Movatterモバイル変換


[0]ホーム

URL:


CN111860547A - Image segmentation method, device, device and storage medium based on sparse representation - Google Patents

Image segmentation method, device, device and storage medium based on sparse representation
Download PDF

Info

Publication number
CN111860547A
CN111860547ACN202010794337.XACN202010794337ACN111860547ACN 111860547 ACN111860547 ACN 111860547ACN 202010794337 ACN202010794337 ACN 202010794337ACN 111860547 ACN111860547 ACN 111860547A
Authority
CN
China
Prior art keywords
image
segmentation
parameters
sparse representation
optimal
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202010794337.XA
Other languages
Chinese (zh)
Other versions
CN111860547B (en
Inventor
陈子仪
范文涛
钟必能
杜吉祥
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Huaqiao University
Original Assignee
Huaqiao University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Huaqiao UniversityfiledCriticalHuaqiao University
Priority to CN202010794337.XApriorityCriticalpatent/CN111860547B/en
Publication of CN111860547ApublicationCriticalpatent/CN111860547A/en
Application grantedgrantedCritical
Publication of CN111860547BpublicationCriticalpatent/CN111860547B/en
Activelegal-statusCriticalCurrent
Anticipated expirationlegal-statusCritical

Links

Images

Classifications

Landscapes

Abstract

Translated fromChinese

本发明提供一种基于稀疏表示的图像分割方法、装置、设备及存储介质,方法包括:收集一定数量的图像及其分割标记,然后用狄利克雷混合模型对其进行无监督分割,并调整其参数,获得每张图像最优参数,组成最优参数列表,然后将每张图像转换为灰度图,提取它们的灰度直方图特征,训练生成一个稀疏表示字典,提取待分割的图像的灰度直方图特征,计算它的稀疏系数,根据得到的稀疏系数,从稀疏表示字典获取与其最接近的图像,从最优参数列表中获取近似图像的最优参数,并用最优参数进行赋值,利用赋值好的参数对待分割图像进行无监督图像分割,得到分割结果。本发明狄利克雷混合模型的优化参数不需要人工调整,而是经过稀疏表示预测后自动生成。

Figure 202010794337

The present invention provides an image segmentation method, device, equipment and storage medium based on sparse representation. The method includes: collecting a certain number of images and their segmentation marks, then using a Dirichlet mixture model to perform unsupervised segmentation on them, and adjusting the parameters, obtain the optimal parameters of each image, form the optimal parameter list, and then convert each image into a grayscale image, extract their grayscale histogram features, train to generate a sparse representation dictionary, and extract the grayscale of the image to be segmented. The degree histogram feature, calculate its sparse coefficient, according to the obtained sparse coefficient, obtain the image closest to it from the sparse representation dictionary, obtain the optimal parameters of the approximate image from the optimal parameter list, and use the optimal parameters to assign values, use The assigned parameters are used for unsupervised image segmentation of the image to be segmented, and the segmentation result is obtained. The optimization parameters of the Dirichlet mixture model of the present invention do not need to be manually adjusted, but are automatically generated after being predicted by sparse representation.

Figure 202010794337

Description

Translated fromChinese
基于稀疏表示的图像分割方法、装置、设备及存储介质Image segmentation method, device, device and storage medium based on sparse representation

技术领域technical field

本发明涉及图像分割技术领域,具体而言,涉及一种基于稀疏表示的图像分割方法、装置、设备及存储介质。The present invention relates to the technical field of image segmentation, and in particular, to an image segmentation method, apparatus, device and storage medium based on sparse representation.

背景技术Background technique

基于狄利克雷的图像分割算法是一种常用的图像分割算法,其主要是基于像素点进行计算分割。原始基于狄利克雷混合模型的图像分割算法,目前其中几个重要参数主要依靠人工经验和实际测试去做调整和优化,无法自动预测最优参数,由于其重要参数在不同图像的分割中存在显著的差异,使得不同图像使用相同参数可能取得完全不一样的分割效果,甚至有的会造成分割的失败。针对不同图像,狄利克雷混合模型重要参数的调整优化是繁琐耗时和难以把控与评价的。Dirichlet-based image segmentation algorithm is a commonly used image segmentation algorithm, which is mainly based on pixel points for computational segmentation. The original image segmentation algorithm based on the Dirichlet mixture model, at present, several important parameters are mainly adjusted and optimized by manual experience and actual testing, and the optimal parameters cannot be automatically predicted, because their important parameters have significant differences in the segmentation of different images The difference of , makes different images use the same parameters to achieve completely different segmentation effects, and some even cause segmentation failure. For different images, the adjustment and optimization of important parameters of the Dirichlet mixture model is tedious and time-consuming, and it is difficult to control and evaluate.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于提供一种基于稀疏表示的图像分割方法、装置、设备及存储介质用以解决无法自动预测最优参数导致耗时的问题。The purpose of the present invention is to provide an image segmentation method, device, device and storage medium based on sparse representation to solve the problem of time-consuming caused by the inability to automatically predict optimal parameters.

为实现上述目的,本发明实施例提供一种基于稀疏表示的图像分割方法,包括以下步骤:To achieve the above purpose, an embodiment of the present invention provides an image segmentation method based on sparse representation, including the following steps:

收集一定数量的图像及其分割标记;Collect a certain number of images and their segmentation markers;

基于所述分割标记,用狄利克雷混合模型对收集的图像进行无监督分割,并调整狄利克雷混合模型的参数,获得使每张图像的分割结果接近最优的最优参数;Based on the segmentation marks, unsupervised segmentation is performed on the collected images by using the Dirichlet mixture model, and the parameters of the Dirichlet mixture model are adjusted to obtain optimal parameters that make the segmentation result of each image close to the optimal;

记录每张图像的最优参数,组成最优参数列表;Record the optimal parameters of each image to form an optimal parameter list;

将每张图像转换为灰度图,并提取它们的灰度直方图特征;Convert each image to grayscale and extract their grayscale histogram features;

将从每张图像提取的灰度直方图特征组成一个字典,训练生成一个稀疏表示字典;The grayscale histogram features extracted from each image are composed of a dictionary, and a sparse representation dictionary is generated by training;

