CN111539966A - Colorimetric sensor array image segmentation method based on fuzzy c-means clustering - Google Patents

Colorimetric sensor array image segmentation method based on fuzzy c-means clustering Download PDF

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CN111539966A
CN111539966A CN202010301194.4A CN202010301194A CN111539966A CN 111539966 A CN111539966 A CN 111539966A CN 202010301194 A CN202010301194 A CN 202010301194A CN 111539966 A CN111539966 A CN 111539966A
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侯瑞
赵云灏
胡阳
李春阳
刘心社
苏凤宇
周伟
费怀胜
刘伟鹏
邓清闯
张小伟
任羽圻
方苏婉
袁梦
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North China Electric Power University
Xuchang Xuji Wind Power Technology Co Ltd
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Xuchang Xuji Wind Power Technology Co Ltd
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Abstract

The invention discloses a colorimetric sensor array image segmentation method based on fuzzy c-means clustering, which comprises the following steps of: determining initial clustering centers and clustering numbers through gray level distribution histogram information of an image, initially segmenting the image to obtain a plurality of regions, marking the regions, determining adjacent relations among the regions to establish a region adjacency graph, calculating integral distance measurement among the regions according to gray level differences and boundary gradients among adjacent regions to obtain weights of all sides in the region adjacency graph, combining the regions capable of being combined into a multi-branch tree structure according to the weights and the areas among the regions to obtain a final segmentation result, and completing the colorimetric sensor array image segmentation method based on fuzzy c-means clustering.

Description

Colorimetric sensor array image segmentation method based on fuzzy c-means clustering
Technical Field
The invention relates to a colorimetric sensor array image segmentation method, in particular to a colorimetric sensor array image segmentation method based on fuzzy c-means clustering.
Background
Image segmentation is an important image segmentation technique. The narrow image processing to image analysis is a key step. Its main purpose is to divide the image into several meaningful areas with different features according to the features in the image. Image segmentation plays an important role in image engineering. On one hand, the method extracts information from an original image, converts the image into more abstract and compact data, and has important influence on subsequent various data measurement. On the other hand, data obtained by image segmentation is the basis of parameter measurement, feature extraction and target expression, and higher-level image processing techniques such as image analysis and image understanding are made possible.
With the advent of the digital age, most of image information can be stored in the form of digital information, which is an integral part of electronic images. The essence of the electronic image is a series of coding matrices, each representing the value of an attribute of a pixel. Thus, the process of image segmentation is essentially a process of classifying elements having different attributes. The clustering analysis can classify the same attribute, distinguish different attributes and is suitable for image segmentation. In addition, clustering analysis does not require much prior knowledge in segmenting the image; it segments the image according to the properties of the image itself.
In the process of segmenting a real image, the problem of pixel inconsistency between different areas often occurs, which indicates that the image segmentation has ambiguity. The fuzzy set theory can well describe the fuzziness in the array image segmentation, and is beneficial to solving the fuzzy problem in the array image segmentation. Therefore, the blur set theory is gradually applied to image segmentation.
The traditional colorimetric sensor array image segmentation algorithm is low in efficiency and automation degree, has the problem of noise sensitivity, is easily interfered by the environment and is poor in segmentation effect.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a colorimetric sensor array image segmentation method based on fuzzy c-means clustering, which can segment a colorimetric sensor array image and has the advantages of good segmentation effect, high segmentation efficiency and high automation degree.
In order to achieve the above purpose, the method for segmenting the colorimetric sensor array image based on the fuzzy c-means clustering comprises the following steps:
determining an initial clustering center and a clustering number through gray distribution histogram information of an image, performing initial segmentation on the image to obtain a plurality of regions, marking each region, determining an adjacent relation between the regions to establish a region adjacency graph, calculating integral distance measurement between the regions according to gray difference and boundary gradient between adjacent regions to obtain weight of each side in the region adjacency graph, combining the regions capable of being combined into a multi-branch tree structure according to the weight and the area between the regions to obtain a final segmentation result, and completing the colorimetric sensor array image segmentation method based on fuzzy c-means clustering.
And performing initial segmentation on the image based on the FCM algorithm.
The region adjacency graph represents the relationship between regions, and is defined as an undirected graph G, i.e.
G＝(V,E,W) (12)
Wherein, V is the set of all regions in the image, E is the edge set of each region in the image, and W is the weight set of all region edges in the image.
Dividing different peak value areas in the pixel set into different clusters according to information of the gray level distribution histogram to determine the number c of the clusters, then determining an initial clustering center by calculating the gray level of the clusters, finally inputting the number c of the clusters and the initial clustering center into an FCM algorithm, and initially segmenting the image through the FCM algorithm to finish the initial segmentation of the image.
