技术领域technical field
本发明属于图像处理领域，更为具体的讲，涉及一种自适应非局部模糊C均值聚类合成孔径雷达(SAR)图像分割算法。The invention belongs to the field of image processing, and more specifically relates to an adaptive non-local fuzzy C-means clustering synthetic aperture radar (SAR) image segmentation algorithm.
背景技术Background technique
随着遥感技术的发展，SAR成像技术已进入高分辨率时代。与中低分辨率SAR相比，高分辨率技术增强了其传感器获取地物信息的能力，能够提供更为复杂精细的场景和丰富的散射信息。但与此同时，有关SAR图像的解析与自主识别领域却进展缓慢。因此，如何高效分析处理大量SAR图像数据，对其中包含的信息进行有效提取，已经成为当前SAR技术研究的一大重心。With the development of remote sensing technology, SAR imaging technology has entered the era of high resolution. Compared with medium and low-resolution SAR, high-resolution technology enhances the ability of its sensors to obtain ground object information, and can provide more complex and detailed scenes and rich scattering information. But at the same time, progress in the field of analysis and autonomous recognition of SAR images has been slow. Therefore, how to efficiently analyze and process a large amount of SAR image data and effectively extract the information contained in it has become a major focus of current SAR technology research.
SAR图像分割作为图像预处理阶段的关键步骤，本质是将整幅图像划分为多个内部具有相似特性的图像块，块与块之间边界区分明显，互不相交，同时所有图像块的并集可重构原图像。图像分割的目的在于区分出人们关注的特定区域和不感兴趣区域，因此之后的解析研究可只在切割出的感兴趣区域进行。要获取这样可被明显区分且内部特征一致的像素簇，常见的算法有以下三大类：SAR image segmentation is a key step in the image preprocessing stage. The essence is to divide the entire image into multiple image blocks with similar internal characteristics. The boundaries between blocks are clearly distinguished and do not intersect each other. At the same time, the union of all image blocks The original image can be reconstructed. The purpose of image segmentation is to distinguish the specific area that people pay attention to and the area that is not of interest, so the subsequent analytical research can only be carried out in the cut out area of interest. To obtain such pixel clusters that can be clearly distinguished and have consistent internal features, common algorithms fall into the following three categories:
(1)基于阈值的图像分割算法。此方法常常用于双分割区域，且目标区域与背景不相关区域在某项特征上有明显区分的情况。通过划定阈值，将每一个像素点进行归类，提取出目标区域。当然此法也可拓展到多分割区域。阈值分割法最明显的缺陷是其受噪声干扰较大，尽管在处理过程中已考虑到噪声影响并做以抑制处理，但在噪声严重区的分割精度依然不理想。(1) Image segmentation algorithm based on threshold. This method is often used in double-segmented areas, and the target area is clearly distinguished from the background unrelated area in a certain feature. By delineating the threshold, each pixel is classified and the target area is extracted. Of course, this method can also be extended to multi-segmented regions. The most obvious defect of the threshold segmentation method is that it is greatly disturbed by noise. Although the influence of noise has been considered and suppressed during the processing, the segmentation accuracy in the severe noise area is still not ideal.
(2)基于边缘检测的图像分割算法。图像分割的最终目的是使图像形成数个互不干扰的子区域，所以准确定位边缘以及各子域的边界相当重要。其基本思想是检测图像中的特征点或边缘点，根据无数点的确定来划分不同子区域的边界。基于边缘检测法进行图像分割的关键在于识别出完整且准确的子区域轮廓，但这只是理想情况，大多数边缘检测的结果中各个区域的轮廓都是一条断断续续未全连接的“虚线”，故一般还需要加入边缘补全以及剔除伪边缘的步骤。此外，该类算法在处理细节较多，变化比较复杂的图像时难以检测出可靠的边缘，降低了图像分割的准确率。(2) Image segmentation algorithm based on edge detection. The ultimate goal of image segmentation is to make the image form several sub-regions that do not interfere with each other, so it is very important to accurately locate the edges and the boundaries of each sub-region. Its basic idea is to detect the feature points or edge points in the image, and divide the boundaries of different sub-regions according to the determination of countless points. The key to image segmentation based on the edge detection method is to identify complete and accurate sub-region contours, but this is only an ideal situation. The contours of each region in most edge detection results are intermittent "dotted lines" that are not fully connected, so Generally, it is also necessary to add the steps of edge completion and removal of false edges. In addition, it is difficult for this type of algorithm to detect reliable edges when processing images with more details and complex changes, which reduces the accuracy of image segmentation.