提取待分割的图像的灰度直方图特征,利用该灰度直方图特征,计算其在所训练的稀疏表示字典中的稀疏系数;Extract the grayscale histogram feature of the image to be segmented, and use the grayscale histogram feature to calculate its sparse coefficient in the trained sparse representation dictionary;

根据计算得到的所述稀疏系数,从所述稀疏表示字典获取与其最接近的近似图像;Obtain the closest approximate image from the sparse representation dictionary according to the calculated sparse coefficient;

从所述最优参数列表中获取所述近似图像的最优参数,并采用所述最优参数对狄利克雷混合模型的参数进行赋值;Obtain the optimal parameters of the approximate image from the optimal parameter list, and use the optimal parameters to assign values to the parameters of the Dirichlet mixture model;

利用赋值好参数的狄利克雷混合模型对待分割图像进行无监督图像分割,得到分割结果。The unsupervised image segmentation is performed on the image to be segmented by using the Dirichlet mixture model with assigned parameters, and the segmentation result is obtained.

优选的,所述图像在灰度直方图的分布上具有差异性以及多的分布类型。Preferably, the image has differences in the distribution of grayscale histograms and multiple distribution types.

优选的的,在获得所述最优参数的过程中,结合分割结果与对应分割标记的精度,判断参数是否达到最优。Preferably, in the process of obtaining the optimal parameters, it is determined whether the parameters are optimal by combining the segmentation results and the accuracy of the corresponding segmentation markers.

优选的的,所述灰度直方图特征包括256维度的特征。Preferably, the grayscale histogram features include 256-dimensional features.

本发明还提供了一种基于稀疏表示的图像分割装置,包括:The present invention also provides an image segmentation device based on sparse representation, comprising:

收集模块,用于收集一定数量的图像及其分割标记;A collection module for collecting a certain number of images and their segmentation markers;

第一分割模块,用于基于所述分割标记,用狄利克雷混合模型对收集的图像进行无监督分割,并调整狄利克雷混合模型的参数,获得使每张图像的分割结果接近最优的最优参数;The first segmentation module is used to perform unsupervised segmentation on the collected images with the Dirichlet mixture model based on the segmentation mark, and adjust the parameters of the Dirichlet mixture model to obtain a segmentation result that makes each image close to the optimal optimal parameters;

记录模块,用于记录每张图像的最优参数,组成最优参数列表;The recording module is used to record the optimal parameters of each image and form the optimal parameter list;

提取模块,用于将每张图像转换为灰度图,并提取它们的灰度直方图特征;Extraction module for converting each image to grayscale and extracting their grayscale histogram features;

训练模块,用于将从每张图像提取的灰度直方图特征组成一个字典,训练生成一个稀疏表示字典;The training module is used to form a dictionary from the grayscale histogram features extracted from each image, and train to generate a sparse representation dictionary;

计算模块,用于提取待分割的图像的灰度直方图特征,利用该灰度直方图特征,计算其在所训练的稀疏表示字典中的稀疏系数;a calculation module, used to extract the grayscale histogram feature of the image to be segmented, and use the grayscale histogram feature to calculate its sparse coefficient in the trained sparse representation dictionary;

获取模块,用于根据计算得到的所述稀疏系数,从所述稀疏表示字典获取与其最接近的近似图像;an obtaining module, configured to obtain the closest approximate image from the sparse representation dictionary according to the calculated sparse coefficient;

赋值模块,用于从所述最优参数列表中获取所述近似图像的最优参数,并采用所述最优参数对狄利克雷混合模型的参数进行赋值;an assignment module, configured to obtain the optimal parameters of the approximate image from the optimal parameter list, and use the optimal parameters to assign values to the parameters of the Dirichlet mixture model;

第二分割模块,用于利用赋值好参数的狄利克雷混合模型对待分割图像进行无监督图像分割,得到分割结果。The second segmentation module is used to perform unsupervised image segmentation on the image to be segmented by using the Dirichlet mixture model with assigned parameters to obtain segmentation results.

本发明还提供了一种存储介质,所述存储介质用于存储至少一个程序,至少一个指令,所述至少一个程序、指令被执行以实现一种基于稀疏表示的参数优化狄利克雷混合模型图像分割的方法。The present invention also provides a storage medium for storing at least one program, at least one instruction, and the at least one program and instruction are executed to realize a sparse representation-based parameter optimization Dirichlet mixture model image method of segmentation.

优选的,所述图像在灰度直方图的分布上具有差异性以及多的分布类型。Preferably, the image has differences in the distribution of grayscale histograms and multiple distribution types.

优选的的,在获得所述最优参数的过程中,结合分割结果与对应分割标记的精度,判断参数是否达到最优。Preferably, in the process of obtaining the optimal parameters, it is determined whether the parameters are optimal by combining the segmentation results and the accuracy of the corresponding segmentation markers.

优选的的,所述灰度直方图特征包括256维度的特征。Preferably, the grayscale histogram features include 256-dimensional features.

本发明还提供了一种基于稀疏表示的图像分割设备,包括存储器以及处理器,所述存储器内存储有计算机程序,所述处理器用于运行所述计算机程序以实现所述一种基于稀疏表示的图像分割方法。The present invention also provides an image segmentation device based on sparse representation, comprising a memory and a processor, wherein a computer program is stored in the memory, and the processor is configured to run the computer program to implement the sparse representation-based image segmentation device. Image segmentation method.

本发明还提供一种存储介质,所述存储介质存储有计算机程序,所述计算机程序能够被所述存储介质所在设备的处理器执行,以实现所述的一种基于稀疏表示的图像分割方法。The present invention also provides a storage medium, where the storage medium stores a computer program, and the computer program can be executed by a processor of a device where the storage medium is located, so as to implement the image segmentation method based on sparse representation.

