LETTERS International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009
A Study on Rough Set Theory for Medical Image Segmentation N. Senthilkumaran1 and R. Rajesh2 School of Computer Science and Engineering, Bharathiar University, Coimbatore -641 046, India. 1
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Abstract—Rough set is approximate representation of a crisp set. Rough set theory provides an approach to approximation of sets that leads to useful forms of granular computing. Several applications have revealed the need to extend the traditional rough set approach. A special place among various extensions is taken by the approach that replaces the relation based on equivalence with a tolerance relation. Rough sets offer an effective approach of managing uncertainties and can be employed for tasks such as feature identification, dimensionality reduction, pattern classification and image segmentation. In this paper, the main aim is to survey the Rough set Theory for medical image segmentation.
image segmentation. The organization of the paper is as follows. In Section II, presents an overview of Rough set theory, and Section III discuss about Medical image segmentation using Rough set theory and Section IV presents conclusion. II. AN OVERVIEW OF ROUGH SETS The Rough set theory is introduced by Zdzislaw Pawlak [4] in the early 1980s and is a new mathematical tool to deal with vagueness and uncertainty[5]. A rough set is an approximately representation of a crisp set. On the rough set theory, we know that a rough set includes an element approximately[2]. So an element is included a rough set, or is not included a rough set, or is included a rough set approximately. A rough set is represented by a pair of crisp sets[9]. The pair of crisp sets are a lower approximation and an upper approximation. The rough set theory overlaps is to some extent with many other mathematical tools developed to deal with vagueness and uncertainly, in particular with the Dempster-Shafer theory of evidence[3]. The difference is that the Dempster-Shafer theory uses belif functions as a main tool, while rough set theory makes use of sets-lower and upper approximations. Another relationship exists between fuzzy set theory and rough set theory [2]. Rough set theory does not compete with fuzzy set theory, with which it is frequently contrasted, but rather complements it. In any case, rough set theory and fuzzy set theory are independent approaches to imperfect knowledge. The problems using rough set theory[2][3][7] include data reduction(i.e, elimination of superfluous data), discovery of data dependencies, estimation of data significance, generation of decision(control) algorithms from data, approximate classification of data, discovery of similarities or differences in data, discovery of patterns in data and discovery of causeeffect relationships[3]. Huang and Zhang [6] presented a new application of rough sets to ECG recognition. First, the recognition rules for characteristic points in ECG are reduced using rough set theory. Then the reduced rules are used as restriction conditions of an eigenvalue determination arithmetic to recognise characteristic points in ECG. The rough set theory approach has found interesting applications in medicine[3][6], pharmacology, business, banking, market research, engineering design, meteorology, vibration analysis, switching functions, conflict analysis, image processing[3], voice recognition, concurrent system analysis, decision analysis, character recognition[1] and other fields[5]. The rough set methodology is being used, among other areas, in market research, medical data analysis, drug research, sensor data analysis for the purpose of control and research leading to the design of new composite materials[2]. The analysis of stock market data has confirmed some well known market rules and has led to the
Index Terms—Rough Set Theory, Medical Image Segmentation, Granular computing.
I. INTRODUCTION Image segmentation[1][7] is one of the most challenging tasks in image processing and is a very important preprocessing step in the problems in the area of image analysis, computer vision, and pattern recognition. Medical image segmentation[1][7][15] is a complex and challenging task due to the intrinsic nature of the images. The brain has a particularly complicated structure and its precise segmentation is very important for detecting tumors, edema, and necrotic tissues, in order to prescribe appropriate therapy[1][6]. The majority of research in medical image segmentation pertains to its use for MR images, especially in brain imaging. Because of its ability to derive contrast from a number of tissue parameters, many different pulse sequences exist for acquiring MR images[9][13][14]. Determining the optimal pulse sequence for obtaining accurate segmentations [15] is therefore an important problem that requires knowledge of the underlying tissue properties of the anatomy to be segmented [1][7]. Magnetic resonance imaging (MRI) is an important diagnostic imaging technique for the early detection of abnormal changes in tissues and organs. Many methods have been proposed in the literature for Medical image segmentation[1][6][7][10][15]. Rough Set Theory proposed by Pawlak[3] is a mathematical tool to analyze vagueness and uncertainty inherent in making decesion[4][5]. It doesnot rely on assessional information out of data set, and it analyses and discovers relint relation amoung data just from the point of view of data’s discreditable attribute, just based on the concept[9] of an upper and lower approximation of a set, as well as approximation space and models of sets[3]. Based on analysis mentioned above, this paper study on rough set theory in to brain image segmentation. Experimental results demonstrate the superiority of the rough set method in brain N. Senthilkumaran is a Senior Research Fellow supported by Rajiv Gandhi National Fellowship, University Grants Commission, India. Dr. R. Rajesh is with SCSE, B.U and he is the Principal Investigator for a major research project funded by U.G.C., India.