(3)基于区域的图像分割算法。该类方法主要是通过区域内部特征的一致性来完成分割。大致可分为区域生长合并法、随机场法以及聚类法。其中基于聚类的分割算法则通过提取出不同像素间的相关性，并由迭代使特征相关性达到最大完成分割，在图像分割领域中大放异彩。将模糊划分知识与聚类算法相结合，采用隶属度平方加权的方法，构成类内加权误差平方和，避免平凡解。再引入模糊指数m，数次迭代，通过最小化目标函数对样本点进行最优c类划分，这就是大众熟知的FCM算法。也由于其优越性，众多的学者们对其做了很多的研究与改进。例如改进后的FCM_S1，FCM_S2，EnFCM，FGFCM，NS_FCM以及QICA_FCM等等。(3) Region-based image segmentation algorithm. This type of method mainly completes the segmentation through the consistency of the internal features of the region. It can be roughly divided into region growing merge method, random field method and clustering method. Among them, the segmentation algorithm based on clustering extracts the correlation between different pixels, and iterates to maximize the feature correlation to complete the segmentation, which shines in the field of image segmentation. Combining the knowledge of fuzzy division with clustering algorithm, the square weighting method of membership degree is adopted to form the weighted error sum of squares within the class to avoid trivial solutions. Then introduce the fuzzy index m, several iterations, and divide the sample points into the optimal c class by minimizing the objective function. This is the well-known FCM algorithm. Because of its superiority, many scholars have done a lot of research and improvement on it. For example, the improved FCM_S1, FCM_S2, EnFCM, FGFCM, NS_FCM and QICA_FCM and so on.
显而易见，最为重要的步骤为构建目标函数，或者可以说找到图像内部特征的相关性。不同于普通的光学图像，SAR图像中由于独特的雷达成像机理，含有复杂的相干斑噪声，在进行分割时要着重考虑此种乘性噪声的影响。Obviously, the most important step is to construct the objective function, or to find the correlation of the internal features of the image. Different from ordinary optical images, due to the unique radar imaging mechanism, SAR images contain complex coherent speckle noise, and the influence of this multiplicative noise should be considered in segmentation.
发明内容Contents of the invention
本发明的目的在于进一步提升SAR图像分割精度，增强算法对于不同场景图像的自适应性，提供一种自适应非局部模糊C均值聚类SAR图像分割算法。针对非局部均值算法中权值分配问题研究了其改进的自适应相似性测度方法使中心像素搜索域中各点权值分配更为合理，加强对相干斑噪声的鲁棒性。同时，利用各像素点邻域灰度直方图的信息熵确定该点非局部空间信息项在目标函数中所占权重，以很好调节相干斑抑制与图像细节保持间的平衡。在此基础上，在目标函数中引入类间离散度作用项完成算法构建。该算法对于SAR图像的分割精度进一步提升，且对于不同场景具备更好适应性，具备优异性能。The purpose of the present invention is to further improve the SAR image segmentation accuracy, enhance the adaptability of the algorithm to different scene images, and provide an adaptive non-local fuzzy C-means clustering SAR image segmentation algorithm. Aiming at the problem of weight distribution in the non-local mean algorithm, the improved adaptive similarity measure method is studied to make the weight distribution of each point in the central pixel search domain more reasonable and enhance the robustness to coherent speckle noise. At the same time, the information entropy of the neighborhood gray histogram of each pixel is used to determine the weight of the non-local spatial information item in the objective function, so as to adjust the balance between coherent speckle suppression and image detail preservation. On this basis, the inter-class dispersion term is introduced into the objective function to complete the algorithm construction. The algorithm further improves the segmentation accuracy of SAR images, and has better adaptability to different scenes, and has excellent performance.
为实现上述目的，本发明提出的SAR图像分割方法包括以下几个步骤：In order to achieve the above object, the SAR image segmentation method proposed by the present invention comprises the following steps:
1.高分辨率合成孔径雷达图像的获取1. Acquisition of high-resolution synthetic aperture radar images
获取观测区域内包含合适且丰富地物类型的高分辨率合成孔径雷达图像。Obtain high-resolution synthetic aperture radar images containing suitable and rich types of ground objects in the observation area.
