital servo platform 1 includes aCCD camera 11, aninfrared sensor 12, and a high-precisiondigital servo turntable 13 , handle 14 and monitor 15 five parts. Wherein theCCD camera 11 and theinfrared sensor 12 are respectively installed on the two ends of the upper part of the high-precisiondigital servo turntable 13, and the two are connected with theinformation interface 21 through the cable to transmit the image data, and thehandle 14 and themonitor 15 are respectively placed on the high-precision digital servo Both sides ofturntable 13 bottoms. The comprehensiveinformation processing platform 2 includes three parts: aninformation interface 21, a high-speeddigital signal processor 22 and aservo control processor 23. The three parts are integrated into the information processing board and placed in the control box, and placed on the high-precisiondigital servo turntable 13 side. Wherein thehandle 14 in thedigital servo platform 1 is connected with theinformation interface 21 to carry out the transmission of the control signal, themonitor 15 in thedigital servo platform 1 is connected with theinformation interface 21 for displaying the image data information obtained, and the high-speeddigital signal processor 22 is connected to theinformation interface 21 for obtaining the image data transmitted by theCCD camera 11 and theinfrared sensor 12, and theservo control processor 23 is connected to theinformation interface 21 for obtaining the target detection identification information and high-precision digital signal processor of the high-speed digital signal processor. The position information fed back by theservo turntable 13 transmits control commands to the high-precisiondigital servo turntable 13 . This compression andtransmission equipment 3 comprises video compression processor 31 and GPRS transmission module 32 two parts, both are integrated on the information processing board respectively, video compression processor 31 rear end is connected with GPRS transmission module 32, video compression processor 31 The front end is connected with the high-speeddigital signal processor 22 in the integratedinformation processing platform 2 . As far as the multi-mode and multi-target precision tracking device is concerned as a whole, thedigital servo platform 1 is at the front end of the multi-mode and multi-target precision tracking device, the comprehensiveinformation processing platform 2 is at the middle end of the multi-mode and multi-target precision tracking device, and the compression andtransmission equipment 3 is at the The back end of the multi-mode multi-target precision tracking device. As shown in Figure 5, a high-precision tracking method for weak and small targets under a complex background and low signal-to-noise ratio in the present invention is completed in a high-speed digital signal processor, and its workflow in the entire multi-mode and multi-target precision tracking device is as follows: First, through theCCD camera 11 and theinfrared sensor 12 to obtain the visible light and infrared images of the target, then the image signal under the complex background and low signal-to-noise ratio is transmitted to the high-speeddigital signal processor 22 through theinformation interface 21, and the image is preprocessed by the processor After the detection, the automatic recognition and tracking of the target are completed, and the tracked target information is sent to theservo control processor 23, and the control command is generated by theservo control processor 23 to the high-precisiondigital servo turntable 13; When thedevice 15 is displayed, the original image information and the image superimposed with the tracking target information are sent to the video compression processor 31 for video compression, and then wirelessly transmitted by the GPRS transmission module 32, so that the command center is in the control center through the decoding processor. Object tracking is observed onmonitor 15 .

如图6所示，本发明一种复杂背景低信噪比下弱小目标高精度跟踪方法，用于在复杂背景下弱小目标自动检测、识别与跟踪，其方法的具体步骤是1、复杂背景、低信噪比条件下的图像预处理，2、基于二项分布判断准则的目标自适应门限分割，3、红外与可见光数据进行多模融合，4、目标运动预测与估计，5、不同情况下的目标特征提取。各步骤的详细说明如下：As shown in Figure 6, a high-precision tracking method for weak and small targets under a complex background and low signal-to-noise ratio of the present invention is used for automatic detection, identification and tracking of weak and small targets in a complex background. The specific steps of the method are 1. complex background, Image preprocessing under low signal-to-noise ratio conditions, 2. Target adaptive threshold segmentation based on binomial distribution judgment criteria, 3. Multi-mode fusion of infrared and visible light data, 4. Target motion prediction and estimation, 5. Different situations target feature extraction. The detailed description of each step is as follows:

1)复杂背景、低信噪比条件下的图像预处理1) Image preprocessing under conditions of complex background and low signal-to-noise ratio

对复杂背景下的弱小目标检测必须选择有效的预处理方法，这对后续的目标检测识别过程中具有很重要的意义。在我们以往的研究中，对很多预处理方法都进行过仿真与工程应用。经过大量实验和分析，本系统的图像预处理采用基于改进的离散平稳小波变换(DSWT)和非线性增强算子的弱小目标图像增强算法。For weak and small target detection in complex backgrounds, an effective preprocessing method must be selected, which is of great significance to the subsequent target detection and recognition process. In our previous research, many preprocessing methods have been simulated and applied in engineering. After a lot of experiments and analysis, the image preprocessing of this system adopts the weak and small target image enhancement algorithm based on the improved Discrete Stationary Wavelet Transform (DSWT) and nonlinear enhancement operator.

小波变换具有完善的重建能力；在时域和频域同时具有局部化特性(伸缩性)，可以聚焦到对象任意细节；多尺度、多分辨率特性；方向选择性，与人类视觉系统的方向性吻合。小波分析的多尺度特性，使得它适合于在信噪比低的环境下进行目标检测。其伸缩特性可使部分图像特征在某个尺度下被有效地抑制，而某些感兴趣的目标(如小目标)可以被突显出来。小波分析不仅可以用在图像预处理中，也可以用在图像分割和目标运动估计上。Wavelet transform has perfect reconstruction ability; it has localization characteristics (scalability) in both time domain and frequency domain, and can focus on any details of objects; multi-scale and multi-resolution characteristics; direction selectivity, and the directionality of the human visual system match. The multi-scale characteristic of wavelet analysis makes it suitable for target detection in the environment with low signal-to-noise ratio. Its stretching properties can effectively suppress some image features at a certain scale, while some interesting objects (such as small objects) can be highlighted. Wavelet analysis can be used not only in image preprocessing, but also in image segmentation and target motion estimation.

从大量国内外文献分析，在复杂背景下，弱小目标识别跟踪这个领域，传统的基于小波变换的图像预处理基本上都是进行如下操作的：From the analysis of a large number of domestic and foreign literature, in the field of weak and small target recognition and tracking under complex backgrounds, the traditional image preprocessing based on wavelet transform basically performs the following operations:

(1)选择合适的小波基，并对图像进行N层小波分解；(1) Select an appropriate wavelet base, and perform N-level wavelet decomposition on the image;

(2)高频系数的阈值选择。对于第一层到第N层的每一层，选择一个阈值进行处理。(2) Threshold selection of high frequency coefficients. For each layer from the first layer to the Nth layer, a threshold is selected for processing.

(3)根据第N层的低频系数和从第一层到第N层经过修改的高频系数，计算出图像的小波重建。(3) Calculate the wavelet reconstruction of the image according to the low-frequency coefficients of the Nth layer and the modified high-frequency coefficients from the first layer to the Nth layer.

