Localized FCM Clustering with Spatial Information for Medical Image Segmentation and Bias Field Estimation

This paper presents a novel fuzzy energy minimization method for simultaneous segmentation and bias field estimation of medical images. We first define an objective function based on a localized fuzzy -means (FCM) clustering for the image intensities in a neighborhood around each point. Then, this objective function is integrated with respect to the neighborhood center over the entire image domain to formulate a global fuzzy energy, which depends on membership functions, a bias field that accounts for the intensity inhomogeneity, and the constants that approximate the true intensities of the corresponding tissues. Therefore, segmentation and bias field estimation are simultaneously achieved by minimizing the global fuzzy energy. Besides, to reduce the impact of noise, the proposed algorithm incorporates spatial information into the membership function using the spatial function which is the summation of the membership functions in the neighborhood of each pixel under consideration. Experimental results on synthetic and real images are given to demonstrate the desirable performance of the proposed algorithm. 1. Introduction Medical image segmentation plays an important role in a variety of biomedical-imaging applications, such as the quantification of tissue volumes, diagnosis, localization of pathology, study of anatomical structure, treatment planning, and computer-integrated surgery [1]. However, segmentation of medical images involves three main image-related problems [2]. First, images contain noise that can alter the intensity of a pixel such that its classification becomes uncertain. Second, images exhibit intensity inhomogeneity where the intensity level of a single tissue class varies gradually over the extent of the image. Third, images have finite pixel size and are subject to partial volume averaging where individual pixel volumes contain a mixture of tissue classes so that the intensity of a pixel in the image may not be consistent with any one class. To overcome these problems, many segmentation techniques have been proposed in the past decades, such as the expectation maximization (EM) algorithm [3–5], level set method [6–9], clustering [10–17], and so on. Clustering for image segmentation usually classifies image pixels into -clusters such that members of the same cluster are more similar to one another than to members of other clusters, where the number, , of clusters is usually predefined or set by some validity criterion or a priori knowledge [18]. In the clustering methods, fuzzy -means (FCM) based algorithms have been widely used in