| Clustering methods have critical and extensive applications in the field of image segmentation.Clustering-based image segmentation is a process of dividing an image into multiple regions with special meanings according to features such as grayscale,color,and texture.By combining multi-objective evolutionary optimization techniques with clustering algorithms,multi-objective evolutionary clustering algorithms(MOCAs)can alleviate the defects of traditional clustering methods,such as the sensitivity to the initial cluster centers and the dependence on a single clustering criterion.However,it is often difficult for MOCAs to directly search for complete Pareto fronts when handling complex image segmentation problems,resulting in slow convergence of traditional MOCAs.In addition,since MOCAs require a large number of expensive objective function calculations,their time costs are usually too high to apply extensively in real-world image segmentation applications.In order to address the above issues,based on the characteristic that knee points can focus on preferred areas on the Pareto front,this thesis combines the advantages of knee points and surrogate models,and designs knee points driven surrogate-assisted multi-objective evolutionary frameworks with fast convergence to search for ideal cluster centroids efficiently.Moreover,by constructing multiple clustering objective functions with abundant image information,this thesis decreases the sensitivity of the clustering to noise,and finally proposes three kinds of knee point driven surrogate-assisted multi-objective evolutionary fuzzy clustering algorithms for image segmentation.The main research work of this thesis is summarized as follows:1)A knee point driven Kriging-assisted multi-objective evolutionary robust fuzzy clustering algorithm(K~2MORFC)is proposed for image segmentation.This thesis uses the non-local spatial information derived from the given image to design a pixel-level objective function that combines Kullback-Leibler(KL)divergence-based spatial constraint,and in the meantime uses image edge information to design a region-level objective function.Furthermore,the image edge information is also utilized to adaptively determine the weight factor of the spatial constraint for K~2MORFC and hence reduce the number of parameters for users.Then,a knee point driven multi-objective evolutionary framework is constructed to optimize the above objective functions simultaneously,in which the Kriging model is employed to predict the objective function values to reduce the computational costs,a dynamic subspace knee point searching strategy to comprehensively identify the knee points,a knee point driven environmental selection strategy to apply the selection pressure,and a knee point driven Kriging model management mechanism to improve the performance of the overall framework.Finally,a fuzzy clustering validity index is constructed by using the non-local spatial information to select the optimal solution from the non-dominated solution set.Experimental results on the DTLZ problems verify the effectiveness of the proposed knee point driven multi-objective evolutionary framework.The segmentation results on Brain Web,IBSR brain magnetic resonance(MR)images and Berkeley natural images demonstrate the good segmentation accuracy and noise robustness of K~2MORFC.2)A knee point driven competitive learning approach to surrogate-assisted multi-objective rough fuzzy clustering algorithm(KCL-SMRFC)is proposed for image segmentation.This thesis employs the rough set theory to improve the fuzzy intra-compactness function with KL divergence-based spatial constraint,and uses the boundary set information described by the rough set to construct the rough fuzzy inter-class separation function,so as to deal with the uncertainty in images and meanwhile evaluate the quality of cluster centers in multiple perspectives.To improve the clustering performance and reduce the number of parameters,this thesis designs an adaptive threshold for judging the upper and lower approximations of the rough fuzzy clustering.Then,a knee point driven competitive learning approach to surrogate-assisted multi-objective particle swarm optimization(KCL-SMPSO)is proposed to simultaneously optimize two objective functions,so as to efficiently search for ideal cluster centers.KCL-SMPSO consists of a knee point driven particle competition optimizer and a knee point driven radial basis function(RBF)model management mechanism.Finally,by using the non-local spatial information,a rough fuzzy clustering validity index is constructed to select the optimal particle.Experimental results on the DTLZ problems verify the effectiveness of KCL-SMPSO.The segmentation results on Brain Web,IBSR brain MR images and Berkeley natural images show that KCL-SMRFC achieves satisfactory noise robustness and time efficiency.3)A knee point driven competitive learning approach to surrogate-assisted semi-supervised multi-objective rough fuzzy clustering algorithm(KCL-S~3MRFC)is proposed for image segmentation.Firstly,by using the supervision information provided by users as well as the non-local spatial information derived from the given image,two semi-supervised KL divergence-based rough fuzzy clustering objective functions are constructed.Then,by converting the prior knowledge of the given image into the supervised particle during the optimization,a knee point driven semi-supervised environment selection strategy and a knee point driven semi-supervised RBF model management mechanism are designed to enhance the overall performance.Finally,by using the non-local spatial information,a semi-supervised rough fuzzy clustering validity index is defined to select the optimal particle from the non-dominated solution set.Experimental results on Brain Web,IBSR brain MR images and Berkeley natural images show that KCL-S~3MRFC behaves better in terms of both segmentation accuracy and noise robustness compared with other MOCAs and semi-supervised clustering algorithms. |
