Quadratic surface center-based possibilistic fuzzy clustering with kernel metric and local information for image segmentation.

Kernel fuzzy weighted local information c-means (KWFLICM) algorithm has good segmentation effect in segmenting noisy images, but it can not effectively segment images with low contrast or high noise. The improved algorithm of KWFLICM is a kernel possibilistic fuzzy c-means clustering with local information (KWPFLICM), which has better anti-noise performance. However, this algorithm loses more details of original image when segmenting the image. In this paper, a kernel-based possibilistic fuzzy local information clustering algorithm based on quadratic polynomial is proposed to overcome the shortcomings of KWPFLICM algorithm. At the same time, the local membership information of neighborhood pixels is introduced as the penalty factor to update the local information, so as to further improve the robustness of the algorithm. By optimizing the objective function of modified possibilistic fuzzy local information clustering with quadratic surface centers, the formulas of fuzzy membership, possibilistic typicality, and the coefficients of quadratic polynomial center are derived theoretically, and the convergence of the proposed algorithm is strictly proved by Zangwill theorem and bordered Hessian matrix. Experimental results show that compared with existing state-of-the-art fuzzy clustering-related algorithms, the proposed algorithm has better segmentation performance and stronger anti-noise robustness, and can effectively suppress noise and retain details. It will have far-reaching significance for the development of robust fuzzy clustering segmentation theory. [ABSTRACT FROM AUTHOR]