Multi-objective Evolutionary Fuzzy Clustering For Image Segmentation

With the rapid development of science and technology,images have become an indispensable medium of information transmission in people's work and life.The purpose of image segmentation is to extract important objects from images,and the results of image segmentation have direct influence on the subsequent image processing and understanding.Hence,image segmentation is a critical and essential component of image analysis systems.Considering the complexity of the real world situations and the diversity of data,this paper combines the fuzzy clustering theory to convert image segmentation into multi-objective problems.Evolutionary algorithms are utilized to deal with multi-objective fuzzy clustering for image segmentation in this paper,because of its excellent performance on multi-objective problems.The main works of this paper are listed as follows:(1)A multi-objective evolutionary fuzzy clustering for image segmentation is proposed.Image segmentation is converted into multi-objective fuzzy clustering.The fitness functions of the multi-objective problem are to preserve image details and restrain noise.The decomposition strategy based on weighted sum approach is utilized to decompose the multi-objective fuzzy clustering problem into several single objective fuzzy clustering problems.Each single objective fuzzy clustering problem has a one-to-one weight vector to control the balance between preserving image details and restraining noise.Optimizing all the single objective fuzzy clustering problems by evolutionary algorithms simultaneously,a trade-off between preserving image details and restraining noise can be obtained.In order to speed up the convergence of the algorithm,a mixed population initialization is designed,and oppositionbased learning is introduced into multi-objective optimization.Through the segmentation experiments on different types of images,it demonstrates that this work can obtain segmentation results with preserving image details and removing noise.(2)A two-layer evolutionary fuzzy clustering framework for image segmentation is proposed.It consists of multi-objective optimization layer and fuzzy clustering segmentation layer.In multi-objective optimization layer,an inhomogeneity measure based sampling is presented.The multi-objective fuzzy clustering based on sampling pixels is to preserve image details while removing noise.Considering the complexity of the real world situations,the decomposition strategy based on Tchebycheff approach is utilized to decompose multiobjective fuzzy clustering problem into several single objective fuzzy clustering problems.All the single objective fuzzy clustering problems are optimized by evolutionary algorithms simultaneously,and a trade-off can be obtained.The corresponding weight vector of the obtained trade-off can balance the relationship between preserving image details and removing noise.In fuzzy clustering segmentation layer,on the basis of the trade-off output by multi-objective optimization layer,an improved fuzzy c-means algorithm with local information and an adaptive evolutionary fuzzy clustering algorithm are proposed to deal with the single objective fuzzy clustering with local information for whole image segmentation,respectively.The improved fuzzy c-means algorithm with local information is able to obtain segmentation results of removing noise within a relatively short span of time.The adaptive evolutionary fuzzy clustering algorithm with local information spends relatively high optimization cost to achieve better segmentation performance.Compared with the previous work,the multi-objective fuzzy clustering of this work is only for inhomogeneous pixels.It is helpful for reducing the cost of multi-objective optimization.Furthermore,the decomposition based on Tchebycheff approach is applicable to both convex and non-convex cases.It is helpful for increasing the universality of the work.The experiments demonstrate that this work can achieve well segmentation performance of removing noise and preserving details of edges and regions on different types of images.(3)A multi-objective evolutionary sampling is proposed.It converts pixel sampling problem into multi-objective problem to maintain image information while reducing numbers of sampling pixels.The fitness function to maintain image information contributes to ensure the performance of subsequent image processing.The fitness function to reduce numbers of sampling pixels is helpful for reducing the cost of subsequent image processing.An adaptive evolutionary algorithm is utilized to optimize the multi-objective problem for sampling pixel.A simple ensemble method is adopted to obtain the final sampling result from several Pareto solutions.By sampling experiments on different types of images,it indicates that this work can obtain as few sampling pixels as possible under the premise of maintaining image information.(4)To deal with image segmentation without prior information about exact number of segments,a multi-objective evolutionary fuzzy clustering is proposed on the basis of multiobjective evolutionary sampling.Global fuzzy compactness and fuzzy separation are the fitness functions of multi-objective problem.To enhance the performance of fuzzy clustering,local and non-local information derived from observed image are introduced into global fuzzy compactness term.Meanwhile,the weight vector to control the balance between local and non-local information are introduced into the multi-objective optimization.To enhance the searching ability of the algorithm,a directed mutation operator and individual repair s-trategy are designed.In order to select the appropriate Pareto solution,local and non-local information was introduced into the index to select solutions.Then the fuzzy clustering result,which is suitable for observed image,can be acquired.By performing on different types of images,it verifies that this work can obtain suitable fuzzy clustering results and numbers of segments for observed images.(5)On the basis of the previous multi-objective evolutionary fuzzy clustering,an improved fuzzy c-means algorithm with local and non-local information and an evolutionary fuzzy clustering algorithm are proposed,respectively.Among them,the improved fuzzy c-means clustering algorithm can acquire feasible segmentation results relatively quickly.The evolutionary fuzzy clustering algorithm with local and non-local information is a method based on global optimization,and it has a relatively strong universality.Additionally,in order to further improve the quality of segmentation results,an entropy based label correction is presented to modify the labels of outliers.Through segmentation on different types of image,it demonstrates that the proposed algorithms can obtain clear edges and smooth regions while restraining noise for image segmentation.