传统的基于小波变换的预处理尽管可以得到不错的处理结果，但是在对高频系数进行处理的时候，大部分采用了线性的统一阈值，图像的边缘等细节遭到了不同程度的削弱。本系统在总结传统的基于小波变换图像预处理的基础上，利用基于离散平稳小波变换(DSWT)和非线性增强算子对弱小目标的图像进行增强。在进行DSWT的基础上，得到的高频子带具有较差的分辨率，对这些高频子带进行非线性算子运算来改善和增强高频子带，从而达到了滤波增强的作用。实验结果表明，这种算法可以有效消除1/f噪声，加性高斯白噪声和乘性噪声，提高图像的信噪比。本算法主要包括以下三个部分：Although the traditional preprocessing based on wavelet transform can get good processing results, most of them use a linear unified threshold when processing high-frequency coefficients, and the details such as the edges of the image are weakened to varying degrees. On the basis of summarizing the traditional image preprocessing based on wavelet transform, this system uses discrete stationary wavelet transform (DSWT) and nonlinear enhancement operator to enhance the image of weak and small targets. On the basis of DSWT, the obtained high-frequency sub-bands have poor resolution. Non-linear operator operations are performed on these high-frequency sub-bands to improve and enhance the high-frequency sub-bands, thereby achieving the effect of filter enhancement. Experimental results show that this algorithm can effectively eliminate 1/f noise, additive Gaussian white noise and multiplicative noise, and improve the signal-to-noise ratio of the image. This algorithm mainly includes the following three parts:

(1)抑制噪声(1) Noise suppression

(2)阈值选取(2) Threshold selection

(3)非线性增强算子(3) Nonlinear enhancement operator

下面就这三部分进行详细说明These three parts are described in detail below

(1)抑制噪声(1) Noise suppression

采用传统的“全局阈值”对图像来去噪，效果不理想。I.M.Johnston证明了相关噪声的小波变换在所有的尺度上都是平稳的，我们可以在每个尺度上分别用不同的阈值来对图像进行去噪。Using the traditional "global threshold" to denoise the image, the effect is not ideal. I.M.Johnston proved that the wavelet transform of correlated noise is stable on all scales, and we can use different thresholds on each scale to denoise the image.

假设离散图像的模型如下：Assume the model of the discrete image as follows:

g[i，j]＝f[i，j]+ε[i，j](4.1)g[i,j]=f[i,j]+ε[i,j] (4.1)

上面的公式可以写成矩阵的格式：The above formula can be written in matrix format:

g＝f+ε(4.2)g=f+ε(4.2)

其中，g＝{g[i，j]}_i，j是观测到的信号。f＝{f[i，j]}_i，j表示没有噪声污染的原始信号，ε＝{ε[i，j]}_i，j，i＝1，...，M；j＝1，...，N是平稳信号。where g={g[i, j]}_{i, j} is the observed signal. f={f[i, j]}_{i, j} represents the original signal without noise pollution, ε={ε[i, j]}_{i, j} , i=1,...,M; j=1,. . . , N is a stationary signal.

对(4.2)进行DSWT，得：Perform DSWT on (4.2), get:

X＝Sf    (4.3)X＝Sf (4.3)

V＝Sε   (4.4)V＝Sε (4.4)

Y＝Sg    (4.5)Y＝Sg (4.5)

Y＝X+V   (4.6)Y=X+V (4.6)

其中S表示二维平稳小波变换算子，在图像中引用Donoho提出的“软阈值”函数对图像进行去噪处理：Among them, S represents the two-dimensional stationary wavelet transform operator, and the "soft threshold" function proposed by Donoho is used in the image to denoise the image:

Y_δ＝T_δοY    (4.7)Y_δ ＝T_δ οY (4.7)

T_δ＝diag{t[m，m]}T_δ =diag{t[m,m]}

$\mathrm{<span><span>t</span>t</span>}<span><span>[</span>[</span>\mathrm{<span><span>m</span>m</span>}<span><span>,</span>,</span>\mathrm{<span><span>m</span>m</span>}<span><span>]</span>]</span><span><span>=</span>=</span>\left\{\begin{array}{cc}\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>& <span><span>|</span>|</span>\mathrm{<span><span>Y</span>Y</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>|</span>|</span><span><span><</span><</span>\mathrm{<span><span>\&delta;</span>\&delta;</span>}\\ \mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\frac{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}{<span><span>|</span>|</span>\mathrm{<span><span>Y</span>Y</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>|</span>|</span>}& <span><span>|</span>|</span>\mathrm{<span><span>Y</span>Y</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>|</span>|</span><span><span>\&GreaterEqual;</span>\&Greater\; Equal;</span>\mathrm{<span><span>\&delta;</span>\&delta;</span>}\end{array}\right.$

其中，i＝1，...，M，j＝1，...，N，m＝1，...，MNAmong them, i=1,..., M, j=1,..., N, m=1,..., MN

根据式(4.5)和(4.7)，输入信号的反变换为：According to equations (4.5) and (4.7), the inverse transformation of the input signal is:

g_δ＝S^-1οY_δ(4.8)g_δ = S^-1 οY_δ (4.8)

其中T_δ与阈值δ和信号g相关。where T_δ is related to threshold δ and signal g.

(2)阈值选取(2) Threshold selection

假设原始信号f(x，y)可以用其邻域像素线性表示。若令

是g[k，l]的线性表示，用邻域均值对图像进行平滑，可以去除一部分噪声。Assume that the original signal f(x, y) can be linearly represented by its neighboring pixels. Ruoling

It is a linear representation of g[k, l]. Smoothing the image with the neighborhood mean can remove part of the noise.

平滑后的可以用来计算去除噪声的阈值。g[i，j]表示g中的[i，j]元素，它被

替代：smoothed Can be used to calculate the threshold for removing noise. g[i, j] represents the [i, j] element in g, which is

Alternate:

$\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>g</span>g</span>}}<span><span>=</span>=</span>\mathrm{<span><span>Z</span>Z</span>}{<span><span>(</span>(</span>\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>1,1</span>1,1</span>}<span><span>]</span>]</span><span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span>\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>M</span>m</span>}<span><span>,</span>,</span>\mathrm{<span><span>N</span>N</span>}<span><span>]</span>]</span><span><span>)</span>)</span>}^{\mathrm{<span><span>T</span>T</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.9</span>4.9</span>}<span><span>)</span>)</span>$

我们认为比g[i，j]能更好的得到优化阈值。We believe It is better than g[i, j] to get the optimized threshold.

如果阈值δ太小，

中主要表现为噪声；如果阈值δ太大，会滤掉很多有用的信号。If the threshold δ is too small,

Mainly manifested as noise; if the threshold δ is too large, many useful signals will be filtered out.

对所有的像素实施同样的操作，最佳的阈值可以通过如下运算来得到：Perform the same operation on all pixels, and the optimal threshold can be obtained by the following operations:

$\mathrm{<span><span>OCV</span>OCV</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>MN</span>MN</span>}}\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{<span><span>(</span>(</span>\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>-</span>-</span>{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>g</span>g</span>}}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.10</span>4.10</span>}<span><span>)</span>)</span>$

的形式有很多种，在这里，令${\tilde{g}}_{\mathrm{\&delta;}}[i,j]=\tilde{g}[i,j],$则：

There are many forms, here, let${\tilde{g}}_{\mathrm{\&delta;}}[i,j]=\tilde{g}[i,j],$ but:

$\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>-</span>-</span>{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>g</span>g</span>}}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>-</span>-</span>{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span>}{\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>z</span>z</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.11</span>4.11</span>}<span><span>)</span>)</span>$

其中：in:

$\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>z</span>z</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>=</span>=</span>\frac{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>-</span>-</span>{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>g</span>g</span>}}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span>}{\mathrm{<span><span>g</span>g</span>}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>-</span>-</span>{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>g</span>g</span>}}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span>}<span><span>\&ap;</span>\&ap;</span>{\mathrm{<span><span>z</span>z</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>[</span>[</span>\mathrm{<span><span>m</span>m</span>}<span><span>,</span>,</span>\mathrm{<span><span>n</span>no</span>}<span><span>]</span>]</span><span><span>=</span>=</span>\frac{{<span><span>\&PartialD;</span>\&PartialD;</span>\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span>}{<span><span>\&PartialD;</span>\&PartialD;</span>{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>[</span>[</span>\mathrm{<span><span>k</span>k</span>}<span><span>,</span>,</span>\mathrm{<span><span>l</span>l</span>}<span><span>]</span>]</span>}$