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LETTERS International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009 in the image can be approximated by rough sets. In case of an information system (U,A ),the is a nonempty set of finite objects and the is a non-empty finite set of attributes such that,
discovery of some interesting new rules. The knowledge discovery methodology that uses an extension of the original model of rough sets, called variable precision rough sets[2]. The rough set methodology[4] has proved its soundness and usefulness in many real-life applications. Rough set theory offers effective methods that are applicable in many branches of artificial intelligence[8]. One of the advantages of rough set theory is that programs implementing its methods may easily run on parallel computers[2][7].
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Then the U is the universe set. In this case, a rough set RX is representing a crisp set X , then the rough set is defined as following, where the RX is the lower approximation of the rough setand the RX is the upper approximation of the rough set. A lower approximation of a rough set RX is composed of all the elementary sets included in X , and a upper approximation of a rough set RX is composed of all the elementary sets which have non-empty set intersection with X.
III. ROUGH SETS IN MEDICAL IMAGE SEGMENTATION The segmentation of medical images is challenging due to the poor image contrast and artifacts that result in missing or diffuse organ/tissue boundaries[1][5][9]. Medical imaging is performed in various modalities, such as magnetic resonance imaging (MRI)[15], computed tomography (CT), ultrasound, etc[5][9]. One of the most important tasks in medical imaging is segmentation as it is often a pre-cursor to subsequent analysis, whether manual or automated[2][3][5][11]. The basic idea behind segmentation-based rough sets is that while some cases may be clearly labelled as being in a set X (called positive region in rough sets theory), and some cases may be clearly labeled as not being in X (called negative region), limited information prevents us from labelling all possible cases clearly[6][7]. The remaining cases cannot be distinguished and lie in what is known as the boundary region[12][16]. An improved clustering algorithm based on rough sets and entropy theory was presented by Chen and Wang [2]. The method avoids the need to pre-specify the number of clusters which is a common problem in clustering based segmentation approaches. Clustering can be performed in both numerical and nominal feature spaces with a similarity introduced to replace the distance index. At the same time, rough sets are used to enhance the algorithm with the capability to deal with vagueness and uncertainty in data analysis[15]. Shannon’s entropy was used to refine the clustering results by assigning relative weights to the set of features according to the mutual entropy values. A novel measure of clustering quality was also presented to evaluate the clusters. The experimental results confirm that both efficiency and clustering quality of this algorithm are improved. They introduced a concept of encrustation of the histogram, called histon, for the visualisation of multi-dimensional colour information in an integrated fashion and study its applicability in boundary region analysis. The histon correlates with the upper approximation of a set such that all elements belonging to this set are classified as possibly belonging to the same segment or segments showing similar colour value. The proposed encrustation provides a direct means of separating a pool of inhomogeneous regions into its components. This approach can then be extended to build a hybrid rough set theoretic approximations with fuzzy c-means based colour image segmentation. The technique extracts colour information regarding the number of segments and the segment centers of the image through rough set theoretic approximations which then serve as the input to a fuzzy c-means algorithm[1][8]. Let the universe U be an image consisting of a collection of pixels. Then if we partition U into a collection of nonoverlapping windows (of size m x n, say) each window can be considered as a granule G. In other words, the induced equivalence classes Imxn have m x n pixels in each nonoverlapping window. Given this granulation, object regions
Fig. 1. An Example brain image of representing a rough set
Fig. 1 shows an example of representing a rough set. There is an object X, and two squares. An first square which include the object is upper approximation (RX), and an next square which included the object is lower approximation (RX). In this situation, rough set theory offers a tool to deal with inconsistencies. The idea is very simple- for each concept X the greatest definable set contained in X and the least definable set containing X are computed. The former set is called a lower approximation of X, the latter is called upper approximation of X. The Experimentation data consists of a number of brain volumes collected from various sources. The segmentation algorithm using Rough set shows good result in all the data sets. Here shows only the results of selected 4 slices of a brain volume. Fig.2 shows selected 4 slices of a brain volume and Fig.3 shows the segmented results using granular rough sets.
