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Image segmentation allows extracting distinctive objects in an image. It is classified in edge segmentation, region segmentation and segmentation by clustering. Fuzzy c-mean (FCM) is widely used in image segmentation. It is considered an effective approach to pixel classification particularly in medical images (Bezdek, 1982). Fuzzy clustering has been improved by integrating parameters such as spatial constraints, local information, kernel metric modification, gaussian noise or multiresolution (Adhikari et al. (2015), Ahmed et al. (2002), Devikar & Jha (2013), Gong et al. (2013), Ghasemi et al. (2014), Meena and Raja (2013), Chuang et al. (2006), Huynh (2009), Cui et al. (2013), El-Melegy and Mokhtar (2014), Sajith and Hariharan (2015), Sivanand and Raj (2013), Kang et al. (2005), Kumar et al. (2012), Lui et al. (2012), Hafiane and Zavidovique (2005), Reddy et al. (2012), Xiao et al. (2013), Zhang et al. (2003), Zhang et al. (2003b), Zhong et al. (2014)).
Fuzzy clustering using spatial information influenced by neighbour elements was proposed in (Adhikari et al. (2015), Ahmed et al. (2002), Barrah et al. (2016), Cui et al. (2013), Devikar & Jha (2013), Chuang et al. (2006), Ghasmi et al. (2014), Kang et al. (2005), Meena and Raja (2013), Reddy et al. (2012), Sajith and Hariharan (2015)). The combination of Kernel metric and local spatial information was proposed in Gong et al. (2013), Lui et al. (2012), Zhang et al. (2003) and applied in the FCM objective function and in the update of membership functions and cluster centers. Gong et al. (2013) introduced local information and kernel metric to their FCM clustering approach. Local information is based on the spatial distance of neighbour pixels and their gray level difference (disparity). It is then used as a distance metric to the kernel for the objective function by using the distance variance of different neighbour pixels. In the article related to Zhang et al. (2003), objective function of classical FCM algorithm is modified by integrating a kernel distance metric and a spatial constraint that takes into account the influence of the neighbouring pixel on the center pixel. Lui et al. (2012) proposed a fuzzy clustering approach by integrating gaussian RBF kernel to the objective function and using spatial information. Barrah et al. (2016) proposed an FCM method that integrates both local spatial and gray level information to compute the weight of the pixel neighborhood.
Chuang et al. (2006) incorporate a spatial classification into the membership function that represents the sum of membership functions in the neighbourhood of each pixel in order to have more homogeneous regions and eliminate the noise present in the image. Adhikari et al. (2015) propose a spatial FCM approach for MRI segmentation by generating local membership values for each pixel which are joined with global membership functions for computing new clustering centers and membership functions.