其中，i，k＝1，...，M，j，l＝1，...，N，m，n＝1，...，MNAmong them, i, k=1,..., M, j, l=1,..., N, m, n=1,..., MN

然而，在(4.11)中，z′[m，m]为1或者是0，在实际计算中不可用。因此给出如下公式来替代(4.10)：However, in (4.11), z'[m, m] is 1 or 0, which is not available in actual calculation. So give the following formula to replace (4.10):

$\mathrm{<span><span>SGCV</span>SGCV</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>MN</span>MN</span>}}{<span><span>|</span>|</span><span><span>|</span>|</span>\mathrm{<span><span>Y</span>Y</span>}<span><span>-</span>-</span>{\mathrm{<span><span>Y</span>Y</span>}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>|</span>|</span><span><span>|</span>|</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{<span><span>[</span>[</span>\frac{\mathrm{<span><span>trace</span>trace</span>}<span><span>(</span>(</span>\mathrm{<span><span>I</span>I</span>}<span><span>-</span>-</span>{\mathrm{<span><span>Z</span>Z</span>}}_{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>MN</span>MN</span>}}<span><span>]</span>]</span>}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.12</span>4.12</span>}<span><span>)</span>)</span>$

其中，trace表示矩阵的迹，||·||表示欧几里德范数。I是M×N的单位矩阵。令δ^*＝argminMSE(δ)，$\widetilde{\mathrm{\&delta;}}=\arg \min \mathrm{SGCV}\left(\mathrm{\&delta;}\right),$M.Jansen证明了

是渐进最优阈值。Among them, trace represents the trace of the matrix, and ||·|| represents the Euclidean norm. I is an M×N identity matrix. Let δ^* = argminMSE(δ),$\widetilde{\mathrm{\&delta;}}=\arg \min \mathrm{SGCV}\left(\mathrm{\&delta;}\right),$ M. Jansen proved

is the asymptotically optimal threshold.

(3)非线性增强算子(3) Nonlinear enhancement operator

1994年，A.Laine曾给出了基于DSWT的非线性增强算子，来增强图像的局部对比度。为了方便起见，在每个尺度上分别定义每个高频子带图像的变换函数：In 1994, A.Laine gave a nonlinear enhancement operator based on DSWT to enhance the local contrast of the image. For convenience, the transformation function of each high-frequency subband image is defined separately at each scale:

g[i，j]＝MAG{f[i，j]}(4.13)g[i,j]=MAG{f[i,j]} (4.13)

其中，g[i，j]是增强的子带，f[i，j]是原始的子带图像，MAG是非线性增强算子。where g[i,j] is the enhanced subband, f[i,j] is the original subband image, and MAG is the non-linear enhancement operator.

令f_s^r[i，j]是s分解尺度上第r个高频子带系数，其中s＝1，2，…，L；r＝1，2，3.maxf_s^r是所有像素f_s^r[i，j]中的最大灰度值。f_s^r[i，j]可以从[-max f_s^r，max f_s^r]映射到[-1，1]。Let_fsr [i, j]^be the rth high-frequency subband coefficient on the decomposition scale of s, where s = 1^, 2, ..., L;_r = 1, 2, 3. maxfsr is all pixels_fs The maximum gray value in^r [i,j]. f_s^r [i, j] can be mapped from [-max f_s^r , max f_s^r ] to [-1, 1].

因此，a、b和c的范围可以分别来设定。对比增强方法可以描述如下：Therefore, the ranges of a, b, and c can be set separately. The contrast enhancement method can be described as follows:

${\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>=</span>=</span>\left\{\begin{array}{cc}{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>,</span>,</span>& <span><span>|</span>|</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>|</span>|</span><span><span><</span><</span>{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}\\ \mathrm{<span><span>a</span>a</span>}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>\mathrm{<span><span>max</span>max</span>}{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>\{</span>\{</span>\mathrm{<span><span>sigm</span>sigm</span>}<span><span>[</span>[</span>\mathrm{<span><span>c</span>c</span>}<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>-</span>-</span>\mathrm{<span><span>b</span>b</span>}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>-</span>-</span>\mathrm{<span><span>sigm</span>sigm</span>}<span><span>[</span>[</span><span><span>-</span>-</span>\mathrm{<span><span>c</span>c</span>}<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>\}</span>\}</span><span><span>,</span>,</span>& <span><span>|</span>|</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>|</span>|</span><span><span>\&GreaterEqual;</span>\&Greater\; Equal;</span>{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}\end{array}\right.<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.14</span>4.14</span>}<span><span>)</span>)</span>$

其中，in,

${\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>=</span>=</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}<span><span>[</span>[</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>]</span>]</span><span><span>/</span>/</span>\mathrm{<span><span>max</span>max</span>}{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}^{\mathrm{<span><span>r</span>r</span>}}$

最后进行小波反变换，即得到预处理后的图像。Finally, inverse wavelet transform is performed to obtain the preprocessed image.

本系统在充分分析研究红外弱小目标的特征与背景模型基础上，采用离散平稳小波变换(DSWT)和非线性增强算子的算法对红外弱小目标进行图像增强的预处理。实验结果表明该算法不仅对弱小目标的背景抑制、目标增强有较好的效果，对大目标的噪声、背景抑制同样有较好的效果。On the basis of fully analyzing and researching the characteristics and background model of small infrared targets, this system uses the algorithm of discrete stationary wavelet transform (DSWT) and nonlinear enhancement operator to preprocess the image enhancement of small infrared targets. Experimental results show that the algorithm not only has a good effect on the background suppression and target enhancement of weak and small targets, but also has a good effect on the noise and background suppression of large targets.

2)基于二项分布判断准则的目标自适应门限分割2) Target adaptive threshold segmentation based on binomial distribution judgment criterion

基于弱小目标的特点(低SNR、复杂背景)，对它的检测依靠单帧是不可能达到的，必须依靠图像序列。在目前所做的弱小目标检测中，给出的检测识别概率一般大于等于98％，虚警概率小于等于10^-6，若这两个参数体现在检测中，就是用它们选取噪声门限。一方面，若按照虚警率小于等于10^-6选取噪声门限，则门限很高，很多目标将会丢失；另一方面，若按照检测识别概率大于等于98％选取噪声门限，则门限的选取应很低，以保证取出所有的目标点，这样会导致很大的虚警率。在这种低信噪比条件下的弱小目标检测，是无法单帧实现的，必须利用多帧图像的相关信息，将目标的运动特征和运动轨迹的连续性、一致性结合起来进行考虑。从总的检测概率与虚警概率计算出单帧的检测概率和虚警概率，从而选取合理的噪声门限为要解决的关键问题。Based on the characteristics of weak and small targets (low SNR, complex background), it is impossible to rely on a single frame to detect it, and must rely on image sequences. In the weak target detection done so far, the given detection and recognition probability is generally greater than or equal to 98%, and the false alarm probability is less than or equal to 10^-6 . If these two parameters are reflected in the detection, they are used to select the noise threshold. On the one hand, if the noise threshold is selected according to the false alarm rate being less than or equal to 10^-6 , the threshold is very high, and many targets will be lost; on the other hand, if the noise threshold is selected according to the detection and recognition probability being greater than or equal to 98%, the selection of the threshold should be It is very low to ensure that all target points are taken out, which will lead to a large false alarm rate. Weak target detection under such low signal-to-noise ratio conditions cannot be realized in a single frame, and the relevant information of multiple frames of images must be used to consider the motion characteristics of the target and the continuity and consistency of the motion trajectory. The detection probability and false alarm probability of a single frame are calculated from the total detection probability and false alarm probability, so that a reasonable noise threshold is selected as the key problem to be solved.