2.自适应非局部均值计算2. Adaptive non-local mean calculation
针对传统非局部均值算法对于图像细节处理的缺陷引入自适应二值权值函数剔除与中心像素差异过大的像素点，得到更为精准的相似性测度公式。具体定义如下：Aiming at the shortcomings of the traditional non-local mean algorithm for image detail processing, an adaptive binary weight function is introduced to eliminate pixels that are too different from the central pixel, and a more accurate similarity measurement formula is obtained. The specific definition is as follows:
其中j∈Ni，ts表示中心像素i与其邻域内像素的灰度差阈值。该值的设置由图像所受噪声程度和整体灰度等级所决定。当图像受相干斑影响严重或图像的灰度等级较高时，阈值需设置较大，反之亦然。因此，改进后的两像素邻域分布间的自适应相似性测度可按如下公式计算得到：Where j∈Ni , ts represents the threshold value of the gray difference between the central pixel i and the pixels in its neighborhood. The setting of this value is determined by the degree of noise and the overall gray level of the image. When the image is seriously affected by speckle or the gray level of the image is high, the threshold needs to be set larger, and vice versa. Therefore, the improved adaptive similarity measure between two pixel neighborhood distributions can be calculated as follows:
其中，Ti＝{tij，j∈Ni}为中心像素i的自适应二值权矩阵，能够滤除与中心像素差异过大的邻域像素，进行准确的平滑处理。Among them, Ti ={tij , j∈Ni } is the adaptive binary weight matrix of the central pixel i, which can filter out the neighboring pixels that are too different from the central pixel and perform accurate smoothing.
将其带入非局部均值算法中即可得到像素自适应非局部均值。算法权值计算公式如下：Bring it into the non-local mean algorithm to get the pixel-adaptive non-local mean. The algorithm weight calculation formula is as follows:
其中，w′ij满足w′ij∈[0，1],且归一化因子Z′j为：Among them, w′ij satisfies w′ij ∈ [0, 1], And the normalization factor Z′j is:
将新的权值w′ij应用于NLM公式中，由此可得像素i的自适应非局部均值为：Apply the new weight w′ij to the NLM formula, so the adaptive non-local mean of pixel i can be obtained for:
同样的，xi表示像素i的灰度值，是以像素i为中心的大小为S×S的搜索窗口。Similarly, xi represents the gray value of pixel i, is a search window of size S×S centered on pixel i.
3.非局部空间信息项自适应权值参数计算3. Calculation of adaptive weight parameters for non-local spatial information items
经由自适应非局部均值算法处理后可得到对相干斑噪声具有强鲁棒性的滤波图像，该图像可作为非局部空间信息项合并至FCM算法中改进图像分割性能。在目标函数中非局部空间信息项的权重参数控制了算法的抗噪能力和区域一致性水平，是平衡算法鲁棒性和细节保持能力的关键。具体而言，对于相干斑噪声，其非局部空间信息项的权值应足够大，以调整噪声像素的属性，削弱其对分割算法的影响。另一方面,对于包含图像细节信息的像素点，如边缘像素，应减小权重值，避免非局部信息影响像素属性，更好保持图像细节。因此，对所有像素都使用固定的单一值是不合理的。After being processed by the adaptive non-local mean algorithm, a filtered image with strong robustness to coherent speckle noise can be obtained, which can be incorporated into the FCM algorithm as a non-local spatial information item to improve image segmentation performance. The weight parameters of non-local spatial information items in the objective function control the anti-noise ability and regional consistency level of the algorithm, which is the key to balance the robustness and detail preservation ability of the algorithm. Specifically, for coherent speckle noise, the weight of its non-local spatial information items should be large enough to adjust the properties of noise pixels and weaken its influence on segmentation algorithms. On the other hand, for pixels containing image detail information, such as edge pixels, the weight value should be reduced to avoid non-local information affecting pixel attributes and better maintain image details. Therefore, it is unreasonable to use a fixed single value for all pixels.
针对这一问题，可考虑利用局部灰度直方图的熵来控制非局部空间信息项对像素的自适应程度，增强算法对异常值的抗干扰能力。对于图像中任一像素i，将其非局部信息项权重由固定值替换为基于灰度直方图信息熵的自适应加权参数λi，其定义如下：To solve this problem, the entropy of the local gray histogram can be considered to control the adaptive degree of non-local spatial information items to pixels, and enhance the anti-interference ability of the algorithm to outliers. For any pixel i in the image, the weight of its non-local information item is replaced by a fixed value with an adaptive weighting parameter λi based on the information entropy of the gray histogram, which is defined as follows:
其中，in,
σ＝median{vari，i∈Ω}σ=median{vari , i∈Ω}
上述公式中表示以像素i为中心的方形邻域内像素灰度直方图的信息熵，以度量邻域无序程度。其中n为灰度量化级数，pl代表量化后的灰度级l所对应频率。此外，vari是像素i的邻域方差值，Ω表示图像像素全集。In the above formula Indicates the information entropy of the pixel gray histogram in the square neighborhood centered on pixel i to measure the degree of disorder in the neighborhood. Among them, n is the number of gray quantization series, and pl represents the frequency corresponding to the quantized gray level l. In addition, vari is the neighborhood variance value of pixel i, and Ω represents the full set of image pixels.
