Automatic Image Segmentation Using Graph Cut

Transcription

1 682 Automatic Segmentation Using Cut Prabhjot Singh 1, Er. Deepak Sharma 2 1 M.Tech Scholar, Deptt. of ECE, MMEC, Mullana, Ambala. 2 Assistant Professor, Deptt.of ECE, MMEC, Mullana, Ambala ABSTRACT segmentation is the process of partitioning an image into multiple segments, so as to change the representation of an image into something that is more meaningful and easier to analyze. Several generalpurpose algorithms and techniques have been developed for image segmentation. segmentation refers to partition of an image into different regions that are homogenous or similar and inhomogeneous in some characteristics as the new graph approach is an emerging technique for image segmentation, as it can minimize an energy function composed of data term estimated in feature space and smoothness term estimated in an image domain. Previous approaches using graph s have shown good performance for image segmentation, they manually obtained prior information to estimate the data term, thus automatic image segmentation is one of issues in application using the graph s method. As it requires low computational complexity and is therefore very feasible for real-time image segmentation processing. In the experiments, we investigated problems of previous methods such as mean shift segmentation, watershed technique and automatic graph based image segmentation As a result, the graph method showed better performance than previous methods. Keywords: - Mean Shift, Watershed, Cuts, Edge Based Segmentation. 1. INTRODUCTION processing refers to processing of a 2D picture by a computer. An image is defined in the real world is considered to be a function of two real variables. An image is an array, or a matrix, of square pixels (picture elements) arranged in columns and rows, which identifies a point in the image and the corresponding matrix element value identifies the gray level at that point. processing is a method to convert an image into digital form and perform some operations on it, in order to get an enhanced image or to extract some useful information from its image domain [1]. Segmentation is the process of partitioning a digital image into multiple regions or sets of pixels. Actually, partitions are different objects in image which have the same texture or color. All of the pixels collectively cover the entire image, or a set of contours to some, or texture [2]. Generally the image segmentation algorithms can be generally classified into two Feature space-based and image domain-based segmentations [3]. Approaches to feature space-based segmentation capture the global characteristics of images through image features expressed in feature space, which are usually based on the color, texture and the image features are grouped into compact, but well-separated clusters by using several clustering algorithm [4]. Although the feature space-based clustering approaches are efficient in finding salient clusters, there was no guarantee at all that these regions showed spatial compactness in an image domain. This means the feature space-based approaches did not exploit the important fact that features of same region are spatially close due to spatial coherence [3]. Therefore, approaches to image domain-based segmentation have been utilized due to the need to preserve the spatial relationship between the features in the image domain. Although many algorithms, such as watershed algorithm and mean shift algorithm in image domain, have been introduced but it may undesirably produce a very large number of small quasi-homogenous regions, thus some merging algorithm should be applied to these region [6]. Recently, a graph s method has taking a lot of attention for image segmentation. The graph s method is one of minimizing energy functions elegantly expressed as MRF (Markov Random Field), and the energy function consists of two terms; the first term, called data term, is to globally capture the characteristics of an image in feature space, and the second term, called smoothness term, is to preserve spatial information in an image domain [1]. Thus, the graph s-based approach can combine above mentioned two approaches, clustering in feature space and preserving spatial relationship in image domain [7]. segmentation is an extremely important operation in several applications of image processing and computer vision, such as object tracking, recognition and many more., video segmentation is a critical step of image analysis occupying the middle layer of image engineering, which means it is influenced not only from data but also from human factors [2]. The remainder of this paper is organized as follows. The energy function for image segmentation and the

