Multivariate morphological reconstruction based fuzzy clustering with a weighting multi-channel guided image filter for color image segmentation

The fuzzy c-means clustering with guided image filter (GF) is a useful method for image segmentation. The single-channel GF can be efficiently applied to the gray-scale guidance image, but for the color guidance image, due to the high run-time overhead on the calculation of the inverse of the covariance matrix, it is a hard work to perform the multi-channel GF. To address this issue, we propose a novel weighting multi-channel guided image filter (WMGF) method. In this method, each channel of the color guidance image is utilized to guide the filtering for the input image independently and a novel weight is defined for each channel according to the variance of the image pixels in a local window, which greatly eliminates the mutual influence between different channels and brings about a low run-time overhead. In addition, based on the WMGF method, we present a new fuzzy c-means clustering algorithm (\(\hbox {FCM}_{\scriptscriptstyle {WMGF }}\)) for the color image segmentation, in which the WMGF is performed on the membership matrix in each iteration of the fuzzy c-means clustering. To further enhance the different noise-immunity and edge preservation, the multivariate morphological reconstruction (MMR) method is introduced into the proposed fuzzy clustering method (MMR\(\_\hbox {FCM}_{\scriptscriptstyle {WMGF }}\)) to obtain higher segmentation precision. Experiments on color images with Salt & Pepper and Gaussian noises demonstrate the superiority of the proposed methods.