以概率论为基础，我们在整个图像检测中，根据单帧检测概率、单帧虚警概率与总检测概率和总虚警概率的关系，解决序列图像检测中相关帧数和门限的确定问题，为低虚警率、高检测率提供了理论保证。Based on probability theory, we solve the problem of determining the number of relevant frames and the threshold in sequence image detection according to the relationship between single frame detection probability, single frame false alarm probability and total detection probability and total false alarm probability in the whole image detection, It provides a theoretical guarantee for low false alarm rate and high detection rate.

将每帧图像中的目标检测看作是独立的重复实验，根据概率论中的原理，检测概率应该服从二项分布，据此建立数学模型，假定预处理后图像噪声为高斯分布的白噪声，根据统计理论，图像进行单帧门限检测时[推导过程参见发表文章]：The target detection in each frame image is regarded as an independent repeated experiment. According to the principle of probability theory, the detection probability should obey the binomial distribution. Based on this, a mathematical model is established, assuming that the image noise after preprocessing is white noise of Gaussian distribution. According to statistical theory, when an image is subjected to single-frame threshold detection [see published articles for the derivation process]:

${\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>=</span>=</span>{<span><span>\&Integral;</span>\&Integral;</span>}_{\mathrm{<span><span>v</span>v</span>}}^{<span><span>+</span>+</span><span><span>\&infin;</span>\&infin;</span>}\mathrm{<span><span>p</span>p</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>)</span>)</span>\mathrm{<span><span>dx</span>dx</span>}<span><span>=</span>=</span>{<span><span>\&Integral;</span>\&Integral;</span>}_{\mathrm{<span><span>v</span>v</span>}}^{<span><span>+</span>+</span><span><span>\&infin;</span>\&infin;</span>}\frac{\mathrm{<span><span>1</span>1</span>}}{\sqrt{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}}\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}\mathrm{<span><span>exp</span>exp</span>}<span><span>(</span>(</span><span><span>-</span>-</span>\frac{{<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&sigma;S</span>\&sigma;S</span>}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>)</span>)</span>\mathrm{<span><span>dx</span>dx</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>v</span>v</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&sigma;S</span>\&sigma;S</span>}}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}<span><span>)</span>)</span>$

$<span><span>=</span>=</span>\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>+</span>+</span>\mathrm{<span><span>\&sigma;S</span>\&sigma;S</span>}<span><span>-</span>-</span>\mathrm{<span><span>v</span>v</span>}}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.15</span>4.15</span>}<span><span>)</span>)</span>$

${\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>f</span>f</span>}}<span><span>=</span>=</span>{<span><span>\&Integral;</span>\&Integral;</span>}_{\mathrm{<span><span>v</span>v</span>}}^{<span><span>+</span>+</span><span><span>\&infin;</span>\&infin;</span>}\frac{\mathrm{<span><span>1</span>1</span>}}{\sqrt{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}}\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}\mathrm{<span><span>exp</span>exp</span>}<span><span>(</span>(</span><span><span>-</span>-</span>\frac{{<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>)</span>)</span>\mathrm{<span><span>dx</span>dx</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>v</span>v</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>-</span>-</span>\mathrm{<span><span>v</span>v</span>}}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}<span><span>)</span>)</span>$

$\frac{\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>+</span>+</span>\mathrm{<span><span>\&sigma;S</span>\&sigma;S</span>}<span><span>-</span>-</span>\mathrm{<span><span>v</span>v</span>}}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.16</span>4.16</span>}<span><span>)</span>)</span>$

其中ν＝μ+σS-σΦ^-1(p_d)或ν＝μ-σΦ^-1(p_f)where ν=μ+σS-σΦ^-1 (p_d ) or ν=μ-σΦ^-1 (p_f )

可推出单帧检测概率和单帧虚警概率的关系：The relationship between single frame detection probability and single frame false alarm probability can be deduced:

Φ^-1(P_f)-Φ^-1(P_d)＝S    (4.17)Φ^-1 (P_f )-Φ^-1 (P_d )＝S (4.17)

式中：ν——检测门限，σ²——噪声均方差In the formula: ν——detection threshold, σ² ——noise mean square error

      μ——为第K帧背景对消后的噪声均值μ——the average value of noise after background cancellation of the Kth frame

      S——信噪比SNR定义为信号的幅值与噪声的均方差之比S——Signal-to-noise ratio SNR is defined as the ratio of the amplitude of the signal to the mean square error of the noise

总检测概率与单帧检测概率的关系：The relationship between the total detection probability and the single frame detection probability:

${\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>D</span>D.</span>}}<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>\&GreaterEqual;</span>\&Greater\; Equal;</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>D</span>D.</span>}}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>i</span>i</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>n</span>no</span>}}^{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>d</span>d</span>}}^{\mathrm{<span><span>k</span>k</span>}}{<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>n</span>no</span>}<span><span>-</span>-</span>\mathrm{<span><span>k</span>k</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.18</span>4.18</span>}<span><span>)</span>)</span>$

在上述实验中，假定单帧检测概率是P_d＝0.90，要求总的检测概率P_D＝0.98。那么当在n幅图像中，目标出现了k次时，可以达到要求。例如，当每次采集16帧图像做判断时，如果目标出现11次，则总检测概率能够达到要求。In the above experiments, it is assumed that the detection probability of a single frame is P_d =0.90, and the total detection probability P_D =0.98 is required. Then when the target appears k times in n images, the requirement can be met. For example, when 16 frames of images are collected each time for judgment, if the target appears 11 times, the total detection probability can meet the requirements.

因此可由单帧检测概率、单帧虚警概率与总检测概率和总虚警概率的关系，解决序列图像检测中相关帧数和门限的确定问题。Therefore, the problem of determining the number of relevant frames and the threshold in sequence image detection can be solved by the relationship between single frame detection probability, single frame false alarm probability, total detection probability and total false alarm probability.

3)红外与可见光数据进行多模融合3) Multi-mode fusion of infrared and visible light data

基于红外与可见光传感器融合的目标检测，可以提高目标的检测概率、降低虚警概率。Target detection based on the fusion of infrared and visible light sensors can improve the detection probability of targets and reduce the probability of false alarms.

对可见光和红外图像融合需要进行图像匹配，首先对不同传感器的目标进行特征提取，然后通过目标匹配结果可以得出可见光和红外图像之间的变换关系，如平移、旋转、缩放等。具体使用的配准方法是基于最小二乘的控制点匹配，相位相关法，模板匹配法等。The fusion of visible light and infrared images requires image matching. First, feature extraction is performed on the targets of different sensors, and then the transformation relationship between visible light and infrared images can be obtained through the target matching results, such as translation, rotation, scaling, etc. The specific registration methods used are control point matching based on least squares, phase correlation method, template matching method and so on.

在图像配准后，根据最近邻原则，同一目标在配准后图像中的坐标应该是重合、或者是非常接近的，通过临近性或相似性测度能够把两种图像中的目标特征对应起来。After image registration, according to the nearest neighbor principle, the coordinates of the same target in the registered image should be coincident or very close, and the target features in the two images can be matched by the proximity or similarity measure.

我们将多传感器概率数据互联滤波器用于可见光和红外图像的融合，来降低虚警率。概率数据互联的基本思想是：只要是有效检测信息，都可能源于目标，只是每个信息源于目标的概率有所不同。这种方法利用了跟踪窗内的所有信息以获得可能的后验信息，并根据大量的相关计算给出各概率加权系数及其加权和，然后用它更新目标状态。本研究采用此方法进行目标特征融合。We use the multi-sensor probabilistic data interconnection filter for the fusion of visible light and infrared images to reduce the false alarm rate. The basic idea of probabilistic data interconnection is: as long as it is effective detection information, it may come from the target, but the probability that each information comes from the target is different. This method uses all the information in the tracking window to obtain possible posterior information, and gives each probability weighting coefficient and its weighted sum according to a large number of correlation calculations, and then uses it to update the target state. This study adopts this method for target feature fusion.

