Robust fuzzy local information and L_p-norm distance-based image segmentation method

A variant of fuzzy c-means (FCM) clustering algorithm for image segmentation is provided. Unlike the L₂-norm distance in FCM, L_p with p ∈ (0,1] norm is used to measure the distance of the pixel intensity to its cluster centre in the energy functional. Moreover, local spatial information and colour information are incorporated into the model to enhance the robustness to noise and outliers. The proposed algorithm is called fuzzy local information L_p (FLILp) clustering. To overcome the difficulty of finding cluster centres, L_p-norm distance is approximated by weighted L₂ distance. The advantages of FLILp are: (i) it is strongly robust to noise and outliers, (ii) it is applied to the original image and (iii) it preserves image edges. Numerical examples and comparisons of image segmentation on both synthetic and real images illustrate the outstanding performance and robustness of the proposed method.