N vectors xjAre divided into c groups GjClustering is carried out, and the target function of the FCM algorithm is as follows:
Figure BDA0002454049840000031
wherein, ciAnd (4) representing the clustering center of the ith group, and obtaining the best clustering result when J obtains the minimum value.
The membership between each sample vector and the final set is represented by a c × n two-dimensional matrix U, where the membership U between the jth vector and the ith setijThe expression of (a) is:
Figure BDA0002454049840000032
the normalization constraint conditions are satisfied as follows:
Figure BDA0002454049840000033
Figure BDA0002454049840000034
c is minimized in the formula (1)iExpressed by the lagrange multiplier method as:
Figure BDA0002454049840000035
the target function of the FCM algorithm is converted to:
Figure BDA0002454049840000036
wherein u isijRepresenting the membership of point j as cluster i, ciRepresenting the clustering center of the ith group, wherein m is a weighting index, and constructing a Lagrange multiplier equation of the target function shown in the formula (7) according to known conditions;
Figure BDA0002454049840000041
the requirement for minimizing formula (6) from formula (7) is:
Figure BDA0002454049840000042
Figure BDA0002454049840000043
the output result of the FCM algorithm is a c cluster central vector and a c multiplied by n fuzzy membership matrix.
For a colorimetric sensor array image, all pixels in each gray scale image are a sample set, the gray scale value of each pixel in the image is the characteristic of a sample point, and the whole sample set is a one-dimensional directionQuantity xj(j ═ 1.. times, n), so the image segmentation problem translates into an optimization problem for the FCM objective function as shown in equation (10);
Figure BDA0002454049840000044
the constraint conditions of the optimization problem are as follows:
Figure BDA0002454049840000045
wherein m is a weighting index of membership degree, n is the number of pixels of the image to be segmented, uijIs a cluster i of pixels xjThe similarity measure is Euclidean distance of gray values between pixels and a clustering center, and a membership matrix U is { U ═ U {ijC × n matrix, and a clustering center matrix V ═ V1,v2,...,vcIs a 1 × c matrix.
The invention has the following beneficial effects:
the colorimetric sensor array image segmentation method based on fuzzy c-means clustering determines initial clustering centers and clustering numbers according to gray distribution histogram information of images during specific operation so as to improve the efficiency and the automation degree of image segmentation, then establishes a region adjacency graph, calculates integral distance measurement among regions according to gray difference and boundary gradient between adjacent regions to obtain the weight of each side in the region adjacency graph, and finally merges the regions capable of being merged into a multi-branch tree structure according to the weight and the area between the regions to obtain a final segmentation result so as to solve the problem of noise-sensitive image segmentation and improve the image segmentation effect.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2a is a graph of the segmentation effect of the Original graph;
FIG. 2b is a graph showing the segmentation effect of the Noise image;
FIG. 2c is a graph of the FCM segmentation effect;
FIG. 2d is a graph of the effect of the FCMS1 on segmentation;
FIG. 2e is a graph of the effect of the FCMS2 on segmentation;
FIG. 2f is a diagram of the effect of the segmentation of the NW-FCM;
FIG. 2g is a graph showing the segmentation effect of the present invention;
FIG. 3 is a PSNR graph of a noise-synthesized image;
FIG. 4 is a MSSIM graph of a noise-synthesized image;
FIG. 5 is a PSNR graph of a noisy natural image;
fig. 6 is a graph of a noisy natural image MSSIM.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
the image segmentation method based on fuzzy c-means clustering (FCM) is characterized in that when the image segmentation method based on fuzzy c-means clustering (FCM) is operated specifically, an image is segmented to obtain a plurality of regions based on the current FCM, meanwhile, the segmentation result of the FCM is used as initial segmentation, then, each region is marked, the adjacent relation between the regions is determined, a region adjacent map is established, integral distance measurement between the regions is calculated according to the gray difference and the boundary gradient between the adjacent regions, the weight of each edge in the region adjacent map is obtained, finally, the regions capable of being combined are combined into a multi-branch tree structure according to the weight and the area between the regions, and the adjacent regions meeting the conditions are combined to obtain the final segmentation result.
The method avoids manual participation of the traditional FCM algorithm, reduces calculation iteration on the basis of the original algorithm, improves calculation efficiency, obtains the number of clusters with reference significance, and has the advantages that test results show that the method can better describe fuzzy information in the image, avoids pixel classification problems, utilizes an exponential function to control influence weights of adjacent pixels, realizes adaptive weighting of pixel gray, improves calculation accuracy of the pixel gray, and realizes image segmentation.