经过目标融合处理后，丰富了目标的特征信息，提高了目标检测概率，降低了虚警率。After target fusion processing, the feature information of the target is enriched, the target detection probability is improved, and the false alarm rate is reduced.

红外与可见光数据的融合采用的处理步骤如下：The processing steps adopted for the fusion of infrared and visible light data are as follows:

a)对可见光和红外图像分别进行目标特征提取；a) Target feature extraction is performed on visible light and infrared images respectively;

b)对提取的特征进行不同传感器的特征匹配，确定可见光和红外图像之间的变换关系；b) Perform feature matching of different sensors on the extracted features, and determine the transformation relationship between visible light and infrared images;

对匹配后图像中的目标特征，使用概率互联滤波器处理获得融合数据，从而提高目标检测识别的置信度，并剔除虚假目标。For the target features in the matched image, the probabilistic interconnection filter is used to process the fused data, so as to improve the confidence of target detection and recognition, and eliminate false targets.

4)目标运动预测与估计4) Target motion prediction and estimation

目标跟踪过程中的多目标、交叉、抖动、记忆跟踪等都涉及目标的运动估计预测问题弱小目标的运动轨迹，帧与帧之间存在抖动，并不具有方向一致性，而其它目标如小鸟的面积比目标稍大，它的运动轨迹比弱小目标更具有方向性。这是由于成像系统、空间光干扰、空气振动等原因造成了图像的抖动，抖动的同时还使目标的几何中心在相邻像素之间发生变化，如果数据不经过处理，连续帧之间的目标位置由于抖动的存在，并不按方向的一致性变化，这就给用方向性进行约束(如常规的滤波器预测)的目标精确跟踪带来误差。In the process of target tracking, multi-target, intersection, jitter, memory tracking, etc. all involve the motion estimation and prediction of the target. The trajectory of the weak target, there is jitter between frames, and there is no direction consistency, while other targets such as birds The area is slightly larger than the target, and its trajectory is more directional than the weak target. This is due to the image shaking caused by the imaging system, spatial light interference, air vibration, etc. The shaking also causes the geometric center of the target to change between adjacent pixels. If the data is not processed, the target between consecutive frames Due to the existence of jitter, the position does not change according to the consistency of the direction, which brings errors to the precise tracking of the target constrained by the directionality (such as conventional filter prediction).

怎样消除抖动现象产生的影响是实际跟踪要解决的一个重要问题。在项目中解决这类方法采用了两种方法：How to eliminate the influence of jitter phenomenon is an important problem to be solved in actual tracking. There are two ways to solve this kind of method in the project:

●基于Kalman滤波器思想改进的曲线拟合的运动预测。解决没有规律的抖动、目标交叠、记忆跟踪等情况下的运动预测问题。●Motion prediction based on improved curve fitting based on Kalman filter idea. Solve the problem of motion prediction in the case of irregular jitter, overlapping targets, memory tracking, etc.

●在识别为目标后，将粗跟踪转为精确跟踪，将形心位置转换为质心位置，减小跟踪时的抖动现象，提高跟踪精度。●After the target is identified, the rough tracking is converted to precise tracking, and the centroid position is converted to the centroid position to reduce the jitter phenomenon during tracking and improve tracking accuracy.

由于Kalman滤波器不能即时反映出目标的运动变化，所以当目标机动性强时，Kalman跟踪的误差会较大。我们从Kalman动力学方程出发，定义了机动性参数，同时对拟合方式进行了改进，增强其跟踪预测的性能。Since the Kalman filter cannot reflect the movement changes of the target in real time, the Kalman tracking error will be larger when the target is highly maneuverable. Starting from the Kalman kinetic equation, we defined the maneuverability parameters, and improved the fitting method to enhance its performance of tracking prediction.

图7所示为基于轨迹预测的目标检测、识别跟踪流程图。目标运动预测与估计的过程为图像经过预处理，进行目标的特征提取，获得潜在的目标，通过二项分布的判断准则来判断是否是新目标，通过kalman理论建立轨迹方程，若轨迹方程已建立，则需要对轨迹方程进行更新，同时预测目标在下一帧的轨迹，得到预测位置，并用拟合修正Kalman跟踪滤波器修正预测位置。Figure 7 shows the flow chart of target detection, recognition and tracking based on trajectory prediction. The process of target motion prediction and estimation is that the image is preprocessed, the feature extraction of the target is carried out, and the potential target is obtained, and whether it is a new target is judged by the judgment criterion of the binomial distribution, and the trajectory equation is established by the Kalman theory. If the trajectory equation has been established , it is necessary to update the trajectory equation, and at the same time predict the trajectory of the target in the next frame to obtain the predicted position, and use the fitting correction Kalman tracking filter to correct the predicted position.

以下为基于Kalman理论改进的曲线拟合预测目标运行轨迹研究的几点讨论和改进：The following are some discussions and improvements based on the improved Kalman theory of curve fitting to predict the target trajectory research:

1)改进的最小二乘直线拟合方法1) Improved least squares straight line fitting method

经典最小二乘拟合中的准则函数是各数据点沿纵坐标y到拟合曲线的距离的平方和。假设数据点(x_i，y_i)，其中y＝f(x)。做最小二乘拟合得到的曲线是基于如下准则：The criterion function in classical least squares fitting is the sum of the squares of the distances of each data point along the ordinate y to the fitting curve. Assume a data point (x_i , y_i ), where y=f(x). The curve obtained by least squares fitting is based on the following criteria:

$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{{\mathrm{\&delta;}}^2}_i=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\left(x_i\right){[s^{*}\left(x\right)-f\left(x_i\right)]}^2=\underset{s\left(x\right)\&Element;\mathrm{\&Phi;}}{\min }\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\left(x_i\right){[s\left(x\right)-f\left(x_i\right)]}^2,$但用距离的平方和$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_i^2=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\left(x_i\right){\left(\frac{|y-a_{i}x-b_i|}{\sqrt{1+a_i^2}}\right)}^2=\min$做准则函数更合适，后者是力学中的最小惯性矩。$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{{\mathrm{\&delta;}}^2}_i=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\left(x_i\right){[{\mathrm{the\; s}}^{*}\left(x\right)-f\left(x_i\right)]}^2=\underset{\mathrm{the\; s}\left(x\right)\&Element;\mathrm{\&Phi;}}{\min }\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\left(x_i\right){[\mathrm{the\; s}\left(x\right)-f\left(x_i\right)]}^2,$ But using the sum of the squares of the distances$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_i^2=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\left(x_i\right){\left(\frac{|\mathrm{the\; y}-a_{i}x-b_i|}{\sqrt{1+a_i^2}}\right)}^2=\min$ It is more appropriate to be a criterion function, which is the minimum moment of inertia in mechanics.

2)截取轨迹点做拟合2) Intercept trajectory points for fitting

在应用中，只考虑临近几个或几十个轨迹点，如果取权系数ω(x_i)≡1，相当于用矩形窗截取轨迹获得近期的轨迹点。矩形窗不能反映重要性的变化，并且不能平滑截断；指数函数可以反映数据点重要性随时间的变化，而且指数函数是光滑的，所以采用指数窗函数来截取数据。In the application, only a few or dozens of nearby trajectory points are considered. If the weight coefficient ω(xi₎ ≡1 is used, it is equivalent to intercepting the trajectory with a rectangular window to obtain the recent trajectory points. The rectangular window cannot reflect the change of importance, and cannot be truncated smoothly; the exponential function can reflect the change of the importance of data points over time, and the exponential function is smooth, so the exponential window function is used to intercept the data.