4.模糊聚类的类间离散度计算4. Inter-class dispersion calculation of fuzzy clustering
模糊聚类总散射矩阵、模糊类内散射矩阵及模糊类间散射矩阵定义为：The fuzzy clustering total scattering matrix, the fuzzy intra-class scattering matrix and the fuzzy inter-class scattering matrix are defined as:
由推导可知SFT＝SFW+SFB，令tr(Z)表示矩阵Z的迹，则有：It can be seen from the derivation that SFT =SFW +SFB , let tr(Z) represent the trace of matrix Z, then:
其中，类内散射矩阵的迹tr(SFW)可用于度量簇内紧致性(类内离散度)，而类间散射矩阵的迹tr(SFB)则表明簇间变化的分离性(类间离散度)。在样本集X＝{x1，x2，...，xn}中，虽然和硬聚类一样有tr(SFT)＝tr(SFW)+tr(SFB)，但模糊聚类总散射矩阵的迹tr(SFT)并非为一个常数，它依赖于uki。这意味着，在模糊聚类中tr(SFW)与tr(SFB)不再具有此消彼长的变化关系。标准FCM算法仅考虑簇内紧致性，其目标函数为因此，为保证算法同时也具有较好的类间分离性，需结合簇内和簇间的模糊变化以最小化tr(SFW)，同时最大化tr(SFB)。Among them, the trace tr(SFW ) of the intra-class scattering matrix can be used to measure the intra-cluster compactness (intra-class dispersion), while the trace tr(SFB ) of the between-class scattering matrix indicates the separation of changes between clusters (class Dispersion between). In the sample set X={x1 , x2 ,...,xn }, although tr(SFT )=tr(SFW )+tr(SFB ) is the same as hard clustering, but fuzzy clustering The trace tr(SFT ) of the total scattering matrix is not a constant, it depends on uki . This means that in fuzzy clustering, tr(SFW ) and tr(SFB ) no longer have a trade-off relationship. The standard FCM algorithm only considers the compactness within the cluster, and its objective function is Therefore, in order to ensure that the algorithm also has good inter-class separation, it is necessary to combine the fuzzy changes within and between clusters to minimize tr(SFW ) and maximize tr(SFB ).
5.图像分割5. Image Segmentation
针对SAR图像固有的相干斑噪声对分割效果所产生的影响，利用自适应非局部均值算法准确提取非局部空间信息，并根据每个像素邻域灰度直方图的熵计算其对应的自适应加权参数λi，确定该点非局部空间信息项在目标函数中的权重，调节相干斑抑制与图像细节保持之间的平衡。另一方面，鉴于标准FCM算法是依据类内离散度所提出，为进一步改善算法性能，考虑在在算法中引入类间离散度作用项得到结合信息熵和类间离散度的自适应非局部模糊C均值聚类(A Robust Non-local FCM with Comentropy and Between-cluster Scatter Matrix,NCBS_FCM)SAR图像分割算法。NCBS_FCM的目标函数被定义为：Aiming at the influence of the coherent speckle noise inherent in SAR images on the segmentation effect, the adaptive non-local mean algorithm is used to accurately extract non-local spatial information, and the corresponding adaptive weighting is calculated according to the entropy of each pixel's neighborhood gray histogram. The parameter λi determines the weight of the point's non-local spatial information item in the objective function, and adjusts the balance between coherent speckle suppression and image detail preservation. On the other hand, since the standard FCM algorithm is proposed based on the intra-class dispersion, in order to further improve the performance of the algorithm, it is considered to introduce the inter-class dispersion into the algorithm to obtain an adaptive non-local fuzzy that combines information entropy and inter-class dispersion. C-means clustering (A Robust Non-local FCM with Comentropy and Between-cluster Scatter Matrix, NCBS_FCM) SAR image segmentation algorithm. The objective function of NCBS_FCM is defined as:
其中，c为图像分割类别数，n表示图像像素个数，m作为模糊指数，一般设置为2。为使算法更好贴合SAR图像特性，选取其后向散射系数作为特征值xi，则和分别表示像素i后向散射系数的自适应非局部均值与全图像素后向散射系数均值。uki为隶属度参数且满足λi是非局部空间信息项的自适应加权参数，μk表示类间离散项参数。Among them, c is the number of image segmentation categories, n is the number of image pixels, and m is the fuzzy index, which is generally set to 2. In order to make the algorithm better fit the characteristics of SAR images, the backscattering coefficient is selected as the eigenvalue xi , then and Respectively represent the adaptive non-local mean value of the backscatter coefficient of pixel i and the mean value of the backscatter coefficient of the whole image pixel. uki is the membership degree parameter and satisfies λi is the adaptive weighting parameter of the non-local spatial information item, and μk represents the parameter of the inter-class discrete item.
