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In daily life, there are many things more or less have ambiguity, although elusive, but is very important. Fuzzy theory emphasizes that fuzzy logic is used to describe things in real life to make up for the shortcoming that binary logic cannot describe things with undefined boundaries. The expression of human natural language is very fuzzy, and it is difficult to describe things in real life with binary logic. Therefore, the fuzzy theory uses the definition of fuzzy set to deal with the fuzzy concept, and fuzzy quantifies the membership function of an event belonging to a certain degree of set to get the membership degree. Fuzzy clustering is to use the method of fuzzy mathematics to quantify the fuzzy relations between samples, so as to cluster objectively and accurately, so that the data differences between various classes should be as large as possible, and the data differences between classes should be as small as possible, that is, to minimize the similarity between classes and maximize the similarity within classes. Fuzzy C means is one of the most widely used and successful fuzzy clustering methods. It obtains the membership degree of each sample point to all class centers by optimizing the objective function, and then determines the class of the sample point to achieve the purpose of sample classification. 2. Application of Fuzzy Theory In 1965, Professor Zadeh proposed the famous fuzzy set theory and created a new subject – fuzzy mathematics, mainly including fuzzy set theory, fuzzy logic, fuzzy reasoning and fuzzy control and other aspects of the content. Fuzzy set theory is a generalization of traditional set theory, which can better describe the fuzziness of human vision. Fuzzy set theory can be used in all levels of pattern recognition. Fuzzy theory mainly solves the uncertainty problems caused by incomplete, inaccurate, ambiguous and contradictory information at different levels of pattern recognition. 2.1 Fuzzy Clustering Theory Based on the characteristics of fuzzy set, fuzzy clustering method emerged at the historic moment. Clustering is to divide a set of samples with a given unknown class label into multiple internal categories, so that the samples in the same category have a high degree of similarity, while the samples in different classes differ greatly. The purpose of cluster analysis is to reveal and characterize the internal structure of data, and its content involves statistics, biology, machine learning and other research fields, and has been widely used in pattern recognition, data analysis and mining, image processing and other fields. In 1973, J.C. Bezdek proposed the landmark fuzzy C-means clustering algorithm (FCM)[1], which not only made the criterion function differentiable, but also softened the attribution of modes by introducing the membership degree of samples to the cluster center. Among many fuzzy clustering algorithms, FCM algorithm is the most widely used and more successful. It obtains the membership degree of each sample point to all class centers by optimizing the objective function, so as to determine the class of the sample point and achieve the purpose of automatic classification of sample data. According to the number of clustering C and a set of data xk containing N L-dimensional vectors, the FCM algorithm is used to output the membership degree UIj of elements, which represents the probability that data Xj belongs to the ith class. It can be obtained by finding the minimum value of the objective function of the following equation (1), usually m=2.
FCM algorithm is superior to the traditional hard c-means clustering algorithm in that the membership degree can be continuously valued at the interval of [0,1]. Considering the “either-either-other” nature of samples belonging to various classes, FCM algorithm can classify data sets with overlapping samples between classes, and has good convergence. Moreover, FCM algorithm has low complexity and is easy to implement. However, FCM also has shortcomings, such as the objective function is easy to fall into the local minimum in the iterative process, the function convergence speed is slow, sensitive to the initial value, noise and so on. From the analysis of the meaning of membership degree and division trend of fuzzy C-means clustering partition matrix, an algorithm that can improve the performance of FCM — IFCM algorithm is discussed below. Before that, a new concept, intuitionistic fuzzy sets, needs to be introduced.
2.2 Intuitive fuzzy clustering theory
2.2.1 Introduction to intuitionistic fuzzy sets
Intuitionistic fuzzy sets (IFS), as an important extension of fuzzy sets, describe the fuzzy properties of the objective world in A more delicate way by adding new attribute parameters — non-membership γ and uncertainty π. It is assumed that intuitionistic fuzzy sets A represent sample X and domain x ={x1,x2… , the relation of xn} can be:
To sum up, the algorithm steps of IFCM can be summarized as follows:
1) The first step is the same as FCM. Firstly, define a criterion function, select C initial clustering centers or initialize a random membership matrix (iterative initial conditions).
2) The membership matrix is changed into fuzzy membership matrix by introducing uncertainty parameters.
3) The fuzzy membership matrix is used to calculate the distance between the samples and the cluster center, and the samples are divided into various classes.
4) Recalculate the clustering center of each class and the distance from the sample to the clustering center. Intuitionistic fuzzy membership matrix is used to replace the original membership matrix in each calculation, and the samples are re-divided into various classes.
5) Repeat steps 2, 3, and 4 until the criterion function minimizes or reaches the specified threshold.
6) For image segmentation, the clustering center after iteration is mapped to various image information, such as gray value, so as to achieve the classification of gray value of each pixel of the image.
3. Image segmentation based on fuzzy clustering
3.1 Overview of image segmentation
Image segmentation is to subdivide an image into objects or sub-regions that constitute it. These regions are mutually disjoint, and each region satisfies the consistency of a specific region. The degree of segmentation mainly depends on the problem people want to solve. When the area or object of interest has been distinguished, segmentation is completed. Image segmentation is an important problem in image processing and a classic problem in computer vision research. Image understanding in computer vision, including target detection, feature extraction and target recognition, depends on the quality of segmentation.
At present, image segmentation algorithms are generally designed around two basic characteristics of brightness value: discontinuity and similarity. The application of the discontinuity of brightness value is mainly based on the discontinuous change of pixel characteristics (such as gray value) to segment images, such as the most common edge detection. By taking advantage of the similarity of brightness values, a mechanism can be formed to segment images into similar regions according to pre-specified criteria. Some examples include threshold processing, region separation, region growth, and clustering. The advantage of fuzzy C-means clustering and its extended algorithm for image segmentation is to avoid the problem of threshold setting, the clustering process does not need manual intervention, just input the expected number of classification can achieve automatic image segmentation.
3.2 Significance of fuzzy membership matrix in image segmentation
In image segmentation, fuzzy membership degree can be used to represent the degree to which a pixel in a gray image belongs to a gray value center. Therefore, it is only necessary to find the maximum membership degree of a pixel to a gray value center to divide the pixel into the region of the gray level. For gray image segmentation, the calculation formula of fuzzy membership can be written as:
Second, the remark
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