考虑到目标运动的连续性和一致性，每帧即时速度的大小、方向和整体运动趋势相比较不应该有大的跳变，当这种变动较大时，其中应该包含了较大的误差，应该给这个数据点较小的权值抑制这种误差。Considering the continuity and consistency of the target motion, the size and direction of the instant speed of each frame should not have a large jump compared with the overall motion trend. When the change is large, it should contain a large error. This data point should be given a smaller weight to suppress this error.

根据以上准则，通过实验和理论推导，定义权系数的取值：According to the above criteria, through experiments and theoretical derivation, the value of the weight coefficient is defined:

$\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>q</span>q</span>}}^{\mathrm{<span><span>n</span>no</span>}}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>{\mathrm{<span><span>p</span>p</span>}}^{{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>i</span>i</span>}}}$

其中|q|＜1，|p|＜1，d_i为数据点到拟合直线Ax+By+C＝0的距离，$d_i=\frac{|{\mathrm{Ax}}_i+{\mathrm{By}}_i+C|}{\sqrt{A^2+B^2}};$n＝N-i，N是当前的帧数，N-M≤i＜N，M是拟合数据点的个数。q和p的值可以通过实验获得，一般取0.7～0.8之间。Where |q|<1, |p|<1, d_i is the distance from the data point to the fitting line Ax+By+C=0,$d_i=\frac{|{\mathrm{Ax}}_i+{\mathrm{By}}_i+C|}{\sqrt{A^2+{\mathrm{<figure-callout\; label="B"\; filenames="H2009101807801E00011.png,H2009101807801E00022.png"\; state="\{\{state\}\}">B</figure-callout>}}^2}};$ n=Ni, N is the current frame number, NM≤i<N, M is the number of fitting data points. The values of q and p can be obtained through experiments, generally between 0.7 and 0.8.

轨迹点个数M可以选择固定，通过调整权系数大小来控制轨迹点对拟合的作用，例如选小的衰减系数，相当于截取较短的轨迹，选择较大的衰减系数，相当于截取较长的轨迹。The number M of trajectory points can be fixed, and the effect of trajectory points on the fitting can be controlled by adjusting the weight coefficient. long track.

3)机动性系数3) Mobility coefficient

前面定义了权系数$\mathrm{\&omega;}\left(x_i\right)=q^n\&CenterDot;p^{d_i},$其中q大小的选取和截取轨迹点长度有关，并且要求机动性强时，截取轨迹短一些，机动性低时，截取轨迹长一些。The weight coefficient was defined earlier$\mathrm{\&omega;}\left(x_i\right)=q^{\mathrm{no}}\&Center\; Dot;p^{d_i},$ The selection of the size of q is related to the length of the intercepted trajectory point, and when the maneuverability is required, the intercepted trajectory is shorter, and when the maneuverability is low, the intercepted trajectory is longer.

设系统方程为：X(k+1)＝F(k)X(k)+w(k)(4.19)Let the system equation be: X(k+1)=F(k)X(k)+w(k)(4.19)

观测方程：    z(k)＝H(k)X(k)+u(k)  (4.20)Observation equation: z(k)=H(k)X(k)+u(k) (4.20)

机动系数定义为：$\mathrm{\&lambda;}=\frac{{\mathrm{\&sigma;}}_w{T}^2}{{\mathrm{\&sigma;}}_u}---\left(4.21\right)$The mobility coefficient is defined as:$\mathrm{\&lambda;}=\frac{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; label="w\; T"\; filenames="H2009101807801E00011.png,H2009101807801E00022.png"\; state="\{\{state\}\}">w</figure-callout>}}{T}^{}{}^2}{{\mathrm{\&sigma;}}_u}---\left(4.21\right)$

其中σ_u是观测噪声方差，σ_w是系统噪声方差，T是采样周期。在实际应用中σ_u和σ_w无法获得，可以用相关参量代替。因为跟踪中目标坐标有三种：预测值、实际观测值和当前估计值。预测值是指在上一帧处理过程中得到的对当前帧目标位置的预测，用

表示；观测值表示当前图像分割得到的目标位置，用z(k)表示；当前估计值是指根据当前观测值估计出的目标在空间中的实际坐标，用X(k)表示。where_σu is the observation noise variance,_σw is the system noise variance, and T is the sampling period. In practical applications,_σu and_σw cannot be obtained and can be replaced by related parameters. Because there are three kinds of target coordinates in tracking: predicted value, actual observed value and current estimated value. The prediction value refers to the prediction of the target position of the current frame obtained during the processing of the previous frame.

Represents; the observed value represents the target position obtained by the current image segmentation, represented by z(k); the current estimated value refers to the actual coordinate of the target in space estimated according to the current observed value, represented by X(k).

在Kalman滤波中$\stackrel{\&OverBar;}{X}\left(k\right)=\hat{X}\left(k\right|k);$而在拟合跟踪中，X(k)是z(k)在拟合直线上的投影。因为可以把X(k)当作目标的真实坐标，则观测值噪声可以表示为u(k)＝z(k)-X(k)，而预测值和真实值的差

体现了系统的不确定性，或者说代表了跟踪系统中不可预测的因素，所以可以认为系统噪声为$w\left(n\right)=\hat{X}(k-1)-\stackrel{\&OverBar;}{X}\left(k\right).$这样σ_u和σ_w可以用以下参量代替：In Kalman filtering$\stackrel{\&OverBar;}{x}\left(k\right)=\hat{x}\left(k\right|k);$ In the fitting tracking, X(k) is the projection of z(k) on the fitting line. Because X(k) can be regarded as the real coordinates of the target, the observed value noise can be expressed as u(k)=z(k)-X(k), and the difference between the predicted value and the real value

reflects the uncertainty of the system, or represents the unpredictable factors in the tracking system, so the system noise can be considered as$w\left(\mathrm{no}\right)=\hat{x}(k-1)-\stackrel{\&OverBar;}{x}\left(k\right).$ Thus σ_u and σ_w can be replaced by the following parameters:

${\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>u</span>u</span>}}<span><span>\&ap;</span>\&ap;</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}}\sqrt{\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>\mathrm{<span><span>z</span>z</span>}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>-</span>-</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>)</span>)</span>{<span><span>(</span>(</span>\mathrm{<span><span>z</span>z</span>}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>-</span>-</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>)</span>)</span>}^{\mathrm{<span><span>T</span>T</span>}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.22</span>4.22</span>}<span><span>)</span>)</span>$

${\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>w</span>w</span>}}<span><span>\&ap;</span>\&ap;</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}}\sqrt{\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span><span><span>-</span>-</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>)</span>)</span>{<span><span>(</span>(</span>\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span><span><span>-</span>-</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>)</span>)</span>}^{\mathrm{<span><span>T</span>T</span>}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.23</span>4.23</span>}<span><span>)</span>)</span>$

T就是红外图像采集的间隔周期，是已知参数，可以计算出机动系数λ。通过试验可以发现σ_w取值大小和目标机动性吻合，就是说σ_w越大，目标运动变化剧烈；相反，σ_w小，则目标运动变化平缓。T is the interval period of infrared image acquisition, which is a known parameter, and the maneuver coefficient λ can be calculated. Through experiments, it can be found that the value_{of σw} is consistent with the maneuverability of the target, that is to say, the larger the_σw , the sharper the change of the target movement; on the contrary, the smaller the_σw , the smoother the change of the target movement.

4)拟合后的数据关联4) Data association after fitting

如果多个跟踪链竞争一个候选目标，通常是处于多目标交叉的状态。拟采取这样处理方法：将候选目标舍弃，竞争的链各自进行记忆跟踪，直到没有竞争为止。If multiple tracking chains compete for a candidate target, it is usually in the state of multi-target intersection. It is proposed to take the following approach: the candidate target is discarded, and the competing chains perform memory tracking on their own until there is no competition.

