Robust semi-supervised spatial picture fuzzy clustering with local membership and KL-divergence for image segmentation

Aiming at existing symmetric regularized picture fuzzy clustering with weak robustness, and it is difficult to meet the need for image segmentation in the presence of high noise. Hence, a robust dynamic semi-supervised symmetric regularized picture fuzzy clustering with KL-divergence and spatial information constraints is presented in this paper. Firstly, a weighted squared Euclidean distance from current pixel value, its neighborhood mean and median to clustering center is firstly proposed, and it is embedded into the objective function of symmetric regularized picture fuzzy clustering to obtain spatial picture fuzzy clustering. Secondly, the idea of maximum entropy fuzzy clustering is introduced into picture fuzzy clustering, and an entropy-based picture fuzzy clustering with clear physical meaning is constructed to avoid the problem of selecting weighted factors. Subsequently, the prior information of the current pixel is obtained by means of weighted local membership of neighborhood pixels, and it is embedded into the objective function of maximum entropy picture fuzzy clustering with multiple complementary spatial information constraints through KL-divergence, a robust dynamic semi-supervised picture fuzzy clustering optimization model and its iterative algorithm are given. In the end, this proposed algorithm is strictly proved to be convergent by Zangwill theorem. The experiments on various images and standard datasets illustrate how our proposed algorithm works. This proposed algorithm has excellent segmentation performance and anti-noise robustness, and outperforms eight state-of-the-art fuzzy or picture fuzzy clustering-related algorithms in the presence of high noise.