本发明的有益技术效果:Beneficial technical effects of the present invention:

本发明通过收集大量的图像及其分割标记,然后利用狄利克雷混合模型对所收集的图像进行无监督分割,分割过程中,通过人工调整和优化狄利克雷参数,确保每张图像的分割结果精度相对较高,并对每张图像的狄利克雷混合模型参数记录下来,下一步,将从每张图像提取的灰度直方图特征组成一个字典,训练生成一个稀疏表示字典,最后,当要使用狄利克雷混合模型去分割一张图像时,先用所训练的稀疏表示字典对该图像进行识别,辨认其与字典中最像的图像,计算其在所训练的稀疏表示字典中的稀疏系数,并用最像图像对应的狄利克雷参数对本次分割中的狄利克雷参数进行赋值再进行无监督分割。本专利中狄利克雷混合模型的优化参数不需要人工调整,而是经过稀疏表示预测之后自动生成,节省时间。The invention collects a large number of images and their segmentation marks, and then uses the Dirichlet hybrid model to perform unsupervised segmentation on the collected images. During the segmentation process, the Dirichlet parameters are manually adjusted and optimized to ensure the segmentation result of each image. The accuracy is relatively high, and the parameters of the Dirichlet mixture model for each image are recorded. In the next step, the grayscale histogram features extracted from each image are formed into a dictionary, and a sparse representation dictionary is generated by training. When using the Dirichlet mixture model to segment an image, first use the trained sparse representation dictionary to identify the image, identify the image that is most similar to the dictionary, and calculate its sparse coefficient in the trained sparse representation dictionary. , and assign the Dirichlet parameters in this segmentation with the Dirichlet parameters corresponding to the most image-like images, and then perform unsupervised segmentation. The optimization parameters of the Dirichlet mixture model in this patent do not need to be manually adjusted, but are automatically generated after sparse representation prediction, which saves time.

附图说明Description of drawings

为了更清楚地说明本发明实施方式的技术方案,下面将对实施方式中所需要使用的附图作简单地介绍,应当理解,以下附图仅示出了本发明的某些实施例,因此不应被看作是对范围的限定,对于本领域普通技术人员来讲,在不付出创造性劳动的前提下,还可以根据这些附图获得其他相关的附图。In order to explain the technical solutions of the embodiments of the present invention more clearly, the following briefly introduces the accompanying drawings used in the embodiments. It should be understood that the following drawings only show some embodiments of the present invention, and therefore do not It should be regarded as a limitation of the scope, and for those of ordinary skill in the art, other related drawings can also be obtained according to these drawings without any creative effort.

图1为本发明第一实施例提供的一种基于稀疏表示的图像分割方法的流程示意图。FIG. 1 is a schematic flowchart of an image segmentation method based on sparse representation provided by the first embodiment of the present invention.

图2为本发明第一实施例提供的一种基于稀疏表示的图像分割方法的流程示意图。FIG. 2 is a schematic flowchart of an image segmentation method based on sparse representation according to the first embodiment of the present invention.

图3为本发明第二实施例提供的一种基于稀疏表示的图像分割装置的流程示意图。FIG. 3 is a schematic flowchart of an apparatus for image segmentation based on sparse representation according to a second embodiment of the present invention.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例仅仅是本发明一部分实施例,而不是全部的实施例。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他实施例,都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

本发明的多个实施例提供了一种基于稀疏表示的图像分割方法、装置、设备及存储介质,其在基于原始狄利克雷混合模型的图像分割算法的基础上,经过稀疏表示预测之后狄利克雷混合模型的优化参数不需要人工调整,而是自动生成,节省时间。Various embodiments of the present invention provide an image segmentation method, device, device and storage medium based on sparse representation, which are based on the image segmentation algorithm based on the original Dirichlet mixture model, and after sparse representation prediction, Dirich The optimization parameters of the Lei mixture model do not need to be manually adjusted, but are automatically generated, saving time.

为便于对本发明的理解,以下先介绍基于狄利克雷混合模型的图像分割算法的算法原理。In order to facilitate the understanding of the present invention, the algorithm principle of the image segmentation algorithm based on the Dirichlet mixture model is first introduced below.

具体地,基于狄利克雷混合模型的图像分割算法,主要是利用有限狄利克雷混合模型结合像素空间约束,实现对目标图像的无监督分割。Specifically, the image segmentation algorithm based on the Dirichlet mixture model mainly uses the finite Dirichlet mixture model combined with the pixel space constraints to achieve unsupervised segmentation of the target image.

首先,给定一个D维的随机向量

Figure BDA0002624985480000051
该向量满足:
Figure BDA00026249854800000514
并且0<<Xd<<1。在随机向量
Figure BDA0002624985480000052
上带有参数向量
Figure BDA0002624985480000053
的狄利克雷分布可以定义为:First, given a D-dimensional random vector
Figure BDA0002624985480000051
The vector satisfies:
Figure BDA00026249854800000514
And 0<<Xd <<1. in random vector
Figure BDA0002624985480000052
with a vector of parameters on
Figure BDA0002624985480000053
The Dirichlet distribution can be defined as:

Figure BDA0002624985480000054
Figure BDA0002624985480000054

这里

Figure BDA0002624985480000055
是一个定义为
Figure BDA0002624985480000056
的gamma函数。狄利克雷分布的均值和方差分别为
Figure BDA0002624985480000057
Figure BDA0002624985480000058
here
Figure BDA0002624985480000055
is a defined as
Figure BDA0002624985480000056
gamma function. The mean and variance of the Dirichlet distribution are
Figure BDA0002624985480000057
and
Figure BDA0002624985480000058

然后,一个包含K个组成部分的有限狄利克雷分布可以表示为:Then, a finite Dirichlet distribution with K components can be expressed as:

Figure BDA0002624985480000059
Figure BDA0002624985480000059

这里的

Figure BDA00026249854800000510
代表一个混合比例集合,并且该混合比例集合满足:0<<πk<<1和
Figure BDA00026249854800000511
假设有一个由狄利克雷分布生成的包含N个独立分布向量的集合
Figure BDA00026249854800000512
则χ的密度函数为:here
Figure BDA00026249854800000510
represents a set of mixing ratios, and the set of mixing ratios satisfies: 0<<πk <<1 and
Figure BDA00026249854800000511
Suppose there is a set of N independent distribution vectors generated by the Dirichlet distribution
Figure BDA00026249854800000512
Then the density function of χ is:

Figure BDA00026249854800000513
Figure BDA00026249854800000513

为了让狄利克雷混合模型能够用于图像分割,对狄利克雷混合模型的无监督分类加上了空间约束条件。假定图像中每个像素的分布满足空间约束的狄利克雷混合模型,那么像素点的密度分布函数可以表示为:To enable the Dirichlet mixture model to be used for image segmentation, spatial constraints are imposed on the unsupervised classification of the Dirichlet mixture model. Assuming that the distribution of each pixel in the image satisfies the spatially constrained Dirichlet mixture model, the density distribution function of the pixel can be expressed as:

Figure BDA0002624985480000061
Figure BDA0002624985480000061

这里的

Figure BDA0002624985480000062
是上下文混合比例,ξik代表的是像素i属于第k个部分的概率,并且满足限制条件:ξik>0,
Figure BDA0002624985480000063
here
Figure BDA0002624985480000062
is the context mixing ratio, ξik represents the probability that pixel i belongs to the k-th part, and satisfies the constraints: ξik >0,
Figure BDA0002624985480000063

接下来,对于每个像素

Figure BDA0002624985480000064
对它指定一个K维的二值随机向量Zik=(Zi1,…,ZiK)作为类别指示变量,其定义为:Next, for each pixel
Figure BDA0002624985480000064
It is assigned a K-dimensional binary random vector Zik = (Zi1 ,...,ZiK ) as the category indicator variable, which is defined as:

Figure BDA0002624985480000065
Figure BDA0002624985480000065

对于集合

Figure BDA0002624985480000066
中的每个类别指示变量
Figure BDA0002624985480000067
满足以下限制条件:for collection
Figure BDA0002624985480000066
each category indicator variable in
Figure BDA0002624985480000067
The following constraints are met:

Figure BDA0002624985480000068
Figure BDA0002624985480000068

为了保证分割的平滑性,对于每个像素点用邻域均值来代替它本身的值,具体表示如下:In order to ensure the smoothness of the segmentation, the neighborhood mean is used to replace its own value for each pixel, which is specifically expressed as follows:

Figure BDA0002624985480000069
Figure BDA0002624985480000069

这里的Ωi表示第i个邻域像素,|Ωi|表示第i个像素的邻域像素个数,(t-1)表示上一次迭代计算。通常3×3的方形窗口被作为邻域区域。Here Ωi represents the ith neighborhood pixel, |Ωi | represents the number of neighborhood pixels of the ith pixel, and (t-1) represents the last iteration calculation. Usually a 3×3 square window is used as the neighborhood area.

Figure BDA00026249854800000610
的狄利克雷分布可以表示为:
Figure BDA00026249854800000610
The Dirichlet distribution of can be expressed as:

Figure BDA00026249854800000611
Figure BDA00026249854800000611

这里的

Figure BDA00026249854800000612
是狄利克雷参数。here
Figure BDA00026249854800000612
is the Dirichlet parameter.

由于

Figure BDA00026249854800000613
必须是正数,因此对它用Gamma分布对它进行先验概率分布赋值:because
Figure BDA00026249854800000613
Must be positive, so assign it a prior probability distribution with a Gamma distribution:

Figure BDA00026249854800000614
Figure BDA00026249854800000614

这里的ukd和vkd是超参数。从而,用于图像无监督分割的空间约束狄利克雷混合模型的联合概率分布可以表示为:Here ukd and vkd are hyperparameters. Thus, the joint probability distribution of the spatially constrained Dirichlet mixture model for unsupervised segmentation of images can be expressed as:

Figure BDA0002624985480000071
Figure BDA0002624985480000071

对于上述模型的自主学习过程,采用了变分贝叶斯学习的方法。变分贝叶斯是一种用于最优化问题中后验概率分布计算的近似方法。通常使用变分分布q(Θ)来近似真正的后验概率分布p(Θ|χ),这里的

Figure BDA0002624985480000072
表示隐藏随机变量。Kullback-Leibler(KL)差异被用来计算近似分布q(Θ)和真实分布p(Θ|χ)之间的差异:For the autonomous learning process of the above model, the variational Bayesian learning method is adopted. Variational Bayes is an approximation method for the computation of posterior probability distributions in optimization problems. The true posterior probability distribution p(Θ|χ) is usually approximated by a variational distribution q(Θ), where
Figure BDA0002624985480000072
represents a hidden random variable. The Kullback-Leibler (KL) difference is used to calculate the difference between the approximate distribution q(Θ) and the true distribution p(Θ|χ):

Figure BDA0002624985480000073
Figure BDA0002624985480000073

这里的

Figure BDA0002624985480000074
是证据下限,并定义如下:here
Figure BDA0002624985480000074
is the lower limit of evidence and is defined as follows:

Figure BDA0002624985480000075
Figure BDA0002624985480000075

从而最小化KL(q||p)等同于最大化证据下限

Figure BDA0002624985480000076
这里,全因子分解被用于限制q(Θ),具体表示如下:Thus minimizing KL(q||p) is equivalent to maximizing the lower bound of evidence
Figure BDA0002624985480000076
Here, full factorization is used to limit q(Θ), which is expressed as follows:

Figure BDA0002624985480000077
Figure BDA0002624985480000077

为了最大化

Figure BDA0002624985480000078
这里对其每个因子做变分优化:in order to maximize
Figure BDA0002624985480000078
Here is a variational optimization for each of its factors:

Figure BDA0002624985480000079
Figure BDA0002624985480000079

Figure BDA00026249854800000710
Figure BDA00026249854800000710

Figure BDA00026249854800000711
Figure BDA00026249854800000711

这里的分布超参数由以下公式给定:The distribution hyperparameters here are given by:

Figure BDA00026249854800000712
Figure BDA00026249854800000712

Figure BDA00026249854800000713
Figure BDA00026249854800000713

Figure BDA00026249854800000714
Figure BDA00026249854800000714

Figure BDA0002624985480000081
Figure BDA0002624985480000081

Figure BDA0002624985480000082
Figure BDA0002624985480000082

Figure BDA0002624985480000083
Figure BDA0002624985480000083

这里的Ψ(.)表示digamma方程。上述方程的期望值可以用如下公式计算:Here Ψ(.) represents the digamma equation. The expected value of the above equation can be calculated using the following formula:

Figure BDA0002624985480000084
Figure BDA0002624985480000084

Figure BDA0002624985480000085
Figure BDA0002624985480000085

Figure BDA0002624985480000086
Figure BDA0002624985480000086

Figure BDA0002624985480000087
Figure BDA0002624985480000087

应用二阶泰勒展开式可以获得公式(10)中

Figure BDA0002624985480000088
的下限近似值:
Figure BDA0002624985480000089
Applying the second-order Taylor expansion to obtain Eq. (10)
Figure BDA0002624985480000088
The lower bound approximation of :
Figure BDA0002624985480000089

在后验概率分布中上下文混合比例的期望值可以表示为:The expected value of the context mixing proportion in the posterior probability distribution can be expressed as:

Figure BDA00026249854800000810
Figure BDA00026249854800000810

在算法中,最佳的分割块数可以通过初始化一个比较大的分割块数K,然后通过迭代把冗余的分割块去除。上述变分更新方程可以通过类似EM算法的迭代过程最优化,具体算法如下:In the algorithm, the optimal number of partitions can be initialized by a relatively large number of partitions K, and then the redundant partitions are removed by iteration. The above variational update equation can be optimized through an iterative process similar to the EM algorithm. The specific algorithm is as follows:

选取初始化分割块数K=20Select the number of initialized partitions K=20

初始化超参数a=50,b=1.5,ukd=10,vkd=0.05.Initialize hyperparameters a = 50, b = 1.5, ukd = 10, vkd = 0.05.

通过K-means聚类算法初始化rikInitializerik via K-means clustering algorithm

重复:repeat:

用当前的模型参数值去评估分割块(公式22-26)Use the current model parameter values to evaluate the partitions (Equations 22-26)

使用公式14-16更新

Figure BDA0002624985480000091
Update using Equations 14-16
Figure BDA0002624985480000091

直到达到收敛条件。until the convergence condition is reached.

以下详述本发明实施例的具体内容。The specific contents of the embodiments of the present invention are described in detail below.

如图1-2所示,本发明第一实施例提供了一种基于稀疏表示的图像分割方法,包括步骤:As shown in Figure 1-2, the first embodiment of the present invention provides an image segmentation method based on sparse representation, including the steps:

S11:收集一定数量的图像及其分割标记;S11: collect a certain number of images and their segmentation marks;

S12:基于所述分割标记,用狄利克雷混合模型对收集的图像进行无监督分割,并调整狄利克雷混合模型的参数,获得使每张图像的分割结果接近最优的最优参数;S12: based on the segmentation mark, use the Dirichlet mixture model to perform unsupervised segmentation on the collected images, and adjust the parameters of the Dirichlet mixture model to obtain optimal parameters that make the segmentation result of each image close to the optimal;

S13:记录每张图像的最优参数,组成最优参数列表;S13: record the optimal parameters of each image to form an optimal parameter list;

S14:将每张图像转换为灰度图,并提取它们的灰度直方图特征;S14: convert each image into a grayscale image, and extract their grayscale histogram features;

S15:将从每张图像提取的灰度直方图特征组成一个字典,训练生成一个稀疏表示字典;S15: form a dictionary from the grayscale histogram features extracted from each image, and train to generate a sparse representation dictionary;

S16:提取待分割的图像的灰度直方图特征,利用该灰度直方图特征,计算其在所训练的稀疏表示字典中的稀疏系数;S16: extract the grayscale histogram feature of the image to be segmented, and use the grayscale histogram feature to calculate its sparse coefficient in the trained sparse representation dictionary;

S17:根据计算得到的所述稀疏系数,从所述稀疏表示字典获取与其最接近的近似图像;S17: According to the calculated sparse coefficient, obtain the approximate image closest to it from the sparse representation dictionary;

S18:从所述最优参数列表中获取所述近似图像的最优参数,并采用所述最优参数对狄利克雷混合模型的参数进行赋值;S18: obtain the optimal parameters of the approximate image from the optimal parameter list, and use the optimal parameters to assign values to the parameters of the Dirichlet mixture model;

S19:利用赋值好参数的狄利克雷混合模型对待分割图像进行无监督图像分割,得到分割结果。S19: Use the Dirichlet mixture model with assigned parameters to perform unsupervised image segmentation on the image to be segmented to obtain a segmentation result.

在本实施例中,所述图像在灰度直方图的分布上选择具有差异性以及尽可能多的分布类型以增大样本量。In this embodiment, the distribution of the grayscale histogram of the image is different and as many distribution types as possible are selected to increase the sample size.

在本实施例中,在获得所述最优参数的过程中,通过人工判断分割结果,通过结合分割结果与对应分割标记的精度,判断参数是否达到最优,若不是最优,则继续修改参数直至分割结果最优。In this embodiment, in the process of obtaining the optimal parameters, the segmentation result is manually judged, and whether the parameters are optimal is determined by combining the segmentation results and the accuracy of the corresponding segmentation markers, and if not, the parameters are continued to be modified until the segmentation result is optimal.

在本实施例中,所述灰度直方图特征可选256维度的特征。In this embodiment, the grayscale histogram feature can be selected as a feature of 256 dimensions.

在本实施例中,所述稀疏字典不做缩减,每张图像都为一个类别。In this embodiment, the sparse dictionary is not reduced, and each image is a category.

本发明第二实施例提供一种基于稀疏表示的图像分割装置,如图3,包括:The second embodiment of the present invention provides an image segmentation device based on sparse representation, as shown in FIG. 3 , including:

110:收集模块,用于收集一定数量的图像及其分割标记;110: a collection module for collecting a certain number of images and their segmentation marks;

120:第一分割模块,用于基于所述分割标记,用狄利克雷混合模型对收集的图像进行无监督分割,并调整狄利克雷混合模型的参数,获得使每张图像的分割结果接近最优的最优参数;120: a first segmentation module, configured to perform unsupervised segmentation on the collected images by using the Dirichlet mixture model based on the segmentation mark, and adjust the parameters of the Dirichlet mixture model to obtain a segmentation result that makes each image close to the best possible segmentation result. optimal parameters;

130:记录模块,用于记录每张图像的最优参数,组成最优参数列表;130: a recording module for recording the optimal parameters of each image to form an optimal parameter list;

140:提取模块,用于将每张图像转换为灰度图,并提取它们的灰度直方图特征;140: an extraction module for converting each image into a grayscale image and extracting their grayscale histogram features;