FCM algorithm
The FCM algorithm is a clustering-based partitioning method, and the core of the method is to improve the similarity between objects in the same cluster to the maximum extent, while the similarity between different clusters is minimum. The FCM algorithm is an improvement of the K-means algorithm, the K-means algorithm is difficult to divide, and the FCM algorithm is flexible to divide.
In the FCM algorithm, the number of clusters c and a parameter m need to be determined in advance, firstly, different peak value areas in a pixel relative set are divided into different clusters through information of a gray level distribution histogram, so that the number of clusters c is determined, in addition, the center of an initial cluster is determined through calculating the gray level value of the cluster, then, the calculation result is used as the input of the FCM algorithm, the cluster division of the FCM is completed, and the FCM algorithm completes the cluster division of the FCM by enabling n vectors x to be inputj(1, 2.. n.) is divided into c groups Gj(i 1, 2.., c) clustering, the objective function of which is:
Figure BDA0002454049840000071
wherein, ciAnd (4) representing the clustering center of the ith group, and obtaining the optimal clustering result when J obtains the minimum value.
The membership between each sample vector and the final set is represented by a c × n two-dimensional matrix U, where the membership U between the jth vector and the ith setijThe expression of (a) is:
Figure BDA0002454049840000072
the normalization constraint conditions are satisfied as follows:
Figure BDA0002454049840000073
Figure BDA0002454049840000074
c minimized in formula (1)iObtained by the Lagrange multiplier method, i.e.
Figure BDA0002454049840000075
The objective function of the FCM algorithm is:
Figure BDA0002454049840000081
in formula (6), uijRepresenting the membership of the point j to the cluster i, ciRepresenting the clustering center of the ith group, wherein m is a weighting index, and constructing a Lagrange multiplier equation of the target function shown in the formula (7) according to known conditions;
Figure BDA0002454049840000082
the requirement for minimizing formula (6) from formula (7) is:
Figure BDA0002454049840000083
Figure BDA0002454049840000084
the output of the FCM algorithm is a c cluster center vector and a c multiplied by n fuzzy membership matrix, and the FCM algorithm uses a fuzzy method to express membership information, so that the membership matrix can more accurately reflect the membership of a sample point, and the cluster center reflects the main characteristics of a class and can also be used as a representative point of the whole class.
Application of FCM algorithm in colorimetric column sensor array image segmentation
During image processing, all pixels in each grayscale image are a sample set. The gray value of each pixel in the image is the characteristic of a sample point, and the whole sample set is a one-dimensional vector xj(j ═ 1.. times, n), therefore, the image segmentation problem can be converted into an optimization problem of the FCM objective function as shown in equation (10);
Figure BDA0002454049840000091
the constraint conditions of the optimization problem are as follows:
Figure BDA0002454049840000092
wherein m is a weighting index of membership degree, n is the number of pixels of the image to be segmented, uijIs a cluster i of pixels xjThe similarity measure is Euclidean distance of gray values between pixels and a clustering center, and a membership matrix U is { U ═ U {ijC × n matrix, and a clustering center matrix V ═ V1,v2,...,vcIs a 1 × c matrix.
The FCM algorithm needs to iterate continuously to converge the objective function to an optimal value, thereby obtaining a final clustering result.
When the initial value is closer to the result of iterative convergence, the iteration times can be greatly reduced, the probability of convergence to the optimal global solution can be increased, otherwise, the calculation complexity is increased, and the optimal local solution is more likely to be trapped, so that the selection of a proper cluster center initial value has an important influence on the FCM process and the result. In the absence of prior knowledge, in many applications, the initial cluster center value can only be determined by a random method, and in colorimetric sensor array image segmentation, it is obviously difficult to obtain a proper initial cluster center value, which inevitably affects the segmentation efficiency of the FCM algorithm.
The colorimetric sensor is used for processing adjacent pixels of the image to generate an influence matrix of the adjacent pixels, and each element in the influence matrix has a degree, namely, the corresponding pixel of the influence matrix is influenced by the adjacent pixels. Then, the influence matrix is called in each calculation to obtain the influence of the adjacent pixels, so that multiple calculations on the adjacent pixels are avoided, two filtering algorithms are usually used for calculating the adjacent pixels, one algorithm (FCMS1) uses mean filtering and the other algorithm (FCMS2) uses median filtering, the two algorithms both obtain good segmentation effect, and the segmentation efficiency of the algorithms is improved.