借助拉格朗日乘数法将其最小化有：It is minimized with the help of Lagrange multipliers:
对每一uki求偏导Take the partial derivative for each uki
令则可以得到：make Then you can get:
代入至约束中得：Substitute into constraints won:
最终uki的更新公式如下所示：The update formula of the final uki is as follows:
同样地，对vk求偏导得：Similarly, the partial derivative of vk is:
令有如下式子：make There are the following formulas:
将上式进一步整理可得到聚类中心vk的迭代更新公式如下：By further sorting the above formula, the iterative update formula of the cluster center vk can be obtained as follows:
其中，类间离散项参数μk的迭代更新公式为Among them, the iterative update formula of the inter-class discrete item parameter μk is
在模糊聚类算法中要求隶属度uki∈[0，1]，而对于某些像素点，其计算结果可能为负。为避免此类情况出现，做出如下处理：对任一给定像素点xi，若则令uki＝1，其余uk′i＝0，k′≠k，即像素i将完全属于第k个聚类群。这意味着在该算法中每一聚类集群都有一个硬边界使得位于该边界内的像素点被硬划分为该类，而边界外的像素点具有模糊隶属度值uki∈[0，1]。在算法中同时具有硬聚类和模糊聚类可在一定程度上避免FCM算法过模糊情况，改善聚类性能。In the fuzzy clustering algorithm, the degree of membership uki ∈ [0, 1] is required, and for some pixels, the calculation result may be negative. In order to avoid this kind of situation, the following processing is done: for any given pixel xi , if Then set uki =1, other uk'i =0, k'≠k, that is, pixel i will completely belong to the kth clustering group. This means that each clustering cluster in the algorithm has a hard boundary so that the pixels located within the boundary are hard classified into this class, while the pixels outside the boundary have a fuzzy membership value uki ∈ [0, 1 ]. Having both hard clustering and fuzzy clustering in the algorithm can avoid the over-fuzziness of the FCM algorithm to a certain extent and improve the clustering performance.
附图说明Description of drawings
为了进一步说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，本发明的示意性实施例及其说明仅用于解释本发明，并不构成对本发明的不当限定。在附图中：In order to further illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings that need to be used in the description of the embodiments or the prior art will be briefly introduced below. The schematic embodiments of the present invention and their descriptions are only used It is used for explaining the present invention, and does not constitute an improper limitation of the present invention. In the attached picture:
图1是本发明实施例中自适应非局部模糊C均值聚类SAR图像分割算法的一种具体实施流程图；Fig. 1 is a kind of specific implementation flowchart of adaptive non-local fuzzy C-means clustering SAR image segmentation algorithm in the embodiment of the present invention;
图2是本发明实施例中的待分割真实SAR图像；Fig. 2 is the real SAR image to be segmented in the embodiment of the present invention;
图3是本发明实施例中的对比算法EnFCM算法分割结果；Fig. 3 is the comparison algorithm EnFCM algorithm segmentation result in the embodiment of the present invention;
图4是本发明实施例中的对比算法FLICM算法分割结果图；Fig. 4 is the comparison algorithm FLICM algorithm segmentation result figure in the embodiment of the present invention;
图5本发明实施例中的自适应非局部模糊C均值聚类SAR图像分割算法结果图。Fig. 5 is a diagram of the result of the adaptive non-local fuzzy C-means clustering SAR image segmentation algorithm in the embodiment of the present invention.
具体实施方式Detailed ways
为使得本发明的发明目的、特征、优点能够更加的明显和易懂，下面结合附图对本发明的具体实施方式进行清楚、完整地描述，以便本领域的技术人员能更好地理解本发明。需要特别提醒注意的是，下面所描述的实施例仅仅是本发明一部分实施例，而非全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其它实施例，都属于本发明保护的范围。In order to make the purpose, features and advantages of the present invention more obvious and understandable, the specific embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings, so that those skilled in the art can better understand the present invention. It should be noted that the embodiments described below are only some of the embodiments of the present invention, but not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.