150:训练模块,用于将从每张图像提取的灰度直方图特征组成一个字典,训练生成一个稀疏表示字典;150: a training module for forming a dictionary from the grayscale histogram features extracted from each image, and training to generate a sparse representation dictionary;

160:计算模块,用于提取待分割的图像的灰度直方图特征,利用该灰度直方图特征,计算其在所训练的稀疏表示字典中的稀疏系数;160: a calculation module for extracting the grayscale histogram feature of the image to be segmented, and using this grayscale histogram feature to calculate its sparse coefficient in the trained sparse representation dictionary;

170:获取模块,用于根据计算得到的所述稀疏系数,从所述稀疏表示字典获取与其最接近的近似图像;170: an acquisition module, configured to acquire the closest approximate image from the sparse representation dictionary according to the calculated sparse coefficients;

180:赋值模块,用于从所述最优参数列表中获取所述近似图像的最优参数,并采用所述最优参数对狄利克雷混合模型的参数进行赋值;180: an assignment module, for obtaining the optimal parameters of the approximate image from the optimal parameter list, and using the optimal parameters to assign values to the parameters of the Dirichlet mixture model;

190:第二分割模块,用于利用赋值好参数的狄利克雷混合模型对待分割图像进行无监督图像分割,得到分割结果。190: The second segmentation module is used to perform unsupervised image segmentation on the image to be segmented by using the Dirichlet mixture model with assigned parameters to obtain a segmentation result.

在本实施例中,所述图像在灰度直方图的分布上选择具有差异性以及尽可能多的分布类型以增大样本量。In this embodiment, the distribution of the grayscale histogram of the image is different and as many distribution types as possible are selected to increase the sample size.

在本实施例中,在获得所述最优参数的过程中,通过人工判断分割结果,通过结合分割结果与对应分割标记的精度,判断参数是否达到最优,若不是最优,则继续修改参数直至分割结果最优。In this embodiment, in the process of obtaining the optimal parameters, the segmentation result is manually judged, and whether the parameters are optimal is determined by combining the segmentation results and the accuracy of the corresponding segmentation markers, and if not, the parameters are continued to be modified until the segmentation result is optimal.

在本实施例中,所述灰度直方图特征可选256维度的特征。In this embodiment, the grayscale histogram feature can be selected as a feature of 256 dimensions.

在本实施例中,所述稀疏字典不做缩减,每张图像都为一个类别。In this embodiment, the sparse dictionary is not reduced, and each image is a category.

本发明第三实施例还提供了一种基于稀疏表示的图像分割设备,包括存储器以及处理器,所述存储器内存储有计算机程序,所述处理器用于运行所述计算机程序以实现所述一种基于稀疏表示的图像分割方法。The third embodiment of the present invention also provides an image segmentation device based on sparse representation, including a memory and a processor, where a computer program is stored in the memory, and the processor is configured to run the computer program to implement the one A sparse representation-based image segmentation method.

本发明第四实施例还提供一种存储介质,所述存储介质存储有计算机程序,所述计算机程序能够被所述存储介质所在设备的处理器执行,以实现所述的一种基于稀疏表示的图像分割方法。A fourth embodiment of the present invention further provides a storage medium, where the storage medium stores a computer program, and the computer program can be executed by a processor of a device where the storage medium is located, so as to implement the sparse representation-based Image segmentation method.

综上所述,本发明通过收集大量的图像及其分割标记,然后,利用狄利克雷混合模型对所收集的图像进行无监督分割,分割过程中,通过人工调整和优化狄利克雷参数,确保每张图像的分割结果都是精度相对较高,并把每张图像的狄利克雷混合模型参数记录下来,下一步,将所收集图像组成一个字典去训练一个稀疏表示字典;当要使用狄利克雷混合模型去分割一张图像时,先用所训练的稀疏表示字典对该图像进行识别,辨认其与字典中哪张图像最像,提取待分割的图像的灰度直方图特征,计算其在所训练的稀疏表示字典中的稀疏系数,并用最像的那张图像对应的狄利克雷参数对本次分割中的狄利克雷参数进行赋值,最后利用赋值好参数的狄利克雷混合模型对待分割图像进行无监督图像分割,得到分割结果。本发明中狄利克雷混合模型的优化参数不需要人工调整,而是经过稀疏表示预测之后自动生成。To sum up, the present invention collects a large number of images and their segmentation marks, and then uses the Dirichlet mixture model to perform unsupervised segmentation on the collected images. During the segmentation process, the Dirichlet parameters are manually adjusted and optimized to ensure that the The segmentation result of each image is relatively high-precision, and the Dirichlet mixture model parameters of each image are recorded. Next, the collected images are formed into a dictionary to train a sparse representation dictionary; when using Dirichlet When the Lei mixture model is used to segment an image, first use the trained sparse representation dictionary to identify the image, identify which image in the dictionary is most similar to it, extract the grayscale histogram feature of the image to be segmented, and calculate its value in the image. The trained sparseness represents the sparse coefficients in the dictionary, and assigns the Dirichlet parameters in this segmentation with the Dirichlet parameters corresponding to the most similar image, and finally uses the Dirichlet mixture model with the assigned parameters to be segmented. The image is subjected to unsupervised image segmentation to obtain the segmentation result. The optimization parameters of the Dirichlet mixture model in the present invention do not need to be adjusted manually, but are automatically generated after being predicted by sparse representation.

尽管结合优选实施方案具体展示和介绍了本发明,但所属领域的技术人员应该明白,在不脱离所附权利要求书所限定的本发明的精神和范围内,在形式上和细节上可以对本发明做出各种变化,均为本发明的保护范围。Although the present invention has been particularly shown and described in connection with preferred embodiments, it will be understood by those skilled in the art that changes in form and detail may be made to the present invention without departing from the spirit and scope of the invention as defined by the appended claims. Various changes are made within the protection scope of the present invention.