Analysis of FCM image segmentation
In order to overcome the defect that the image segmentation result of the colorimetric sensor array based on global information is easy to generate over-segmentation, on the basis of the existing FCM algorithm, a merging strategy of segmented regions is provided by using local information among the regions, the invention provides an improved FCM algorithm based on region merging, a flow chart of the improved algorithm is shown in figure 1, in the region merging technology, an effective method for representing the relationship among the regions by a weighted region adjacency graph is defined as an undirected graph G, and specifically comprises the following steps:
G＝(V,E,W) (12)
wherein, V is a set of all regions in the image, called a vertex set, E is an edge set of each region in the image, called an edge set, and W is a weight set of edges of all regions in the image. Calculating the weight of a pair of region edges to be larger than 0 according to the characteristics between the regions, wherein the weighted region adjacency graph can be represented by a matrix, and the specific process is as follows:
firstly, creating a mark matrix with the same size as an image, and calling the mark matrix as a label; each 4-connected region in the initial segmentation image is marked, the first connected region is marked as 1, the second connected region is marked as 2, v regions are obtained in the same way, and the value of each coordinate in the label is the label number corresponding to the coordinate in the image, for example, when the image size is M × N, the label size is M × N, and the pixel with the coordinate (ij) in the image is marked as belonging to the second region, the value at the coordinate (G) in the label is l.
And then, calculating an adjacency matrix by using the mark matrix, wherein the processing methods are similar in a 4-connected region including upper and lower adjacency and left and right adjacency, and table 1 shows that the detection and storage methods of the upper and lower adjacent regions are described in detail by using pseudo codes, and the processing of the left and right adjacent regions is similar.
TABLE 1
Figure BDA0002454049840000101
Figure BDA0002454049840000111
In the pseudo code, the Label matrix is an M × N matrix, the maximum value of the M × N matrix is v, the V areas in the image are represented, and the Label1 intercepts the first row to the (M-1) th row of the Label matrix, namely the upper half part of the matrix; similarly, label2 intercepts the second to M-th rows of the tag matrix, i.e., the lower half of the matrix, then finds the upper and lower neighboring regions through mismatch alignment, the processing of the left and right neighboring regions is similar to the processing of the upper and lower neighboring regions, changes the second and third rows of the pseudo code, and intercepts the first to (N-1) -th columns and the second to N-th columns of the tag matrix, respectively, then the pseudo codes 8 and 9 become vall ═ label (i, j) and val2 ═ label (i, j +1), respectively, and finally, runs 2 to 11 rows to detect and record the left and right neighboring regions in the matrix a.
The validity of the algorithm is verified through a segmentation experiment on a composite image and a physical image, and compared with a traditional FCM algorithm, an FCMS1 algorithm, an FCMS2 algorithm and an NW-FCM algorithm, in the experiment, m is 2, a neighborhood of other improved methods uses a 5 x 5 neighborhood slider with the radius r being 2, the neighborhood radius r is the distance from a neighborhood center to a neighborhood boundary, penalty factors of the FCMS1, the FCMS2 and the NW-FCM are alpha 5, noise added in the experiment is predicted to be 0, the variance is 0.01 Gaussian noise or salt and pepper noise, a composite chessboard image part is used for the segmentation experiment, and the Gaussian noise is added in a black-white-gray grid. The results of the experiments on FCM, FCMS1, FCMS2, NW-FCM and the present invention are shown in FIGS. 2a to 2 g.
As shown in fig. 2c, since the conventional FCM clustering algorithm lacks the addition of spatial information, a large amount of noise still exists after segmentation. Although the FCMS1 algorithm considers the influence of neighboring pixels, the method of directly calculating the neighborhood mean is adopted, so there is much noise at the intersection of different gray values and different image differences, as shown in fig. 2d, and the segmentation effect is relatively not ideal. As shown in fig. 2e, 2f and 2g, the segmentation effect of the FCMS2, NW-FCM and the present invention on the artificially synthesized image is ideal, but the segmentation effect of the present invention is most prominent with almost no residual noise, as shown in fig. 3 to 6.
Table 2 shows the result data of FCM, FCMs1, FCMs2, and NW-FCM, and the result data when the checkerboard image including gaussian noise is divided according to the present invention, where Vpc is the division coefficient, Vpe is the division entropy, and SA is the division accuracy in table 2.
