Patch-Based Fuzzy Local Weighted C-Means Clustering Algorithm with Correntropy Induced Metric for Noise Image Segmentation

Fuzzy clustering is widely used in image segmentation because of its ability to describe the uncertain information presented in images. However, traditional fuzzy clustering ignores the spatial contextual information in the image, which makes it poor in processing images corrupted by high noise. In this paper, we present a novel fuzzy clustering algorithm called PFLWCM-CIM algorithm for noise image segmentation by introducing the image patches, the correntropy induced metric (CIM), and a fuzzy local weighted factor. Firstly, we use image patches as samples in clustering. Compared with individual pixels, image patches can preserve the local geometry of images by considering comprehensive features. Secondly, a new distance measure is developed on the basis of image patches and CIM to describe the relationship between samples and cluster centers. The CIM is more robust to noise than the traditional L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document}-norm. Next, a novel weighting method to characterize the similarity between two pixels named local weights is proposed. The local weights combine the spatial location relationship and the pixel value relationship of two pixels simultaneously, which describes the relationship between pixels from a more reasonable perspective. Furthermore, a new fuzzy local weighted factor is put forward by integrating the new distance measure and the local weights, then the PFLWCM-CIM algorithm is proposed based on the new factor and the idea of image patches. Several commonly used fuzzy clustering algorithms are incorporated into the experiments in segmenting images polluted by various types of noise. Experimental results demonstrate that our algorithm has reached state-of-the-art results in several metrics.