Surrogate-Assisted Optimization Driven Multi-objective Rough Fuzzy Clustering For Image Segmentation

Unsupervised image segmentation,as one of the key technologies of digital image processing,has attracted extensive attention due to its features such as good universality and no need for manual annotation of images in advance.Rough fuzzy C-means clustering algorithm(RFCM)has been widely studied and applied in the unsupervised image segmentation field due to the advantages of high efficiency and simple principle.By combining both rough set theory and fuzzy set theory with C-means clustering method,RFCM uses the integration of upper and lower approximations and fuzzy membership to deal with the incompleteness and ambiguity in data.However,traditional rough fuzzy Cmeans clustering algorithms have the disadvantages of being sensitive to initialization,easily falling into local optimum,and considering only one clustering criterion which cannot meet various segmentation requirements.Although the multi-objective evolutionary clustering algorithms(MOCAs)can handle the above problems,they suffer from numerous and expensive objective function evaluations in image segmentation applications.To address this issue,this thesis combines the advantages of surrogate-assisted multi-objective evolutionary algorithm with rough fuzzy clustering,and proposes three surrogate-assisted optimization driven multi-objective rough fuzzy clustering algorithms for image segmentation.The main research work of this thesis is summarized as follows:(1)This thesis proposes a reliable region information driven Kriging-assisted multiobjective rough fuzzy clustering(RRI-KMRFC)algorithm for image segmentation.Combining the advantages of multiple superpixel methods,this algorithm designs a reliability-based region information extraction strategy,so as to maintain relatively abundant image details under the premise of suppressing noise.Then,using the uncertain information described by the rough set and the region information,the pixel-level rough fuzzy intra-class compactness function,the prototype-level rough inter-class separation function,and the superpixel-level probability entropy function are designed to simultaneously evaluate the cluster centers in multiple perspectives.To efficiently optimize the above three objective functions,this thesis designs an incremental Kriging-assisted multi-objective evolutionary clustering framework,which includes an initial population repairing strategy and an improved infill sampling criterion.Finally,by using the reliable region information,a rough fuzzy clustering validity index is constructed to select the optimal solution from the nondominated solution set.Experimental results on synthetic images,Berkeley and Weizmann images show that RRI-KMRFC performs well in terms of segmentation accuracy,noise robustness and running time.(2)This thesis proposes an ensemble classification and regression tree surrogate-assisted automatic multi-objective rough fuzzy clustering(ECS-AMRFC)algorithm for image segmentation.In order to automatically identify the number of clusters and the rough degree of clusters,three complementary objective functions for kernelized rough fuzzy clustering are designed.To overcome the defect that the traditional multi-objective automatic clustering algorithms cannot employ surrogate techniques to reduce the computational burden,ECSAMRFC adopts a cluster medoid-based encoding strategy.According to the characteristics of the coding scheme,an ensemble classification and regression tree(CART)surrogate model is designed to better fit the objective functions.Moreover,a density-based uncertainty estimation method is designed in the infill sampling strategy,which provides a new scheme for assessing the uncertainty of individuals.Finally,a kernelized rough fuzzy clustering validity index is defined by using the relations of upper and lower approximations of the rough fuzzy sets to select the optimal solution.Experimental results on synthetic images,brain magnetic resonance images,remote sensing images,and Berkeley images show that ECS-AMRFC can not only determine the appropriate number of clusters efficiently,but also achieve satisfactory image segmentation performance and universality.(3)This thesis proposes a multiple surrogate-assisted density-sensitive automatic multiobjective rough fuzzy clustering(MSDS-AMRFC)algorithm for image segmentation.By constructing the rough fuzzy clustering objective functions with multiple pairs of complementary relations,MSDS-AMRFC achieves the self-adaptation to the degree of roughness,the degree of fuzziness,and the number of clusters,thereby reducing the requirements for users’ prior knowledge.To improve the performance of the algorithm for the optimization of cluster centers,a gray histogram-based fast pixel density estimation strategy and a gray level-based encoding scheme are designed.Then,a multiple surrogate model consisting of CART,Kriging and radial basis function models is constructed to improve the prediction accuracy of the surrogate model.Finally,by using the pixel density information and the boundary set information described by rough fuzzy set,a rough fuzzy clustering validity index is constructed to select the optimal solution from non-dominated solution set.Experimental results on simulated brain MR images,real brain MR images and chest radiographic images show that MSDS-AMRFC performs well in terms of noise robustness,cluster number adaptation and time efficiency.