International Journal of Advanced Engineering Research and Technology (IJAERT)Volume 2 Issue 1, April 2014, ISSN No.: 2348 8190

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REVIEW PAPER ON SEGMENTATION WITH GRAPH-CUTPrabhjot Kaur1, Sumit Kaushik2

1M.Tech. Scholar, 2Assistant Professor,Kurukshetra University

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Abstract:In the current work, A technique which performsSegmentation of a image based on Graph-Cut approachis discussed. An image is considered as a group of nodesin a Graph G(V,E) where V are Nodes & E are Edgeswhereas Energy Minimization technique were employedin order to have a minimal Cut.Some of the work is discussed here.

Keywords: Energy function, Min-cut/max-flow,Segmentation..

1. INTRODUCTIONEnergy Function Minimized With Graph-CutThe energy function encodes the problem constraints,and its minimization gives the optimal solution. Thegeneral form of energy function for graph-cut isexplained from Markov Random Field by using theGibbs free energy and the Maximum PosterioriEstimation function [2, 3, 4]The energy function is denoted as

E(f) = Vp,q(fp,fq) + Dp(fp)

where F = {Fp |p P} is a labeling of image P,Dp(fp) is a data penalty function,Vp,q is an interaction potential,N is a set of all pairs of neighboring pixels[4, 3]

1.1 Markov Random FieldMRF provide a convenient prior for modelling spatialinteraction b/w pixels. The MRF framework can expressa wide variety of spatially varying priors.[11]A Markov process can be thought of as 'memoryless':loosely speaking, a process satisfies the Markov propertyif one can make predictions for the future of the processbased solely on its present state just as well as one couldknowing the process's full history. I.e., conditional onthe present state of the system, its future and pastare independent.[4, 8,10]

To give a formal definition of MRF, we 1st definelabeling field, Pixels and their Neighbours, Cliques andClique Potentials, Gibbs Distribution, Energyfunction.[2, 4,11]The objective of MRF is to either minimizes ormaximizes the Energy of the system. It also maximizesthe posterior probability function[8,10,11]i.e. E(A) = Elikelihood(A) + Eprior(A)

1.2 Energy Minimization.The energy minimization function minimizes the error ofthe image. It minimizes the noise from the image. In thelast few years, several new algorithms based on graphcuts have been developed to solve energy minimizationproblems in computer vision. Each of these techniquesconstructs a graph such that the minimum cut on thegraph also minimizes the energy[5]

Then E is graph-representable if and only if each termEi,j satisfies the inequality.

Ei,j(0, 0) + Ei,j(1, 1) Ei,j(0, 1) + Ei,j(1, 0).

1.3 Graph-CutGraph is an abstract representation of objects, whereobjects are connected by links.[7,12] Graph G = (V, E)consists of a set of nodes V and a set of directed edges Ethat connect them. Usually the nodes corresponds topixels etc.The graph have two special nodes called terminal nodesone is sink(T) and the other is source(S).[1,3,4,6,7] Theweights are given in the way that the minimal cutgoes along the borders of object.[7]An s-t cut in the graph is a subset of edges, such that theterminal nodes S and T get completely separated in thegraph.[1,3,4,7]The cost function that we use as a soft constraint forsegmentation is general enough to include both regionand boundary properties of segments. But the hardconstraints for segmentation include certain pixels fromobject and certain pixels background.[6]

International Journal of Advanced Engineering Research and Technology (IJAERT)Volume 2 Issue 1, April 2014, ISSN No.: 2348 8190

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fig1: Graph of 3-by-3 image[12]

2. LITERATURE SURVEYIn standard graph cuts, extraction of foreground objectsin a complex background often leads to manysegmentation errors. Iterated graph cuts algorithm, startsfrom the sub-graph that comprises the user labelledforeground/background regions and works iteratively tolabel the surrounding unsegmented regions[1]. Thegraph cuts framework proposed by Boykov and Jollyaddresses the segmentation of a monochrome image,which solves a labeling problem with two labels[3, 7]The interactive segmentation method is that it provides

a globally optimal solution for an N-dimensionalsegmentation when the cost function is clearlydefined.[6]In image segmentation, we want the boundary to lie onthe edges in the image can typically be found by B(p;q)in[1,6]Many methods are used for partitioning the image intoobject and background. Each method comes with its ownfeatures. The main method that i read is a computeboundary function. The function penalizes a lot fordiscontinuities between pixels of similar intensities when|Ip Iq | < .However, if pixels are very different, |Ip Iq | > , thenthe penalty is small.[1]

