Coarse–fine surrogate model driven multiobjective evolutionary fuzzy clustering algorithm with dual memberships for noisy image segmentation

Abstract To improve the segmentation performance and boost evolutionary efficiency of multiobjective evolutionary clustering algorithms on noisy images, this paper proposes a coarse–fine surrogate model driven multiobjective evolutionary fuzzy clustering algorithm with dual membership functions (CFS-MOEFC). The existing fuzzy clustering validity-based fitness functions generally consider one single fuzzy membership function, which cannot fully process the uncertainty in an image. Moreover, most existing fitness functions used in image segmentation only utilize one type of spatial information derived from the image, which cannot behave robust on images with uncertain types of noise. To deal with the above problems, dual fuzzy membership functions are first designed by utilizing the local and non-local image spatial information. Then, the designed dual membership functions and the two kinds of spatial information are both used to construct spatial information-motivated fitness functions for image segmentation. To promote the time efficiency, the coarse–fine surrogate model is employed to assist the evolutionary optimization process, such as approximating the fitness functions instead of real function evaluations and evolving satisfactory cluster centers for CFS-MOEFC. Besides, a dual memberships-driven cluster validity index combining the local and non-local spatial information is designed for selecting an optimal solution from the final non-dominated solution set of CFS-MOEFC. Experiments on Berkeley and Magnetic Resonance (MR) images indicate that CFS-MOEFC greatly improves the segmentation accuracy on images with multiple types of noise, preserves more significant detailed image information, and behaves well on time cost comparing with state-of-the-art methods.