也可以将候选目标看作是可疑新目标，对它进行跟踪，由连续性判断是否为新目标；当轨迹链找不到匹配的候选目标时，应该记忆跟踪，直到重新找回目标；如果超过一定时间仍无法找回目标，则认为跟踪目标丢失，此时数据关联的关系变得简单。The candidate target can also be regarded as a suspicious new target, track it, and judge whether it is a new target by the continuity; when the trajectory chain cannot find a matching candidate target, it should remember to track until the target is found again; if more than If the target cannot be retrieved within a certain period of time, it is considered that the tracking target is lost, and the relationship of data association becomes simple at this time.

在跟踪预测中，一阶多项式拟合即直线拟合最能反映出运动趋势。经典最小二乘的误差函数是y坐标距离曲线的距离函数，对于直线而言用点到直线距离平方作误差函数更为合适；另外在拟合中引入时间加权因子，解决时效性的问题；通过调整权系数，使拟合的迭代运算量固定，从而整个跟踪的运算量可以控制，便于系统设计和实现。In tracking prediction, the first-order polynomial fitting, that is, straight line fitting, can best reflect the motion trend. The error function of the classical least squares is the distance function of the y-coordinate distance curve. For a straight line, it is more appropriate to use the square of the point-to-line distance as the error function; in addition, a time weighting factor is introduced in the fitting to solve the problem of timeliness; through By adjusting the weight coefficients, the iterative calculation amount of fitting is fixed, so the calculation amount of the whole tracking can be controlled, which is convenient for system design and implementation.

5)不同情况下的目标特征提取5) Target feature extraction in different situations

当目标形状发生改变时，利用边缘特征归一化的形状识别寻找从电场角度引出的特征不变量达到目标精确跟踪。When the shape of the target changes, the feature invariant derived from the electric field angle is found by using the shape recognition normalized by the edge feature to achieve accurate target tracking.

当目标由远距离几个像素点变大时，由于探测器成像角度不同，同一目标的形状会发生改变，这时如何保证跟踪点不变，继续精确跟踪是关键问题。在图像目标的匹配识别中，人们希望的是要找到一个能表征目标图形特征的量，然后通过该特征量来表征两图形是否为同一目标。传统的匹配，对不规则图形的识别常用以下几种方法：傅里叶描叙子的匹配识别、基于不变矩特征方法的匹配识别及近些年来的通过神经网络学习方法的匹配识别等。傅里叶描叙子的识别方法是从频率域的角度进行匹配识别；不变矩特征方法是用矩表征一幅图像，并通过提取与统计学和力学中相似特征这一途径来进行匹配识别；神经网络学习方法是通过样本特征学习来进行识别；该申请项目的研究方法是把像素点赋予电荷点的含义，从电场这个全新角度来对不规则图形进行有效的识别，经过理论推导、研究和实验，找出一个不随形状改变而变化的特征量。以下详细介绍电场强度与电势识别形状算法算法When the target becomes larger from a few pixels at a distance, the shape of the same target will change due to the different imaging angles of the detectors. At this time, how to ensure that the tracking point remains unchanged and continue to accurately track is the key issue. In the matching and recognition of image targets, people hope to find a quantity that can characterize the characteristics of the target figure, and then use this feature quantity to characterize whether the two figures are the same target. In traditional matching, the following methods are commonly used for the recognition of irregular graphics: matching recognition of Fourier descriptors, matching recognition based on invariant moment feature methods, and matching recognition through neural network learning methods in recent years. The recognition method of the Fourier descriptor is to perform matching and recognition from the perspective of the frequency domain; the invariant moment feature method is to use moments to characterize an image, and to perform matching and recognition by extracting similar features in statistics and mechanics ; The neural network learning method is to identify through sample feature learning; the research method of this application is to assign the meaning of the charge point to the pixel point, and effectively identify the irregular figure from the new perspective of the electric field. After theoretical derivation and research And experiment to find a feature quantity that does not change with the shape change. The following is a detailed introduction to the electric field strength and potential recognition shape algorithm algorithm

在电学中，电荷均匀分布的任意带电体在自身周围空间中所产生静电场的分布是唯一的，而且该带电体与它在三维空间所产生的静电场是一一对应的。静电场只与该导体的大小、电荷密度大小及形状有关。以上概念得到一个结论：形状不同的均匀带电体在三维空间产生的电场分布是不相同的。In electricity, the distribution of electrostatic field generated by any charged object with uniform charge distribution in its surrounding space is unique, and the charged object corresponds to the electrostatic field generated by it in three-dimensional space. The electrostatic field is only related to the size, charge density and shape of the conductor. The above concept leads to a conclusion: the electric field distribution generated by uniform charged bodies with different shapes in three-dimensional space is different.

利用这个结论，推导出识别形状的特征不变量。在推导方法时，不过多考虑带电体的表面电荷密度的分布，着重考虑带电体的大小和形状对电场分布产生的影响。Using this conclusion, feature invariants for recognizing shapes are derived. When deriving the method, the distribution of the surface charge density of the charged body is not considered too much, and the influence of the size and shape of the charged body on the electric field distribution is emphasized.

由于图形的形状信息主要在边缘，因此通过图像处理的边缘检测方法，二值化后能够得到图形的边缘信息，如果把这些边缘像素点看作带电体，那么就可以计算出该图形在三维空间的电势与电场强度分布，也就可以将电场和电势的分布作为判别两个图形是否相同或相似的依据。Since the shape information of the graph is mainly at the edge, the edge information of the graph can be obtained after binarization through the edge detection method of image processing. The distribution of electric potential and electric field intensity can be used as the basis for judging whether two figures are the same or similar.

如图8所示，本研究采用多边形逼近的方法，以“直”代“曲”，来将图形边缘用近似多边形表示。As shown in Figure 8, this study adopts the method of polygonal approximation, replacing "curved" with "straight" to represent the edges of graphics with approximate polygons.

由于电势是个标量，因此各条边在空间任意一点产生的电势是可以直接代数相加的。电场强度虽然是矢量，但投影到z方向上，各条边的电场强度也可以代数相加。这样通过多边形逼近后，Since the electric potential is a scalar quantity, the electric potential generated by each edge at any point in space can be directly algebraically added. Although the electric field strength is a vector, but projected in the z direction, the electric field strength of each side can also be added algebraically. After this approximation by polygons,

任意图形的边缘是由线段组成，那么图形边缘对空间任意一点(以下称这种点为观测点)所产生的电势与电场强度大小公式为The edge of any graph is composed of line segments, then the electric potential and electric field intensity generated by the edge of the graph to any point in space (hereinafter referred to as the observation point) are as follows:

电势大小公式：Potential size formula:

$\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>|</span>|</span>\mathrm{<span><span>ln</span>ln</span>}<span><span>|</span>|</span>\frac{\mathrm{<span><span>tan</span>the\; tan</span>}\frac{{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}}{\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>tan</span>the\; tan</span>}\frac{{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>2</span>2</span>}}}<span><span>|</span>|</span><span><span>|</span>|</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.24</span>4.24</span>}<span><span>)</span>)</span>$

电场强度大小公式：The electric field strength formula:

$\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{<span><span>|</span>|</span>{\mathrm{<span><span>PO</span><figure-callout\; label="PO"\; filenames="H2009101807801E00022.png"\; state="\{\{state\}\}">PO</figure-callout></span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>|</span>|</span>}{{<span><span>|</span>|</span>\mathrm{<span><span>OP</span>OP</span>}<span><span>|</span>|</span>}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>|</span>|</span><span><span>(</span>(</span>\mathrm{<span><span>cos</span>cos</span>}{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>cos</span>cos</span>}\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span><span><span>|</span>|</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.25</span>4.25</span>}<span><span>)</span>)</span>$

其中θ_i，1，θ_i，2分别表示组成图形边缘的第i条线段的θ₁与θ₂。Among them, θ_i,1 and θ_i,2 respectively denote θ₁ and θ₂ of the ith line segment forming the edge of the graph.

