2010 IEEE International Conference on Bioinformatics and Biomedicine
A Fast and Noise-Adaptive Rough-Fuzzy Hybrid Algorithm for Medical Image Segmentation Arpit Srivastava, Abhinav Asati Department of Electronics and Communication Mualana Azad National Institute of Technology Bhopal, India
[email protected]
Mahua Bhattacharya ABV Indian Institute of Information Technology and Management Gwalior, India
[email protected]
Abstract and other defects that add to the already existing major problems of mixed noises and intensity in-homogeneity induced by the radio-frequency coil in MRI [3]. Many authors have proposed spatial pre-filtering of images to overcome the intensity in-homogeneity and presence of outliers in MRI data, which takes into account the neighbourhood correlation of pixels. This way, an attempt is made to reduce the pressure of noise and outliers while the clustering process is going on.
Abstract—An Accurate, Fast and Noise-Adaptive segmentation of Brain MR Images for clinical Analysis is a challenging problem. An improved Hybrid Clustering Algorithm is presented here, which integrates the concept of recently popularized Rough Sets and that of Fuzzy Sets. The concept of lower and upper approximations of rough sets is incorporated to handle uncertainty, vagueness, and incompleteness in class definition. For making the segmentation robust to Noise and intensity inhomogeneity, the images are proposed to be pre-processed with a neighbourhood averaging spatial filter. To accelerate the segmentation process, a novel Suppressed Rough Fuzzy C-Means model is presented in which a membership suppression mechanism has been implemented, which creates competition among clusters to speed-up the clustering process. The effectiveness of the presented algorithm along with comparison with other related algorithm has been demonstrated on a set of MR and CT scan images. The results using MRI data show that our method provides better results compared to standard Fuzzy C-Means based algorithms and other modified similar techniques.
One of the recently popularised soft-computing techniques is Rough set theory. Rough Sets proposed by Pawlak [6], is a tool which handles vagueness, uncertainty and incompleteness well in information systems. The theory of rough sets arises from the notion of approximation spaces. The use of rough sets in clustering has been reported in literature [5]. Rough sets when implied in C-Means framework, resulted into Rough C-Means Clustering (RCM) algorithm [5]. Now, RCM alone not being sufficient for Image segmentation was proposed to be incorporated with Fuzzy sets by Pal [4] to give Hybrid Rough-Fuzzy CMeans algorithm. While membership in FCM enables efficient handling of overlapping partitions, the concept of rough sets deals with uncertainty, vagueness and incompleteness in data in terms of upper and lower approximations. The clustering procedure using RFCM model has been demonstrated in [8].
Keywords-Rough Sets; Fuzzy C-Means; Clustering; Medical Images; Image Segmentation
I. INTRODUCTION Magnetic resonance imaging (MRI) is one of the most important computer-based diagnostic tools for detecting abnormal changes in tissue. In recent years, Fuzzy C-Means (FCM) algorithm has been the most extensively used algorithm for brain MRI segmentation [1]. However standard FCM is found to be inefficient as it does not take into account the spatial property of MR images that neighborhood pixels are strongly correlated with each other, due to which the fuzzy Memberships do not describe well the degree of belongingness. This leads to enhanced noise sensitivity
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One of the foremost requirements of computerassisted analysis of Medical images, specifically MRI is to reduce the processing time, while not degrading the quality of clustering. The complexity of computation of RFCM leads to extended time duration of the whole Clustering procedure. To enhance the speed of clustering, Fan [10] proposed a modified version of the standard FCM algorithm which created competition among the clusters and involved the suppression of Fuzzy Membership values after each iteration so as to speed up the convergence process.
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noise and/or Gaussian noise) and intensity inhomogeneities, is then applied to various Clustering procedures.
The application of this suppression mechanism in enhancing the computational speed of RFCM has been proposed and demonstrated in this paper. Initially, the MR images are pre-processed using Context Dependent spatial filter, so as to remove mixed Noises that are present in the MRI data due to external sources. The images are then segmented by using Suppressed RFCM. The effectiveness of the Enhanced S-RFCM algorithm, along with a comparison with the existing CMeans algorithms, is demonstrated on a set of MR and CT Scan Images. Also, DB index and XB index have been used to validate the suitability of S-RFCM Algorithm. The rest of the paper is organised as: Section II discusses the need and use of Context Dependent Prefiltering. Section III gives an overview of famous FCM algorithm. In Section IV and V we discuss Rough Clustering schemes and RFCM respectively, along with their merits and demerits. Section VI elaborates the concept of suppression and Suppressed RFCM Model. Section VII and VIII inncludes our experimental analysis and comparison of various C-Means algorithms.
III. FCM The c-means (or k-means) families are the best known and well developed families of batch clustering models because they are ‘‘least square’’ models [4]. Out of CMeans clustering algorithms, Fuzzy C-Means is much popular due to its ability to handle overlapping clusters. The FCM assigns each data point (or pixel) to clusters based on its fuzzy membership. Let X ={x1,...,xk,...,xN} be the set of n objects and V = {vi,...,vi,...,vc} be the set of c centroids, where xkאRm , viאRm , and vi אX. It partitions X into c clusters by iteratively minimizing the objective function: c
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Where 1 ≤ m or simply called the rough set of X. The lower Approximation of a set represents all those elements that definitely belong to X, whereas the upper
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Assign initial cluster centers (or centroids) Vi ,i=1 to c for c clusters, where c is the number of clusters. Also choose the value of fuzzifier operator m and threshold value Ɛ. Set iteration counter t=1. Calculate initial membership values of N data objects for c clusters as follows,
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