REGION-BASED IMAGE SEGMENTATION VIA GRAPH CUTS Cevahir Çığla and A. Aydın Alatan Department of Electrical and Electronics Engineering, M.E.T.U, Turkey e-mail: cevahir@eee.metu.edu.tr, alatan@eee.metu.edu.tr ABSTRACT A graph theoretic color image segmentation algorithm is proposed, in which the popular normalized cuts image segmentation method is improved with modifications on its graph structure. The image is represented by a weighted undirected graph, whose nodes correspond to over-segmented regions, instead of pixels, that decreases the complexity of the overall algorithm. In addition, the link weights between the nodes are calculated through the intensity similarities of the neighboring regions. The irregular distribution of the nodes, as a result of such a modification, causes a bias towards combining regions with high number of links. This bias is removed by limiting the number of links for each node. Finally, segmentation is achieved by bipartitioning the graph recursively according to the minimization of the normalized cut measure. The simulation results indicate that the proposed segmentation scheme performs quite faster than the traditional normalized cut methods, as well as yielding better segmentation results due to its region- based representation. Index Terms— Over segmentation, normalized cuts, color segmentation 1. INTRODUCTION One of the most challenging problems in computer vision is color segmentation, which is also an irreplaceable tool for image understanding. Although many different approaches have been proposed for its solution, the problem has not been (and still far from being) completely solved due to its complicated, as well as subjective, range space. In the literature, most of the research has focused on solutions based on local properties [1][2][3]. Although they are quite efficient in general, the global characteristics might be lost during segmentation. On the other hand, within the last decade, graph theoretic segmentation methods have gained popularity, while utilizing graph cuts as their global optimization technique [4]-[10]. The graph theoretic approach introduces a top-to-bottom segmentation scheme in contrast to the local methods [4]. The image is considered as a “big picture” and mapped onto a weighted graph G, whose nodes (V) correspond to the pixels and the links (E) between the nodes are based on the similarities between these pixels. In different methods [4][5][7][9], segmentation is achieved by recursively bipartitioning the graph via minimizing cut measures according to the eigenvector decomposition of some special matrices. In [10], however, the partitioning is performed by utilizing nested cuts. A stochastic segmentation algorithm is also proposed in [8], based on k-way cuts. It should also be noted that in global methods, the clustering is performed by a similar mechanism as in human perception, from the whole to the details. Although the global methods take advantage of this realistic assumption, their execution can be time- consuming as the image size increases. The computation problem is usually tried to be alleviated by only down sampling the images [4] or performing a multi-scale approach [7]. Unfortunately, the visual details of the images are usually lost during these operations. In the proposed method, the normalized cuts image segmentation algorithm [4] is improved in order to decrease its computation time and increase its performance while preserving the visual details. To this aim, the graph structure is modified by assigning over- segmented regions as the nodes of the graph, instead of pixels, in order to decrease the graph complexity. Such a modification results in an irregular node distribution creating a bias towards combining regions with higher number of links. A solution to this problem is also proposed in order to remove the drawbacks of such a bias on the segmentation quality. This paper is organized as follows; in Section 2 the overview of the normalized cuts image segmentation algorithm is given. The details of the proposed method are explained in Section 3. After presenting the experimental results in Section 4, the final section is devoted to the concluding remarks. 2. OVERVIEW OF NORMALIZED CUTS IMAGE SEGMENTATION Normalized Cut Image Segmentation (NCIS) [4] is a global graph- based segmentation method that utilizes a splitting process beginning from the whole picture to the bottom. There are two main steps in NCIS, construction of the graph and iterative partitioning. The top-down property of the normalized cut method is provided by initially mapping the image onto a graph that holds the relations between pixels. An undirected weighted graph is constructed, in which the vertices correspond to the pixels and the link weights are evaluated via a linking cost function, given below. elsewhere R j X i X e w x I j X i X j I i I j i 0 ) ( ) ( 2 / ) ( ) ( . / ) ( ) ( , 2 2 (1) In (1), I is the intensity image, I(i) indicates the intensity value of the i th pixel and X represents the location of these pixels. In the graph, the pixels which are located within a circle of radius R are linked to each other; hence the graph is partial and the link weights define similarities between nodes as a function whose range space is [0,1].