Claims (10)

Translated fromChinese
1.一种基于稀疏表示的图像分割方法,其特征在于,包括以下步骤:1. an image segmentation method based on sparse representation, is characterized in that, comprises the following steps:收集一定数量的图像及其分割标记;Collect a certain number of images and their segmentation markers;基于所述分割标记,用狄利克雷混合模型对收集的图像进行无监督分割,并调整狄利克雷混合模型的参数,获得使每张图像的分割结果接近最优的最优参数;Based on the segmentation marks, unsupervised segmentation is performed on the collected images by using the Dirichlet mixture model, and the parameters of the Dirichlet mixture model are adjusted to obtain optimal parameters that make the segmentation result of each image close to the optimal;记录每张图像的最优参数,组成最优参数列表;Record the optimal parameters of each image to form an optimal parameter list;将每张图像转换为灰度图,并提取它们的灰度直方图特征;Convert each image to grayscale and extract their grayscale histogram features;将从每张图像提取的灰度直方图特征组成一个字典,训练生成一个稀疏表示字典;The grayscale histogram features extracted from each image are composed of a dictionary, and a sparse representation dictionary is generated by training;提取待分割的图像的灰度直方图特征,利用该灰度直方图特征,计算其在所训练的稀疏表示字典中的稀疏系数;Extract the grayscale histogram feature of the image to be segmented, and use the grayscale histogram feature to calculate its sparse coefficient in the trained sparse representation dictionary;根据计算得到的所述稀疏系数,从所述稀疏表示字典获取与其最接近的近似图像;Obtain the closest approximate image from the sparse representation dictionary according to the calculated sparse coefficient;从所述最优参数列表中获取所述近似图像的最优参数,并采用所述最优参数对狄利克雷混合模型的参数进行赋值;Obtain the optimal parameters of the approximate image from the optimal parameter list, and use the optimal parameters to assign values to the parameters of the Dirichlet mixture model;利用赋值好参数的狄利克雷混合模型对待分割图像进行无监督图像分割,得到分割结果。The unsupervised image segmentation is performed on the image to be segmented by using the Dirichlet mixture model with assigned parameters, and the segmentation result is obtained.2.根据权利要求1所述的一种基于稀疏表示的图像分割方法,其特征在于,所述图像在灰度直方图的分布上具有差异性以及多的分布类型。2 . The image segmentation method based on sparse representation according to claim 1 , wherein, the distribution of the gray histogram of the image has differences and many distribution types. 3 .3.根据权利要求1所述的一种基于稀疏表示的图像分割方法,其特征在于,在获得所述最优参数的过程中,结合分割结果与对应分割标记的精度,判断参数是否达到最优。3. A sparse representation-based image segmentation method according to claim 1, characterized in that, in the process of obtaining the optimal parameters, it is determined whether the parameters reach the optimal value by combining the segmentation results and the accuracy of the corresponding segmentation markers. .4.根据权利要求1所述的一种基于稀疏表示的图像分割方法,其特征在于,所述灰度直方图特征包括256维度的特征。4 . The sparse representation-based image segmentation method according to claim 1 , wherein the grayscale histogram features include features of 256 dimensions. 5 .5.一种基于稀疏表示的图像分割装置,其特征在于,包括:5. an image segmentation device based on sparse representation, is characterized in that, comprises:收集模块,用于收集一定数量的图像及其分割标记;A collection module for collecting a certain number of images and their segmentation markers;第一分割模块,用于基于所述分割标记,用狄利克雷混合模型对收集的图像进行无监督分割,并调整狄利克雷混合模型的参数,获得使每张图像的分割结果接近最优的最优参数;The first segmentation module is used to perform unsupervised segmentation on the collected images with the Dirichlet mixture model based on the segmentation mark, and adjust the parameters of the Dirichlet mixture model to obtain a segmentation result that makes each image close to the optimal optimal parameters;记录模块,用于记录每张图像的最优参数,组成最优参数列表;The recording module is used to record the optimal parameters of each image and form the optimal parameter list;提取模块,用于将每张图像转换为灰度图,并提取它们的灰度直方图特征;Extraction module for converting each image to grayscale and extracting their grayscale histogram features;训练模块,用于将从每张图像提取的灰度直方图特征组成一个字典,训练生成一个稀疏表示字典;The training module is used to form a dictionary from the grayscale histogram features extracted from each image, and train to generate a sparse representation dictionary;计算模块,用于提取待分割的图像的灰度直方图特征,利用该灰度直方图特征,计算其在所训练的稀疏表示字典中的稀疏系数;a calculation module, used to extract the grayscale histogram feature of the image to be segmented, and use the grayscale histogram feature to calculate its sparse coefficient in the trained sparse representation dictionary;获取模块,用于根据计算得到的所述稀疏系数,从所述稀疏表示字典获取与其最接近的近似图像;an obtaining module, configured to obtain the closest approximate image from the sparse representation dictionary according to the calculated sparse coefficient;赋值模块,用于从所述最优参数列表中获取所述近似图像的最优参数,并采用所述最优参数对狄利克雷混合模型的参数进行赋值;an assignment module, configured to obtain the optimal parameters of the approximate image from the optimal parameter list, and use the optimal parameters to assign values to the parameters of the Dirichlet mixture model;第二分割模块,用于利用赋值好参数的狄利克雷混合模型对待分割图像进行无监督图像分割,得到分割结果。The second segmentation module is used to perform unsupervised image segmentation on the image to be segmented by using the Dirichlet mixture model with assigned parameters to obtain segmentation results.6.根据权利要求5所述的一种基于稀疏表示的图像分割装置,其特征在于,所述图像在灰度直方图的分布上具有差异性以及多的分布类型。6 . The image segmentation device based on sparse representation according to claim 5 , wherein, the distribution of the grayscale histogram of the image has differences and many distribution types. 7 .7.根据权利要求5所述的一种基于稀疏表示的图像分割装置,其特征在于,在获得所述最优参数的过程中,结合分割结果与对应分割标记的精度,判断参数是否达到最优。7 . The image segmentation device based on sparse representation according to claim 5 , wherein, in the process of obtaining the optimal parameters, it is determined whether the parameters have reached the optimal value by combining the segmentation results and the accuracy of the corresponding segmentation markers. 8 . .8.根据权利要求5所述的一种基于稀疏表示的图像分割装置,其特征在于,所述灰度直方图特征包括256维度的特征。8 . The apparatus for image segmentation based on sparse representation according to claim 5 , wherein the grayscale histogram features include features of 256 dimensions. 9 .9.一种基于稀疏表示的图像分割设备,其特征在于,包括存储器以及处理器,所述存储器内存储有计算机程序,所述处理器用于运行所述计算机程序以实现如权利要求1-4任意一项所述的一种基于稀疏表示的图像分割方法。9. An image segmentation device based on sparse representation, characterized by comprising a memory and a processor, wherein a computer program is stored in the memory, and the processor is configured to run the computer program to implement any one of claims 1-4. A method for image segmentation based on sparse representation.10.一种存储介质,其特征在于,所述存储介质存储有计算机程序,所述计算机程序能够被所述存储介质所在设备的处理器执行,以实现如权利要求1-4任意一项所述的一种基于稀疏表示的图像分割方法。10. A storage medium, characterized in that, the storage medium stores a computer program, and the computer program can be executed by a processor of a device where the storage medium is located, so as to realize any one of claims 1-4. A sparse representation-based image segmentation method.
CN202010794337.XA2020-08-102020-08-10Image segmentation method, device and equipment based on sparse representation and storage mediumActiveCN111860547B (en)

