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

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Abstract

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.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants with No. 61873324, No. 61903156, and No. 61872419, the Natural Science Foundation of Shandong Province under Grant with No. ZR2019MF040 and No. ZR2017MF044.

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Correspondence to Jin Zhou.

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Xu, G., Zhou, J., Dong, J. et al. Multivariate morphological reconstruction based fuzzy clustering with a weighting multi-channel guided image filter for color image segmentation. Int. J. Mach. Learn. & Cyber. 11, 2793–2806 (2020). https://doi.org/10.1007/s13042-020-01151-1

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