NOVEL GRAPH BASED METHOD FOR IMAGE SEGMENTATION

Automatic grouping and segmentation of images remains a challenging problem in computer vision. Recently , a number of authors have demonstrated g o od performance on this task using methods that are b ased on eigenvectors of the aanity matrix. These approaches are extremely attractive in that they are b ased on simple eigendecomposition algorithms whose stability is well understood. Nevertheless, the use of eigen-decompositions in the context of segmentation is far from well understood. In this paper we give a uni-ed t r eatment of these algorithms, and show the close connections between them while highlighting their distinguishing features. We then prove results on eigen-vectors of block matrices that allow us to analyze the performance of these algorithms in simple grouping settings. Finally, we use our analysis to motivate a variation on the existing methods that combines aspects from diierent eigenvector segmentation algorithms. We illustrate our analysis with results on real and synthetic images. Human perceiving a scene can often easily segment it into coherent segments or groups. There has been a tremendous amount of eeort devoted to achieving the same level of performance in computer vision. In many cases, this is done by associating with each pixel a feature vector e.g. color, motion, texture, position and using a clustering or grouping algorithm on these feature vectors. Perhaps the cleanest approach to segmenting points in feature space is based on mixture models in which one assumes the data were generated by m ultiple processes and estimates the parameters of the processes and the number of components in the mixture. The assignment of points to clusters can then be easily performed by calculating the posterior probability o f a point belonging to a cluster. Despite the elegance of this approach, the estimation process leads to a notoriously diicult optimization. The frequently used EM algorithm 3 often converges to a local maximum that depends on the initial conditions. Recently, a n umber of authors 11, 10, 8, 9, 22 have suggested alternative segmentation methods that are based on eigenvectors of the possibly normalized aanity matrix". Figure 1a shows two clusters of points and gure 1b shows the aanity matrix deened by: Wi; j = e ,dxi;xj=2 2 1 with a free parameter. In this case we h a ve used dx i ; x j = kx i ,x j k 2 but diierent deenition of aani-ties are possible. The aanities do not even have t o obey the metric axioms e.g. 7, we will only assume that dx i ; x j = dx j ; x i. Note that we h a ve ordered the points so that all points belonging to the rst cluster appear rst and the points in the second cluster. This helps the visualization of the matrices but does not change the algorithms | eigenvectors of permuted matrices are the permutations of the eigenvectors of the original matrix. From visual inspection, the aanity matrix contains information about the correct segmentation. In the next section we review four algorithms that look at eigenvectors of aanity matrices. We show that while seemingly quite diierent, these algorithms are closely related and all use dominant eigenvectors of matrices to perform segmentation. However, these approaches use diierent matrices, focus on diierent eigenvectors and use a diierent method of going from the continuous eigenvectors to the discrete segmentation. In section 2 we prove results on eigendecompositions of block matrices and use these results to analyze the behavior of these algorithms and motivate a new hybrid algorithm. Finally, in section 3 we discuss the application of these algorithms to aanity matrices derived from images.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006

Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem. This approach produces the high quality segmentations of spectral methods, but with improved speed and stability.

2012

The graph partitioning has been widely used as a mean of image segmentation. One way to partition graphs is through a technique known as Normalized Cut, which analyzes the graph’s Laplacian matrix eigenvectors and uses some of them for the cut. This work proposes the use of Normalized Cut in graphs generated by structures based on Quadtree and Component Tree to perform image segmentation. Experiments of image segmentation by Normalized Cut in these models are made and a specific benchmark compares and ranks the results obtained by other graph-conversion techniques proposed in the literature. The results are promising and allow us to conclude that the use of different graph models combined with the Normalized Cut can yield better segmentations according to the characteristics of images. Keywords-Image Segmentation; Normalized Cut; Quadtree; Component Tree

2012 Fourth International Conference on Computational Intelligence, Communication Systems and Networks (CICSyN)

Image segmentation with low computational burden has been highly regarded as important goal for researchers. Various image segmentation methods are widely discussed and more noble segmentation methods are expected to be developed when there is rapid demand from the emerging machine vision field. One of the popular image segmentation methods is by using normalised cuts algorithm. It is unfavourable for a high resolution image to have its resolution reduced as high detail information is not fully made used when critical objects with weak edges is coarsened undesirably after its resolution reduced. Thus, a graph-based image segmentation method done in multistage manner is proposed here. In this paper, an experimental study based on the method is conducted. This study shows an alternative approach on the segmentation method using k-means clustering and normalised cuts in multistage manner.

Journal of Computer Science and Cybernetics, 2015

Cluster analysis is an unsupervised technique of grouping related objects without considering their label or class. The objects belonging to the same cluster are relatively more homogeneous in comparison with other clusters. The application of cluster analysis is in areas like gene expression analysis, galaxy formation, natural language processing and image segmentation etc. The clustering problem can be formulated as a graph cut problem where a suitable objective function has to be optimized. This study uses different graph cluster formulations based on graph cut and partitioning problems. A special class of graph clustering algorithm known as spectral clustering algorithms is used for the study. Two widely used spectral clustering algorithms are applied to explaining solution to these problems. These algorithms are generally based on the Eigen-decomposition of Laplacian matrices of either weighted or non-weighted graphs.