2 683 previous methods for image segmentation are introduced in section 2, and section 3 automatic obtain the prior information for each class using graph. Experimental results are presented in section 4, and the final conclusions are given in section 5. Energy Function for Segmentation for labeling problems solving the pixel labeling problem is one of the most frequent applications of energy minimization in Computer Vision. Through pixel labeling problems image restoration, segmentation, problems as stereo and motion are generalized. In general energy functions like E are non convex functions in large dimension spaces and hence very difficult to minimize. However, when these energy functions have special characteristics, it is possible to find their exact minimum using dynamic programming [8-9]. A property of a graph C is that it can be related to a labeling f, mapping the set of vertices V {s, t} of a graph G to the set {0, 1}, where f(v) = 0, if v S, and f(v) = 1, if v T. A labeling problem is specified in terms of a set of site S and a set of label L. Consider a random field consisting of a set of discrete random variable F = {F1,F2,,Fn} defined on the set S, such that each variable Fs takes one of labels fs in L, where s is index of the set of sites. For a discrete label set L, the probability that random variable Fs takes the value fs is denoted P(fs), and the joint probability is denoted P(f), where f = {f1,f2,,fn}. Here, f is a configuration of F, corresponding to a realization of the field [7]. 2. PREVIOUS APPROACHES Mean shift method Its a non-parametric feature-space analysis technique, a so-called mode seeking algorithm. Mean shift is a procedure for locating the maxima of a density function given discrete data sampled from that function. It is useful for detecting the modes of this density. This is an iterative method, and we start with an initial estimate x. Let a kernel function ( )be given. This function determines the weight of nearby points for re-estimation of the mean [10]. Typically Gaussian kernel on the distance to the current estimate is used, ( ) =. The weighted mean of the density in the window determined by k is: ( ) = ( ) ( ) ( ) ( ) (1) Where ( )is the neighborhood of x, a set of points for which k(x) 0. The MS algorithm is a robust featurespace analysis approach which can be applied to discontinuity preserving smoothing and image segmentation problems. It can significantly reduce the number of basic image entities, and due to the good discontinuity preserving filtering characteristic, the salient features of the overall image are retained. The latter property is particularly important in the partitioning of natural images, in which only several distinct regions are used in representing different scenes such as sky, lake, sand beach, person, and animal, where as other information within a region is often less important and can be neglected. However, it is difficult to partition a natural image into significative regions to represent distinct scenes, depending only on the MS segmentation algorithm. The main reason is that the MS algorithm is an unsupervised clustering-based segmentation method, where the number and the shape of the data cluster are unknown a priori. Moreover, the termination of the segmentation process is based on some region-merging strategy applied to the filtered image result, and the number of regions in the segmented image is mainly determined by the minimum number of pixels in a region, which is denoted as M (i.e. regions containing less than M pixels will be eliminated and merged into its neighboring region) [10]. Mean Shift is considered a robust technique used for image segmentation, visual tracking etc. Mean shift method is an iterative mode detection algorithm in the density distribution space or a tool for finding modes in a set of data samples. Mean shift procedure is as follows: 1. Find a window around each data point. 2. Compute the mean of data within the window. 3. Translate density estimation window. 4. Shift the window to the mean and repeat till convergence [11]. Watershed technique A grey-level image may be seen as a topographic relief, where the grey level of a pixel is interpreted as its altitude in the relief. A drop of water falling on a topographic relief flows along a path to finally reach a local minimum. Intuitively, the watershed of a relief corresponds to the limits of the adjacent catchment basins of the drops of water. In image processing, different watershed lines may be computed. In graphs, some may be defined on the nodes, on the edges, or hybrid lines on both nodes and edges. Watersheds may also be defined in the continuous domain. There are also many different algorithms to compute watersheds. For a segmentation purpose, the gradient magnitude (i.e., the length of the gradient vectors) is interpreted as elevation information. Watershed transformation also called, as watershed method is a powerful mathematical morphological tool for the image segmentation. It is more popular in the fields like biomedical and medical

