Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure

Fuzzy c-means clustering (FCM) with spatial constraints (FCM_S) is an effective algorithm suitable for image segmentation. Its effectiveness contributes not only to the introduction of fuzziness for belongingness of each pixel but also to exploitation of spatial contextual information. Although the contextual information can raise its insensitivity to noise to some extent, FCM_S still lacks enough robustness to noise and outliers and is not suitable for revealing non-Euclidean structure of the input data due to the use of Euclidean distance (L₂ norm). In this paper, to overcome the above problems, we first propose two variants, FCM_S₁ and FCM_S₂, of FCM_S to aim at simplifying its computation and then extend them, including FCM_S, to corresponding robust kernelized versions KFCM_S, KFCM_S₁ and KFCM_S₂ by the kernel methods. Our main motives of using the kernel methods consist in: inducing a class of robust non-Euclidean distance measures for the original data space to derive new objective functions and thus clustering the non-Euclidean structures in data; enhancing robustness of the original clustering algorithms to noise and outliers, and still retaining computational simplicity. The experiments on the artificial and real-world datasets show that our proposed algorithms, especially with spatial constraints, are more effective.