Priority Applications (1)

Application NumberPriority DateFiling DateTitle
CN202010794337.XACN111860547B (en)2020-08-102020-08-10Image segmentation method, device and equipment based on sparse representation and storage medium

Applications Claiming Priority (1)

Application NumberPriority DateFiling DateTitle
CN202010794337.XACN111860547B (en)2020-08-102020-08-10Image segmentation method, device and equipment based on sparse representation and storage medium

Publications (2)

Publication NumberPublication Date
CN111860547Atrue CN111860547A (en)2020-10-30
CN111860547B CN111860547B (en)2023-04-18

Family

ID=72971788

Family Applications (1)

Application NumberTitlePriority DateFiling Date
CN202010794337.XAActiveCN111860547B (en)2020-08-102020-08-10Image segmentation method, device and equipment based on sparse representation and storage medium

Country Status (1)

CountryLink
CN (1)CN111860547B (en)

Citations (5)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
US20070047789A1 (en)*2005-08-302007-03-01Agfa-Gevaert N.V.Method of Constructing Gray Value or Geometric Models of Anatomic Entity in Medical Image
US20090208106A1 (en)*2008-02-152009-08-20Digitalsmiths CorporationSystems and methods for semantically classifying shots in video
US20100081931A1 (en)*2007-03-152010-04-01Destrempes FrancoisImage segmentation
CN102819747A (en)*2012-07-182012-12-12浙江农林大学Method for automatically classifying forestry service images
CN105321178A (en)*2015-10-122016-02-10武汉工程大学Image segmentation method and apparatus based on sparse principal component analysis

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
US20070047789A1 (en)*2005-08-302007-03-01Agfa-Gevaert N.V.Method of Constructing Gray Value or Geometric Models of Anatomic Entity in Medical Image
US20100081931A1 (en)*2007-03-152010-04-01Destrempes FrancoisImage segmentation
US20090208106A1 (en)*2008-02-152009-08-20Digitalsmiths CorporationSystems and methods for semantically classifying shots in video
CN102819747A (en)*2012-07-182012-12-12浙江农林大学Method for automatically classifying forestry service images
CN105321178A (en)*2015-10-122016-02-10武汉工程大学Image segmentation method and apparatus based on sparse principal component analysis

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
LI SHEN 等: "A Semisupervised Latent Dirichlet Allocation Model for Object-Based Classification of VHR Panchromatic Satellite Images"*
ZIYI CHEN 等: "Corse-to-Fine Road Extraction Based on Local Dirichlet Mixture Models and Multiscale-High-Order Deep Learning"*
李璐: "基于t混合模型的脑部核磁共振图像分割方法研究"*

Also Published As

Publication numberPublication date
CN111860547B (en)2023-04-18

Similar Documents

PublicationPublication DateTitle
CN108345911B (en) Surface defect detection method of steel plate based on multi-level features of convolutional neural network
CN112507901B (en)Unsupervised pedestrian re-identification method based on pseudo tag self-correction
CN113159048A (en)Weak supervision semantic segmentation method based on deep learning
CN117611932B (en)Image classification method and system based on double pseudo tag refinement and sample re-weighting
CN114155213A (en) Chip defect detection method and device based on active learning
CN111860596B (en) Unsupervised road crack classification method and model establishment method based on deep learning
CN108595558B (en)Image annotation method based on data equalization strategy and multi-feature fusion
CN113642655B (en)Small sample image classification method based on support vector machine and convolutional neural network
CN114998202B (en) A Semi-Supervised Deep Learning Defect Detection Method
CN106709421B (en)Cell image identification and classification method based on transform domain features and CNN
CN114492581A (en)Method for classifying small sample pictures based on transfer learning and attention mechanism element learning application
CN114202694A (en)Small sample remote sensing scene image classification method based on manifold mixed interpolation and contrast learning
CN119313928B (en) Intelligent identification system and method for violations at new energy stations based on machine vision
CN106157330A (en)A kind of visual tracking method based on target associating display model
CN114049541B (en) Visual scene recognition method based on structured information feature decoupling and knowledge transfer
CN111652265A (en) A Robust Semi-Supervised Sparse Feature Selection Method Based on Self-Adjusting Graphs
CN112734037A (en)Memory-guidance-based weakly supervised learning method, computer device and storage medium
CN117541562A (en)Semi-supervised non-reference image quality evaluation method based on uncertainty estimation
CN114187506A (en)Remote sensing image scene classification method of viewpoint-aware dynamic routing capsule network
CN119152502A (en)Landscape plant image semantic segmentation method based on weak supervision
CN118570447A (en)Feature balance-based remote sensing image fine-grained target detection method and system
CN116012903B (en) A method and system for automatically labeling facial expressions
CN114998585B (en) Open-world semantic segmentation method and device based on region-aware metric learning
CN115019183B (en)Remote sensing image model migration method based on knowledge distillation and image reconstruction
CN119049113B (en) A facial expression recognition method integrating uncertainty estimation and active learning

Legal Events

DateCodeTitleDescription
PB01Publication
PB01Publication
SE01Entry into force of request for substantive examination
SE01Entry into force of request for substantive examination
GR01Patent grant
GR01Patent grant

[8]ページ先頭

©2009-2025 Movatter.jp