Image segmentation is the process of subdividing a digital image into its systematized regions or objects which is useful in image analysis. In this review paper, we carried out an organized survey of many image segmentation techniques which are flexible, cost effective and computationally more efficient. We classify these segmentation methods into three categories: the traditional methods, graph theoretical methods and combination of both traditional and graph theoretical methods. In the second and third category of image segmentation approaches, the image is modeled as a weighted and undirected graph. Normally a pixel or a group of pixels are connected with nodes. The edge weights represent the dissimilarity between the neighborhood pixels. The graph or the image is then divided according to a benchmark designed to model good clusters. Every partition of the nodes or the pixels as output from these algorithms is measured as an object segment in an image representing a graph. Some of the popular algorithms are thresholding, normalized cuts, iterated graph cut, clustering method, watershed transformation, minimum cut, grey graph cut, and minimum spanning treebased segmentation.

International Journal for Research in Applied Science and Engineering Technology

In image processing, segmentation is the process of partitioning digital image into multiple sets of pixels, according to some homogeneity standard. The goal of segmentation is to simplify or change the representation of an image into something that is more meaningful and easier to analyze. Segmentation by computing a minimal cut in a graph is a new and quite general approach for segmenting images. This approach guarantees global solutions, which always find best solution. Graph cut has emerged as a preferred method to solve a class of energy minimization problems such as Image Segmentation. In this paper we used graph cut method to solve image segmentation problem and we got successful results in image segmentation. In this project we proposed a new approach by using optimized normalized cut with combination with K-means algorithm to do the segmentation of static image. In this method we used efficient computational technique based on eigen values and eigen vectors to get optimized segmented image.

2000

I mage segmentation is an essential tool to enhance the ability of computer systems to efficiently perform elementary cognitive tasks such as detection, recognition and tracking. In this thesis we concentrate on the investigation of two fundamental topics in the context of image segmentation: spectral clustering and seeded image segmentation. We introduce two new algorithms for those topics that, in summary, rely on Laplacian-based operators, spectral graph theory, and minimization of energy functionals. The effectiveness of both segmentation algorithms is verified by visually evaluating the resulting partitions against state-of-the-art methods as well as through a variety of quantitative measures typically employed as benchmark by the image segmentation community. Our spectral-based segmentation algorithm combines image decomposition, similarity metrics, and spectral graph theory into a concise and powerful framework. An image decomposition is performed to split the input image into texture and cartoon components. Then, an affinity graph is generated and weights are assigned to the edges of the graph according to a gradient-based inner-product function. From the eigenstructure of the affinity graph, the image is partitioned through the spectral cut of the underlying graph. Moreover, the image partitioning can be improved by changing the graph weights by sketching interactively. Visual and numerical evaluation were conducted against representative spectral-based segmentation techniques using boundary and partition quality measures in the well-known BSDS dataset. vii Unlike most existing seed-based methods that rely on complex mathematical formulations that typically do not guarantee unique solution for the segmentation problem while still being prone to be trapped in local minima, our segmentation approach is mathematically simple to formulate, easy-to-implement, and it guarantees to produce a unique solution. Moreover, the formulation holds an anisotropic behavior, that is, pixels sharing similar attributes are preserved closer to each other while big discontinuities are naturally imposed on the boundary between image regions, thus ensuring better fitting on object boundaries. We show that the proposed approach significantly outperforms competing techniques both quantitatively as well as qualitatively, using the classical "GrabCut" dataset from Microsoft as a benchmark. While most of this research concentrates on the particular problem of segmenting an image, we also develop two new techniques to address the problem of image inpainting and photo colorization. Both methods couple the developed segmentation tools with other computer vision approaches in order to operate properly.

Intelligent Multidimensional Data Clustering and Analysis

Different graph theoretic approaches are prevalent in the field of image analysis. Graphs provide a natural representation of image pixels exploring their pairwise interactions among themselves. Graph theoretic approaches have been used for problem like image segmentation, object representation, matching for different kinds of data. In this chapter, we mainly aim at highlighting the applicability of graph clustering techniques for the purpose of image segmentation. We describe different spectral clustering techniques, minimum spanning tree based data clustering, Markov Random Field (MRF) model for image segmentation in this respect.

Concepts, Methodologies, Tools, and Applications, 2013

Segmentation is a fundamental step in image analysis and remains a complex problem. Many segmentation methods have been proposed in the literature but it is difficult to compare their efficiency. In order to contribute to the solution of this problem, some evaluation criteria have been proposed for the last decade to quantify the quality of a segmentation result. Supervised evaluation criteria use some a priori knowledge such as a ground truth while unsupervised ones compute some statistics in the segmentation result according to the original image. The main objective of this chapter is to first review both types of evaluation criteria from the literature. Second, a comparative study is proposed in order to identify the efficiency of these criteria for different types of images. Finally, some possible applications are presented.