在本实施例中，图1为自适应非局部模糊C均值聚类SAR图像分割算法方法的一种具体实施流程图，如图1所示，主要步骤如下：In this embodiment, Fig. 1 is a specific implementation flow chart of an adaptive non-local fuzzy C-means clustering SAR image segmentation algorithm method, as shown in Fig. 1, the main steps are as follows:
步骤1：高分辨率合成孔径雷达图像的获取Step 1: Acquisition of high-resolution SAR images
获取观测区域内包含合适且丰富地物类型的高分辨率合成孔径雷达图像。Obtain high-resolution synthetic aperture radar images containing suitable and rich types of ground objects in the observation area.
本实施例中，选择为C波段RadarSat-2于2010年5月获取的方位向×距离向为0.5m×0.5m的无锡地区SAR图像，图像大小为265×264。得到的SAR图像如图2所示。In this embodiment, the SAR image of Wuxi area with azimuth x range of 0.5m x 0.5m acquired by C-band RadarSat-2 in May 2010 is selected, and the image size is 265 x 264. The obtained SAR image is shown in Figure 2.
步骤2：自适应非局部均值计算Step 2: Adaptive non-local mean calculation
针对传统非局部均值算法对于图像细节处理的缺陷引入自适应二值权值函数剔除与中心像素差异过大的像素点，得到更为精准的相似性测度公式。具体定义如下：Aiming at the shortcomings of the traditional non-local mean algorithm for image detail processing, an adaptive binary weight function is introduced to eliminate pixels that are too different from the central pixel, and a more accurate similarity measurement formula is obtained. The specific definition is as follows:
其中j∈Ni，ts表示中心像素i与其邻域内像素的灰度差阈值。该值的设置由图像所受噪声程度和整体灰度等级所决定。当图像受相干斑影响严重或图像的灰度等级较高时，阈值需设置较大，反之亦然。因此，改进后的两像素邻域分布间的自适应相似性测度可按如下公式计算得到：Where j∈Ni , ts represents the threshold value of the gray difference between the central pixel i and the pixels in its neighborhood. The setting of this value is determined by the degree of noise and the overall gray level of the image. When the image is seriously affected by speckle or the gray level of the image is high, the threshold needs to be set larger, and vice versa. Therefore, the improved adaptive similarity measure between two pixel neighborhood distributions can be calculated as follows:
其中，Ti＝{tij，j∈Ni}为中心像素i的自适应二值权矩阵，能够滤除与中心像素差异过大的邻域像素，进行准确的平滑处理。Among them, Ti ={tij , j∈Ni } is the adaptive binary weight matrix of the central pixel i, which can filter out the neighboring pixels that are too different from the central pixel and perform accurate smoothing.
将其带入非局部均值算法中即可得到像素自适应非局部均值。算法权值计算公式如下：Bring it into the non-local mean algorithm to get the pixel-adaptive non-local mean. The algorithm weight calculation formula is as follows:
其中，w′ij满足w′ij∈[0，1],且归一化因子Z′j为：Among them, w′ij satisfies w′ij ∈ [0, 1], And the normalization factor Z′j is:
将新的权值w′ij应用于NLM公式中，由此可得像素i的自适应非局部均值为：Apply the new weight w′ij to the NLM formula, so the adaptive non-local mean of pixel i can be obtained for:
同样的，xi表示像素i的灰度值，是以像素i为中心的大小为S×S的搜索窗口。Similarly, xi represents the gray value of pixel i, is a search window of size S×S centered on pixel i.
步骤3：非局部空间信息项自适应权值参数计算Step 3: Calculation of adaptive weight parameters for non-local spatial information items
经由自适应非局部均值算法处理后可得到对相干斑噪声具有强鲁棒性的滤波图像，该图像可作为非局部空间信息项合并至FCM算法中改进图像分割性能。在目标函数中非局部空间信息项的权重参数控制了算法的抗噪能力和区域一致性水平，是平衡算法鲁棒性和细节保持能力的关键。具体而言，对于相干斑噪声，其非局部空间信息项的权值应足够大，以调整噪声像素的属性，削弱其对分割算法的影响。另一方面,对于包含图像细节信息的像素点，如边缘像素，应减小权重值，避免非局部信息影响像素属性，更好保持图像细节。因此，对所有像素都使用固定的单一值是不合理的。After being processed by the adaptive non-local mean algorithm, a filtered image with strong robustness to coherent speckle noise can be obtained, which can be incorporated into the FCM algorithm as a non-local spatial information item to improve image segmentation performance. The weight parameters of non-local spatial information items in the objective function control the anti-noise ability and regional consistency level of the algorithm, which is the key to balance the robustness and detail preservation ability of the algorithm. Specifically, for coherent speckle noise, the weight of its non-local spatial information items should be large enough to adjust the properties of noise pixels and weaken its influence on segmentation algorithms. On the other hand, for pixels containing image detail information, such as edge pixels, the weight value should be reduced to avoid non-local information affecting pixel attributes and better maintain image details. Therefore, it is unreasonable to use a fixed single value for all pixels.