Fig. 2. Selected 4 Slices from MRI brain volume
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LETTERS International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009 [9] Sankar K. Pal, B. Uma Shankar and Pabitra, “Granular computing, Rough entropy and object extraction”, Pattern Recognition Letters, 26, 2005, pp.2509-2517. [10] N. Senthilkumaran and R. Rajesh, “Edge Detection Techniques for Image Segmentation - A Survey of Soft Computing Approaches”, International Journal of Recent Trends in Engineering(IJRTE), Vol. 1, No.2, May 2009, pp. 250-254. [11] N. Senthilkumaran and R. Rajesh, “Image Segmentation - A Survey of Soft Computing Approaches”, Proceedings of the International Conference on Advances in Recent Technologies in Communication And Computing (ARTCom 2009), October 2009,(Accepted). [12] N. Senthilkumaran and R. Rajesh, “A Study on Edge Detection Techniques for Image Segmentation”, Proceedings of the International Conference on Mathematics and Computer Science, (ICMCS-2009), January 2009. pp.255-259. [13] N. Senthilkumaran and R. Rajesh, “Edge Detection Techniques for Image Segmentation - A Survey”, Proceedings of International Conference on Managing Next Generation Software Applications, (MNGSA-08), December 2008. pp.749760. [14] N. Senthilkumaran and R. Rajesh, “A Study on Split and Merge for Region based Image Segmentation”, Proceedings of UGC Sponsored National Conference on Network Security, (NCNS08), September 2008. pp.57-61. [15] Shan Shen, William Sandham, Malcolm Granat and Annette Sterr, ”MRI Fuzzy Segmentation of Brain Tissue Using Neighborhood Attraction With Neural-Network Optimization”, IEEE Transactions on Information Technology in Biomedicine, VOL.9, NO.3, September 2005, pp.459-467. [16] A.Wakulicz - Deja and P. Paszek, “ Applying rough set theory to Multi stage medical diagnosing”, Fundamenta Informaticae, 54(4), 2003, pp.387408.
Fig. 3. The Segmented result images using Granular Rough Sets
IV. CONCLUSION The goal of image segmentation process is to identify the segments of the image according to the image characteristic e.g., image color, objects shape etc. In this paper, we have provided a brief overview of rough sets and their use in various medical tasks. A more comprehensive review of the literature on rough sets in medical imaging can be found in [2][7][15][16]. This paper mainly focus on the study of medical image segmentation using rough sets. ACKNOWLEDGMENT The authors are thankful to all the staff members of the School of Computer Science and Engineering, Bharathiar University for their valuable support. The first author is thankful to UGC for the Rajiv Gandhi National Fellowship. The second author is also thankful to UGC for Major Research Project fund. REFERENCES [1] Bouchet A, Pastore J and Ballarin V, ”Segmentation of Medical Images using Fuzzy Mathematical Morphology”, JCS and T, Vol.7, No.3, October 2007, pp.256-262. [2] P.Chen, G.Wang, Y.Yang and J.Zhou, “Facial Expression Regcognition based on Rough set theory and SVM”, Lecture Notes in Computer Science, Springer Berlin/ Heidelberg, Rough sets and knowledge Technology, Vol. 4062, 2006, pp. 772777. [3] Pawlak. Z, “Rough Sets”, International Journal of Computer and Information Science, Vol. 11, 1982, pp.341-356. [4] Pawlak. Z and Slowinski. R, “Rough Set approach to multiattribute decision analysis”, Invited Review, Eur. Journal of Oper. Res., Vol.72, 1994, pp. 443-459. [5] Komorouski.J, Pawlak.Z, Polkowski.L,Skowron.A, “Rough Sets: A tutorial”,In Pal.S.K,Skowron.A (Eds) Rough Fuzzy Hybridization: A new trend in Decision making, springer, singapore, 1999, pp.3-98. [6] X-M. Huang and Y-H. Zhang, “A new application of rough set to ECG recognition”, In Int. Conference on Machine Learning and Cybernetics, volume 3,2003, pp.17291734. [7] Jianxun Zhang, Quanli Liu and Zhuang Chen,”A Medical Image Segmentation Method Based on SOM and Wavelet Transforms”, Journal of Communication and Computer , Vol.2, No.5, May 2005, pp.46-50. [8] Szladow. A and Ziarko. W, “ Rough sets: Working with imperfect data”, AI Expert, 7, 1993, pp. 36-41.
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