A knee point driven Kriging-assisted multi-objective robust fuzzy clustering algorithm for image segmentation

Abstract

To enhance the segmentation performance and optimization efficiency of multi-objective evolutionary clustering algorithms for noisy images, this study presents a knee point driven Kriging-assisted multi-objective robust fuzzy clustering algorithm for image segmentation (K2 MORFC). First, pixel and region-level fitness functions are developed to comprehensively consider the spatial constraints and region consistency in an image. In the pixel-level fitness function, a Kullback–Leibler (KL) divergence-based spatial constraint term is employed and combined with intra-class compactness to preserve the membership similarity between an arbitrary image pixel and its non-local neighbors. In the region-level fitness function, image edge information is utilized to evaluate the regional consistency of the partition. Moreover, an adaptive determination mechanism of the weight factor for the spatial constraint term is designed in the pixel-level fitness function to control the influence of the spatial constraint for each pixel. Furthermore, considering that the preference toward knee points can effectively improve the convergence performance, a knee point driven Kriging-assisted evolutionary algorithm (K2EA) is proposed to efficiently optimize these two fitness functions, including a dynamic subspace knee point searching strategy, a knee point guided environmental selection strategy, and a Kriging model management mechanism. Finally, we construct a fuzzy clustering validity index with a KL divergence-based non-local spatial constraint term to select the optimal solution from the nondominated solution set. Competitive experimental results on the DTLZ benchmark verify the effectiveness of K2EA. Segmentation results on color images from the Berkeley dataset and magnetic resonance images from the BrainWeb and IBSR datasets confirm the performance of K2MORFC.