3 684 image processing, and computer vision [12]. In geography, watershed means the ridge that divides areas drained by different river systems. If image is viewed as geological landscape, the watershed lines determine boundaries which separate image regions. The watershed transform computes catchment basins and ridgelines (also known as watershed lines), where catchment basins corresponding to image regions and ridgelines relating to region boundaries [13]. Segmentation by watershed embodies many of the concepts of the three techniques such as threshold based, edge based and region based segmentation. 3. GRAPH CUT METHOD segmentation relates basically background and object which can be employed as binary labeling problem. Boykov et al. [14] mentioned the segmentation of a monochrome image that solves a two labels problem in the graph method. Considering a set of labels L and a set of sites S, the labeling problem can be assigned as a label and each of the site. The label set L= {0, 1} where 0 indicates background and 1 indicates object. For a labeling problem if f= for all pixels, the energy minimization Markov Random Field (MRF) equation [10] can be written as: ( ) = + ( ). {, } ) (2) In the energy minimization equation, the first term called as data term consists of constraints from the observed data and measures how the labels are assigned. Label fp fits with site p and is measured by Dp. The second term which is the smoothness term measures to what extent f is not piecewise smooth. N represents the neighborhood system like 4 or 8- connected system. If f = f, T(f f )becomes 0 and 1 otherwise. In image segmentation it is expected the boundary to be positioned on the edges. Hence the typical selection of is: = ( ) 2 1 (, ) (3) Color values of Sites p and q are represented by Ip and Iq along with distance between p and q is presented by dist (p,q). Level of variation between neighboring sites is expressed by the parameter. The relative importance of the data term versus smoothness term is revealed by the parameter [14]. s method has attracted a lot of attention for image segmentation. The graph s method is one of minimizing energy functions elegantly expressed as MRF (Markov random field), Such energy minimizations problems can be reduced to instances of the maximum flow problem in a graph (and thus, by the max-flow min- theorem, define a minimal of the graph). Under most formulations of such problems in computer vision, the minimum energy solution corresponds to the maximum a posteriori estimate of a solution. Although many computer vision algorithms involve ting a graph (e.g. normalized s), the term "graph s" is applied specifically to those models which employ a max-flow/min- optimization (other graph ting algorithms may be considered as graph partitioning algorithms)."binary" problems (such as denoising a binary image) can be solved exactly using this approach; problems where pixels can be labelled with more than two different labels (such as stereo correspondence, or denoising of a grayscale image) cannot be solved exactly, but solutions produced are usually near the global optimum. In the Bayesian statistical context of smoothing noisy (or corrupted) images, they showed how the maximum a posteriori estimate of a binary image can be obtained exactly by maximizing the flow through an associated image network, involving the introduction of a source and sink, using min max flow algorithm [8]. Fig.1: for image segmentation (source and sink) [8]. Notations: : {,, } Output: Segmentation (also called opacity) S {R} (soft segmentation). For hard segmentation S { 0 for background, 1 for foreground/ object to be detected } Energy function: (,,, )where C is the color parameter and λ is the coherence parameter. (,,, ) = + Optimization: The segmentation can be estimated as a global minimum over : (,,, ) [7].

4 EXPERIMENTS RESULTSS To verify the effectiveness of the proposedposed graph method, quantitative evaluation was tested ted with natural color and the real MRI brain images, and for comparison, two methods were applied to the same test. The performance of image segmentation n on the test set was evaluated in terms of visually and the subjective parameters such as PSNR, MSE and the computational TIME. Table 1 shows list the PSNR, MSE and TIME on the test set. The proposed method outperformed the previous two methods on the test set, and it was closer to human segmentation than other algorithms. The problems of previous two methods for image segmentation are as follows the result of The MS undesirably produced a very large number of small but quasi-homogeneous regions as shown in figure shown. This is equal to the problem of the image domain-based segmentation, as the mean shift procedure is performed only in an image domain. Thus, the MS is sensitive to noises, as affected by edge information. Therefore, the gradient based method (watershed technique) is also not found suitable as these are observed that t they are highly sensitive to noise and not segmenting the discontinuities in the image, only identifies the outer boundaries so this is a major drawback of the watershed algorithm. showed better performance than other two methods, in any cases of classes with arbitrary-shapes, then proposed method is applied to real brain MRI images. As the PSNR and MSE and TIME of the proposed method is high, low, less respectively. This makes this method accurate and efficient for real images. From figure (a -o) the results obtained by applying the image segmentation methods on the any of the image and the real MRI images. The results are compared visually and using subjective parameter such as PSNR, MSE and Computational Time. Fig. a: shows input and grey Fig. b: Shows result for level image mean shift Table 1: Comparison using different parameters Segmentati on Tech. PSNR MS E COMPUTA TION TIME Mean shift Watershed (adjacant) (k-nearest) 7 Mean shift Watershed (adjacant) (k-nearest) Mean shift Watershed (adjacant) (k-nearest) Fig. c: shows result for Watershed Fig. d: shows result for adjacent neighborhood G.C The proposed method as shown in figure shown have properly segments the image consist of two outputs (adjacent neighbourhood and k nearest neighboured), less sensitive to noises and overcame the problem and Fig. e: result for k nearest Fig. f: shows input and grey Neighborhood graph level image

5 686 Fig. g: shows result for mean shift Fig. i: shows result for adj acent neighborhood Fig. k: shows input and grey level image Fig. h: shows result for watershed Fig. j: shows result for k- nearest Neighborhood Fig. l: result show for mean shift Fig. o: result for k nearest Neighborhood graph PSNR image 3 image 4 image 5 MEAN SHIFT WATERSHED GRAPH CUT(A) GRAPH CUT(K) Figure p: Comparison of PSNR for image 1, image 2 and image 3 with different methods MSE image 1image 2image 3 MEAN SHIFT WATERSHED GRAPH CUT(A) GRAPH CUT(K) Figure q: Comparison of MSE for image 1, image 2 and image 3 with different methods TIME image 3 image 4 image 5 Fig. m: shows result for Watershed Fig. n: shows result for adj- -acent neighborhood graph MEAN SHIFT WATERSHED GRAPH CUT(A) GRAPH CUT(K) Figure r: Comparison of TIME for image 1, image 2 and image 3 with different methods