针对这一问题，可考虑局利用局部灰度直方图的熵来控制非局部空间信息项对像素的自适应程度，增强算法对异常值的抗干扰能力。对于图像中任一像素i，将其非局部信息项权重由固定值替换为基于灰度直方图信息熵的自适应加权参数λi，其定义如下：To solve this problem, it can be considered to use the entropy of the local gray histogram to control the degree of adaptation of non-local spatial information items to pixels, and enhance the anti-interference ability of the algorithm to outliers. For any pixel i in the image, the weight of its non-local information item is replaced by a fixed value with an adaptive weighting parameter λi based on the information entropy of the gray histogram, which is defined as follows:
其中，in,
σ＝median{vari，i∈Ω}σ=median{vari , i∈Ω}
上述公式中表示以像素i为中心的方形邻域内像素灰度直方图的信息熵，以度量邻域无序程度。其中n为灰度量化级数，pl代表量化后的灰度级l所对应频率。此外，vari是像素i的邻域方差值，Ω表示图像像素全集。In the above formula Indicates the information entropy of the pixel gray histogram in the square neighborhood centered on pixel i to measure the degree of disorder in the neighborhood. Among them, n is the number of gray quantization series, and pl represents the frequency corresponding to the quantized gray level l. In addition, vari is the neighborhood variance value of pixel i, and Ω represents the full set of image pixels.
步骤4：模糊聚类的类间离散度计算Step 4: Calculation of between-class dispersion of fuzzy clustering
模糊聚类总散射矩阵、模糊类内散射矩阵及模糊类间散射矩阵定义为：The fuzzy clustering total scattering matrix, the fuzzy intra-class scattering matrix and the fuzzy inter-class scattering matrix are defined as:
由推导可知SFT＝SFW+SFB，令tr(Z)表示矩阵Z的迹，则有：It can be seen from the derivation that SFT =SFW +SFB , let tr(Z) represent the trace of matrix Z, then:
其中，类内散射矩阵的迹tr(SFW)可用于度量簇内紧致性(类内离散度)，而类间散射矩阵的迹tr(SFB)则表明簇间变化的分离性(类间离散度)。在样本集X＝{x1，x2，...，xn}中，虽然和硬聚类一样有tr(SFT)＝tr(SFW)+tr(SFB)，但模糊聚类总散射矩阵的迹tr(SFT)并非为一个常数，它依赖于uki。这意味着，在模糊聚类中tr(SFW)与tr(SFB)不再具有此消彼长的变化关系。标准FCM算法仅考虑簇内紧致性，因此，为保证算法同时也具有较好的类间分离性，需结合簇内和簇间的模糊变化以最小化tr(SFW)，同时最大化tr(SFB)。Among them, the trace tr(SFW ) of the intra-class scattering matrix can be used to measure the intra-cluster compactness (intra-class dispersion), while the trace tr(SFB ) of the between-class scattering matrix indicates the separation of changes between clusters (class Dispersion between). In the sample set X={x1 , x2 ,...,xn }, although tr(SFT )=tr(SFW )+tr(SFB ) is the same as hard clustering, but fuzzy clustering The trace tr(SFT ) of the total scattering matrix is not a constant, it depends on uki . This means that in fuzzy clustering, tr(SFW ) and tr(SFB ) no longer have a trade-off relationship. The standard FCM algorithm only considers intra-cluster compactness. Therefore, in order to ensure that the algorithm also has good inter-class separation, it is necessary to combine the fuzzy changes within and between clusters to minimize tr(SFW ) and maximize tr (SFB ).