观测点的归一化如下：The normalization of observation points is as follows:

各个图形的观测点选取要求“一致”，其目的是由于要保证相同形状图形在各自对应的观测点所产生的电势与电场强度相同，所以先要对图形的观测点进行“一致”化，称之为观测点的归一化。The selection of observation points of each graph requires "consistency", the purpose is to ensure that the electric potential and electric field intensity generated by the same shape graph at their corresponding observation points are the same, so the observation points of the graph must be "consistent", called It is the normalization of observation points.

为寻找归一化观测点，在本研究中对原来公式做了一定的修改，对应的归一化观测点应满足：从各图形的中心到各个观测点做射线，各条射线应与图形平面相垂直或在图形平面上的投影与以各需识别图形的主方向的偏角一致，且射线与图形平面的夹角相同，则此时对应观测点到各图形中心的距离之比等于各图形面积开方之比[证明见所发表文章]。In order to find the normalized observation points, the original formula has been modified in this study, and the corresponding normalized observation points should meet the following requirements: a ray is drawn from the center of each graph to each observation point, and each ray should be consistent with the graph plane The projections perpendicular to or on the graphics plane are consistent with the declination angles of the main directions of the graphics to be identified, and the angle between the ray and the graphics plane is the same, then the ratio of the distance from the corresponding observation point to the center of each graphics is equal to that of each graphics Ratio of square root of area [see published article for proof].

这样如图9所示，公式(4.24)(4.25)改进为如下In this way, as shown in Figure 9, the formula (4.24) (4.25) is improved as follows

电势大小变换公式：The electric potential size transformation formula:

$\mathrm{<span><span>U</span>u</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>|</span>|</span>\mathrm{<span><span>ln</span>ln</span>}<span><span>|</span>|</span>\frac{\mathrm{<span><span>tan</span>the\; tan</span>}\frac{{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}}{\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>tan</span>the\; tan</span>}\frac{{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>2</span>2</span>}}}<span><span>|</span>|</span><span><span>|</span>|</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.26</span>4.26</span>}<span><span>)</span>)</span>$

电场强度大小变换公式：The electric field strength magnitude conversion formula:

$\mathrm{<span><span>E</span>E.</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>z</span>z</span>}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}}\sqrt{\mathrm{<span><span>S</span>S</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{<span><span>|</span>|</span>{\mathrm{<span><span>PO</span><figure-callout\; label="PO"\; filenames="H2009101807801E00022.png"\; state="\{\{state\}\}">PO</figure-callout></span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>|</span>|</span>}{{<span><span>|</span>|</span>\mathrm{<span><span>OP</span>OP</span>}<span><span>|</span>|</span>}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>|</span>|</span><span><span>(</span>(</span>\mathrm{<span><span>cos</span>cos</span>}{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>\mathrm{<span><span>cos</span>cos</span>}{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span><span><span>|</span>|</span>\sqrt{\mathrm{<span><span>S</span>S</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4.27</span>4.27</span>}<span><span>)</span>)</span>$

其中θ_i，1，θ_i，2分别表示组成图形边缘的第i条线段的(如图8所示)θ₁与θ₂。Among them, θ_i,1 and θ_i,2 denote respectively θ₁ and θ₂ of the i-th line segment (as shown in Fig. 8 ) forming the edge of the graph.

虽然修改了以上公式，但电场强度仍然保留了需要的物理意义。这样通过对应观测点的归一化，就解决了大小不同形状相同图形的可比性问题。Although the above formula is modified, the electric field strength still retains the required physical meaning. In this way, through the normalization of the corresponding observation points, the comparability problem of the same graphics with different sizes and shapes is solved.

采用本发明中的技术和装置，整个系统对复杂背景下的弱小目标的检测识别与精确跟踪可达到如下的技术指标：By adopting the technology and device of the present invention, the whole system can achieve the following technical indicators for the detection, recognition and precise tracking of weak and small targets in complex backgrounds:

1)输入信号：红外、电视视频信号(GPS信号、激光测距仪信号输入接口及处理能力)；1) Input signal: infrared, TV video signal (GPS signal, laser rangefinder signal input interface and processing capacity);

2)输出误差信号：目标相对于视场中心的角位置偏移值；2) Output error signal: the angular position offset value of the target relative to the center of the field of view;

3)最小跟踪对比度：≤3％；3) Minimum tracking contrast: ≤3%;

4)捕获能力：能同时自动捕获和跟踪视场内4个目标；4) Acquisition capability: it can automatically capture and track 4 targets in the field of view at the same time;

5)记忆跟踪：当目标暂时被遮挡，跟踪器应能自动转入记忆跟踪状态，输出保持目标丢失时刻的值不变；目标再出现时，能重新自动捕获；5) Memory tracking: When the target is temporarily blocked, the tracker should be able to automatically switch to the memory tracking state, and the output value remains unchanged at the time when the target is lost; when the target reappears, it can be automatically captured again;

6)误差输出延迟：≤20ms；接口：并口、RS232、PCI6) Error output delay: ≤20ms; interface: parallel port, RS232, PCI

7)ATR(自动检测系统参数)：全屏(768×576)实时检测，误差信息可按场、帧输出。7) ATR (automatic detection system parameters): full-screen (768×576) real-time detection, error information can be output by field and frame.

目标特性：天空、地面目标。Target characteristics: sky, ground targets.

8)环境条件：工作温度：-35℃～+55℃，相对湿度：95％。8) Environmental conditions: Working temperature: -35℃～+55℃, relative humidity: 95%.

Claims (2)

1. A high-precision tracking method for a small target under a complex background and a low signal-to-noise ratio is characterized by comprising the following steps: the method comprises the following steps:

(1) image preprocessing under the conditions of complex background and low signal-to-noise ratio: the method comprises the steps of denoising an image by respectively selecting different thresholds on each scale of wavelet transformation by adopting a small and weak target image enhancement algorithm based on improved discrete stationary wavelet transformation and a nonlinear enhancement operator;

(2) and target self-adaptive threshold segmentation based on the binomial distribution judgment criterion: a model based on a probability theory two-item distribution criterion is established for the relation among the single-frame detection probability, the single-frame false alarm probability, the total detection probability and the total false alarm probability, so that the problem of determining the related frame number and the threshold in the sequence image detection is solved;

(3) and performing multimode fusion on the infrared and visible light data: matching the visible images and the infrared images, and then adopting a multi-sensor probability data interconnection filter to correspond target features in the two images to obtain fusion data, so that the confidence of target detection and identification is improved, and false targets are removed;

(4) target motion prediction and estimation: the motion prediction is carried out by adopting a curve fitting algorithm improved based on the Kalman filter thought, so that the motion prediction problem under the conditions of irregular jitter, target overlapping and memory tracking is solved;

(5) extracting target features when the target shape is changed: when the shape of the target changes, the method of searching for the feature invariant led out from the angle of the electric field by using the shape recognition of edge feature normalization is adopted to achieve the purpose of accurately tracking the target.

2. The method for tracking the weak and small target with the complex background and the low signal-to-noise ratio at high precision as claimed in claim 1, wherein the method comprises the following steps: in the step (5), the target feature extraction method when the target shape changes is to give the meaning of the charge point to the pixel point and find out a feature quantity which does not change along with the change of the shape from the angle of the electric field to effectively identify the irregular figure.

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