6 CONCLUSION From the results obtained, it is evident that the automatic graph method is capable of accurately segmenting any of the arbitrary shapes at the cost of computational time, as it overcame the problems from the graph using GMM approach of segmentation which is only applicable to the hyper-spherical and hyper-ellipsoidal classes. This technique is also highly efficient in segmenting the brain tissues and other brain element in brain MRI images. REFRENCES [1] H.P. Narkhede, Review of Segmentation Techniques International Journal of Science and Modern Engineering (IJISME) ISSN: , Vol.1, Issue 8, July, [2] S. Tripathi, K. Kumar, B.K.Singh, R.P.Singh, Segmentation: A Review, International Journal of Computer Science and Management Research, Vol. 1, Issue 4, November, [3] L. Lucchese and S.K. Mitra, Color Segmentation: A State-of-the-Art Survey, Proceedings of the Indian National Science Academy (INSA -A), 67(2): pp , [4] L. Vincent and P. Soille, Watersheds in Digital Space: An Efficient Algorithm based on Immersion Simulation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(6): pp , [5] D. Comaniciu and P. Meer, Mean Shift: A Robust Approach toward Feature Space Analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(5): pp , [6] S. Makrogiannis, G. Economou, and S. Fotopoulos, A Region Dissimilarity Relation that Combines Feature-Space and Spatial Information for Color Segmentation, IEEE Transactions on System, Man, and Cybernetics, Part B, 35(1): pp , [7] A. Park, J. Kim, S. Min, S. Yun, K. Jung, Cuts based Automatic Color Segmentation using Mean Shift Analysis IEEE Digital Computing: Techniques and Applications, [8] Y. Boykov, V. Kolmogorov, An experimental comparison of min-/max-flow algorithms for energy minimization in vision, IEEE Trans, Pattern Anal. Machine Intell., 26, pp , [9] Geman, S., Geman, D., Stochastic relaxation, gibbs distributions, and the Bayesian restoration of images, IEEE Trans, Pattern Anal. Machine Intell, pp , [10]M. Sonka, V. Hlavac and R. Boyle, processing, analysis, and machine vision, Third edition, Thomson, USA, [11] G. kaur Seerha, R. kaur, Review on Recent Segmentation Techniques, International Journal on Computer Science and Engineering (IJCSE) ISSN: Vol. 5 No. 02, Feb, [12] Md. Shakowat Z. Sarker, T. Wooi Haw and R. Logeswaran, Morphological based technique for image segmentation, International Journal of Information Technology, Vol. 14, No. 1, [13] M. Bhagwat, R. K. Krishna and V. Pise, Simplifed Watershed Transformation, International Journal of Computer Science and Communication, Vol.1, No. 1, pp , [14] Y. Boykov and M. Jolly, Interactive graph s for optimal boundary and region segmentation of objects in n-d images, Proceedings of ICCV, [15] W. Tao, H. Jin, Senior Member, IEEE, and Yimin Zhang, Senior Member, IEEE, Color Segmentation Based on Mean Shift and Normalized Cuts IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, Vol. 37, No. 5, pp , October [16] J. Mo, C. Wang, T. Zhang, H. Yua, Improved graph-based image segmentation based on Mean Shift 1 Communications and Networking in China, 8th International ICST Conference on Digital Object Identifier: /ChinaCom , pp , [17] W. Ming Chen, S. Hao Jhang, Improving Cuts algorithm to transform sequence of stereo image to depth map The Journal of Systems and Software 86, pp , [18] Dedic, R. Allili, Madjid, A novel cooperative approach for cardiac PET image segmentation Information Science, Signal Processing and their Applications (ISSPA), th International Conference on Digital Object Identifier: /ISSPA pp ,2012. [19] B. Padmapriya, T. Kesavamurthi, H. Wassim Ferose, Edge Based Segmentation Technique for Detection and Estimation of the Bladder Wall Thickness Procedia Engineering 30, pp , [20] C. Ballangan, X. Wang, M. Fulham, S. Eberl, D. Dagan Feng, lung tumor segmentation in pet images using graph s computer methods and programs in biomedicine 1 09, pp , 2013.