TABLE 2
Algorithm Vpc Vpe SA Time consumption of 30 executions
FCM 0.9640 0.0411 0.9598 11.610
FCMS1 0.8600 0.1180 0.9490 6.500
FCMS2 0.9430 0.0463 0.9961 5.979
NW-FCM 0.9613 0.0395 0.9970 12.568
The invention 0.9724 0.0217 0.9998 18.467
As can be seen from table 2, the FCM and FCMs1 algorithms have weak segmentation effect and accuracy, while FCMs2, NW-FCM and the present invention have ideal segmentation effect, the present invention has the best segmentation effect, and as can be seen from time consumption, the present invention has longer calculation time in neighborhood processing and longer operation time than other algorithms.
It will be appreciated by those skilled in the art that the invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The embodiments disclosed above are therefore to be considered in all respects as illustrative and not restrictive. All changes which come within the scope of or equivalence to the invention are intended to be embraced therein.

Claims (7)

1. A colorimetric sensor array image segmentation method based on fuzzy c-means clustering is characterized by comprising the following steps:
determining an initial clustering center and a clustering number through gray distribution histogram information of an image, performing initial segmentation on the image to obtain a plurality of regions, marking each region, determining an adjacent relation between the regions to establish a region adjacency graph, calculating integral distance measurement between the regions according to gray difference and boundary gradient between adjacent regions to obtain weight of each side in the region adjacency graph, combining the regions capable of being combined into a multi-branch tree structure according to the weight and the area between the regions to obtain a final segmentation result, and completing the colorimetric sensor array image segmentation method based on fuzzy c-means clustering.
2. The method of image segmentation for colorimetric sensor arrays based on fuzzy c-means clustering as claimed in claim 1, wherein the image is initially segmented based on the FCM algorithm.
3. The method of claim 2, wherein the region adjacency graph represents the relationship between regions, and the region adjacency graph is defined as an undirected graph G (that is, an undirected graph)
G＝(V,E,W) (12)
Wherein, V is the set of all regions in the image, E is the edge set of each region in the image, and W is the weight set of all region edges in the image.
4. The colorimetric sensor array image segmentation method based on fuzzy c-means clustering of claim 2, wherein the different peak regions in the pixel set are divided into different clusters according to the information of the gray distribution histogram to determine the number c of the clusters, then the initial clustering center is determined by calculating the gray value of the clusters, finally the number c of the clusters and the initial clustering center are input into the FCM algorithm, and the initial segmentation of the image is performed through the FCM algorithm to complete the initial segmentation of the image.
5. The method of claim 3, wherein n vectors x are divided intojAre divided into c groups GjClustering is carried out, and the target function of the FCM algorithm is as follows:
Figure FDA0002454049830000021
wherein, ciAnd (4) representing the clustering center of the ith group, and obtaining the best clustering result when J obtains the minimum value.
6. The method of claim 5, wherein the membership between each sample vector and the final group is represented by a c × n two-dimensional matrix U, wherein the membership between the jth vector and the ith group UijThe expression of (a) is:
Figure FDA0002454049830000022
the normalization constraint conditions are satisfied as follows:
Figure FDA0002454049830000023
Figure FDA0002454049830000024
c is minimized in the formula (1)iExpressed by the lagrange multiplier method as:
Figure FDA0002454049830000025
the target function of the FCM algorithm is converted to:
Figure FDA0002454049830000026
wherein u isijRepresenting the membership of point j as cluster i, ciRepresenting the clustering center of the ith group, wherein m is a weighting index, and constructing a Lagrange multiplier equation of the target function shown in the formula (7) according to known conditions;
Figure FDA0002454049830000031
the requirement for minimizing formula (6) from formula (7) is:
Figure FDA0002454049830000032
Figure FDA0002454049830000033
the output result of the FCM algorithm is a c cluster central vector and a c multiplied by n fuzzy membership matrix.
7. The method of claim 5, wherein for the colorimetric sensor array image, all pixels in each gray scale image are a sample set, the gray scale value of each pixel in the image is a feature of a sample point, and the whole sample set is a one-dimensional vector xj(j ═ 1.. times, n), so the image segmentation problem translates into an optimization problem for the FCM objective function as shown in equation (10);
Figure FDA0002454049830000034
the constraint conditions of the optimization problem are as follows:
Figure FDA0002454049830000035
wherein m is a weighting index of membership degree, n is the number of pixels of the image to be segmented, uijIs a cluster i of pixels xjThe similarity measure is Euclidean distance of gray values between pixels and a clustering center, and a membership matrix U is { U ═ U {ijC × n matrix, and a clustering center matrix V ═ V1,v2,...,vcIs a 1 × c matrix.
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CN112801949A (en) * 2021-01-15 2021-05-14 国网江苏省电力有限公司电力科学研究院 Method and device for determining discharge area in ultraviolet imaging detection technology
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