步骤5：图像分割Step 5: Image Segmentation
针对SAR图像固有的相干斑噪声对分割效果所产生的影响，利用自适应非局部均值算法准确提取非局部空间信息，并根据每个像素邻域灰度直方图的熵计算其对应的自适应加权参数λi，确定该点非局部空间信息项在目标函数中的权重，调节相干斑抑制与图像细节保持之间的平衡。另一方面，鉴于标准FCM算法是依据类内离散度所提出，为进一步改善算法性能，依据5.3节的分析，考虑在在算法中引入类间离散度作用项得到结合信息熵和类间离散度的自适应非局部模糊C均值聚类(A Robust Non-local FCM with Comentropyand Between-cluster Scatter Matrix,NCBS_FCM)SAR图像分割算法。NCBS_FCM的目标函数被定义为：Aiming at the influence of the coherent speckle noise inherent in SAR images on the segmentation effect, the adaptive non-local mean algorithm is used to accurately extract non-local spatial information, and the corresponding adaptive weighting is calculated according to the entropy of each pixel's neighborhood gray histogram. The parameter λi determines the weight of the point's non-local spatial information item in the objective function, and adjusts the balance between coherent speckle suppression and image detail preservation. On the other hand, since the standard FCM algorithm is proposed based on the intra-class dispersion, in order to further improve the performance of the algorithm, according to the analysis in Section 5.3, consider introducing the inter-class dispersion into the algorithm to obtain the combination of information entropy and inter-class dispersion Adaptive non-local fuzzy C-means clustering (A Robust Non-local FCM with Comentropy and Between-cluster Scatter Matrix, NCBS_FCM) SAR image segmentation algorithm. The objective function of NCBS_FCM is defined as:
其中，c为图像分割类别数，n表示图像像素个数，m作为模糊指数，一般设置为2。为使算法更好贴合SAR图像特性，选取其后向散射系数作为特征值xi，则和分别表示像素i后向散射系数的自适应非局部均值与全图像素后向散射系数均值。uki为隶属度参数且满足λi是非局部空间信息项的自适应加权参数，μk表示类间离散项参数。Among them, c is the number of image segmentation categories, n is the number of image pixels, and m is the fuzzy index, which is generally set to 2. In order to make the algorithm better fit the characteristics of SAR images, the backscattering coefficient is selected as the eigenvalue xi , then and Respectively represent the adaptive non-local mean value of the backscatter coefficient of pixel i and the mean value of the backscatter coefficient of the whole image pixel. uki is the membership degree parameter and satisfies λi is the adaptive weighting parameter of the non-local spatial information item, and μk represents the parameter of the inter-class discrete item.
此外，隶属度uki和聚类中心vk的更新迭代公式如下：In addition, the update iteration formula of membership degree uki and cluster center vk is as follows:
其中，类间离散项参数μk的迭代更新公式为Among them, the iterative update formula of the inter-class discrete item parameter μk is
在模糊聚类算法中要求隶属度uki∈[0，1]，而对于某些像素点，其计算结果可能为负。为避免此类情况出现，做出如下处理：对任一给定像素点xi，若则令uki＝1，其余uk′i＝0，k′≠k，即像素i将完全属于第k个聚类群。这意味着在该算法中每一聚类集群都有一个硬边界使得位于该边界内的像素点被硬划分为该类，而边界外的像素点具有模糊隶属度值uki∈[0，1]。在算法中同时具有硬聚类和模糊聚类可在一定程度上避免FCM算法过模糊情况，改善聚类性能。In the fuzzy clustering algorithm, the degree of membership uki ∈ [0, 1] is required, and for some pixels, the calculation result may be negative. In order to avoid this kind of situation, the following processing is done: for any given pixel xi , if Then set uki =1, other uk'i =0, k'≠k, that is, pixel i will completely belong to the kth clustering group. This means that each clustering cluster in the algorithm has a hard boundary so that the pixels located within the boundary are hard classified into this class, while the pixels outside the boundary have a fuzzy membership value uki ∈ [0, 1 ]. Having both hard clustering and fuzzy clustering in the algorithm can avoid the over-fuzziness of the FCM algorithm to a certain extent and improve the clustering performance.
算法对应结果图如图5所示。图3与图4分别为EnFCM算法分割结果和FLICM算法分割结果图。The corresponding results of the algorithm are shown in Figure 5. Figure 3 and Figure 4 are the segmentation results of the EnFCM algorithm and the segmentation results of the FLICM algorithm, respectively.
除上述实施例外，本发明还可以有其他实施方式，凡采用等同替换或等效变换形成的技术方案，均落在本发明的保护范围内。尽管上面对本发明说明性的具体实施方式进行了描述，以便于本技术领域的技术人员理解本发明，但应该清楚，本发明不限于具体实施方式的范围，对本技术领域的普通技术人员来讲，只要各种变化在所附的权利要求限定和确定的本发明的精神和范围内，这些变化是显而易见的，一切利用本发明构思的发明创造均在保护之列。In addition to the above-mentioned embodiments, the present invention can also have other implementations, and all technical solutions formed by equivalent replacement or equivalent transformation fall within the protection scope of the present invention. Although the illustrative specific embodiments of the present invention have been described above, so that those skilled in the art can understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, As long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are included in the protection list.
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