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.

带有指导图像滤波器（GF）的模糊c均值聚类是一种有用的图像分割方法。单通道GF可以有效地应用于灰度引导图像，但是对于彩色引导图像，由于协方差矩阵的逆计算的运行时开销较高，因此执行起来很困难多渠道GF。为了解决这个问题，我们提出了一种新颖的加权多通道导引图像滤波器（WMGF）方法。该方法利用色彩引导图像的每个通道独立地对输入图像进行滤波，并根据局部窗口中图像像素的变化为每个通道定义了新颖的权重，从而大大消除了相互影响。在不同通道之间切换时，运行时开销较低。此外，基于WMGF方法，\（\ hbox {FCM} _ {\ scriptscriptstyle {WMGF}} \））用于彩色图像分割，其中在模糊c均值聚类的每次迭代中，对成员矩阵执行WMGF。为了进一步增强不同的抗噪性和边缘保留性，将多维形态重建（MMR）方法引入了所提出的模糊聚类方法（MMR \（\ _ \ hbox {FCM} _ {\ scriptscriptstyle {WMGF}} \））以获得更高的分割精度。在带有椒盐和高斯噪声的彩色图像上进行的实验证明了所提出方法的优越性。