The penalty for discontinuity in the boundary cost is

B(p,q) = { 1 if Ip = Iq }{0.2 if Ip != Iq }

2.1 MIN-CUT/MAX-FLOW PROBLEM

In min-cut/max-flow problem the nodes of the graphare partitioned into two sub-sets one connected tosource(S) and other to sink (T)[3]. The theorem of Fordand Fulkerson[3] that is used for min-cut/max-flowproblem states that a maximum flow from s to t saturatesa set of edges in the graph dividing the nodes into twodisjoint parts {S, T } corresponding to a minimum cut

fig 2 : a) Original image b) Maimum flow c) Minimumflow

Some of the standard algorithms are:Dinic algorithm, Push-relabel method and the importantone is Ford-Fulkerson method[3]Dinic algorithm uses breadth-first search to find theshortest paths from s to t on the residual graph Gf. Theworst case running time complexity for Dinic algorithmis O(mn2) where n is the number of nodes and m is thenumber of edges in the graph. Another method isPreflow push that not only exploits the structuralproperties inherent in image based grid graphs but alsocombines the basic paradigms of max-flow theory in anovel way.[9]Push-relabel algorithms use quite a different approach.They do not maintain a valid flow during the operation;there are active nodes that have a positive flowexcess.

2.3 New Min-Cut/Max-Flow AlgorithmThe new min-cut/max-flow algorithm presented belongsto the group of algorithms based on augmentingpaths.[3] Similarly to Dinic algorithm it builds searchtrees for detecting augmenting paths. In that, we buildtwo search trees, one from the source and the other fromthe sink. The other difference is that we reuse these treesand never start building them from scratch.

International Journal of Advanced Engineering Research and Technology (IJAERT)Volume 2 Issue 1, April 2014, ISSN No.: 2348 8190

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fig 3: Example of the Search tree

The above figure illustrates the basic terms. We maintaintwo non-overlapping search trees S and T with roots atthe source s and the sink t, correspondingly. The nodesin the search trees S and T can be either active orpassive[3]

The algorithm iteratively repeats the following threestages:

1. growth stage: Search trees S and T grow untilthey touch giving an s-> t path.[3]

2. augmentation stage: The found path isaugmented, search tree break into forest[3]

3. adoption stage: Trees S and T are restored[3]

REFERENCES[1]. YURI BOYKOVGraph Cuts and Efficient N-DImage Segmentation. Computer Science, University ofWestern Ontario, London, ON, Canada and GARETHFUNKA-LEA, USA (2004)[2]. Bo Peng, Lei Zhang, and Jian Yang Iterated GraphCuts for Image Segmentation Department ofComputing, The Hong Kong Polytechnic University,Kowloon, Hong Kong, China. School of ComputerScience and Technology, Nanjing University of Scienceand Technology, Nanjing 210094, China.

[3]. Yuri Boykov and Vladimir Kolmogorov AnExperimental Comparison of Min-Cut/Max-FlowAlgorithms for Energy Minimization in Vision In IEEETransactions on PAMI, Vol. 26, No. 9, pp. 1124-1137,Sept. 2004.[4]. Olga Veksler, August(1999) Efficient Graph-BasedEnergy Minimization Methods in Computer Visionfaculty of Graduate School of Cornell University.[5]. Vladimir Kolmogorov member IEEE and RaminZabih member IEEE What Energy Functions Can BeMinimized via Graph Cuts? Computer ScienceDepartment, Cornell University, Ithaca, NY 14853.[6]. Boykov,Y., Jolly,M. P Interactive graph cuts foroptimal boundary and region segmentation of objects inN-D Images International Conference on ComputerVision, vol. I, pp 105-112(2001).[7]. Zhayida Simayijiang & Stefanie GrimmSegmentation Graph-Cut.[8]. Fahim Masnnan (260 266 294) Interactive ImageSegmentation.[9]. Chetan Arora, Subhashis Banerjee, Prem Kalra, andS.N. Maheshwari An Efficient Graph Cut Algorithmfor Computer Vision Problems Department ofComputer Science and Engineering, Indian Institute ofTechnology, Delhi, India.[10]. Michael Mc Grath Markov Random FieldImageModelling Degree Of Master Of Science at theUniversity of Cape Town, South Africa, June 2003.[11]. Yuri Boykov, Olga Veksler, Ramin Zabih MarkovRandom Fields with Efficient ApproximationsProceedings of IEEE conference on Computer ScienceDepartment Cornell University Computer Vision andPattern Recognition (CVPR), 1998.[12]. Anders P. Eriksson, Olof Barr and Kalle _Astr omImage Segmentation using minimal graph-cut Centrefor Mathematical Sciences, Lund University, SWEDEN.