Salient closed boundary extraction with ratio contour

We present ratio contour, a novel graph-based method for extracting salient closed boundaries from noisy images. This method operates on a set of boundary fragments that are produced by edge detection. Boundary extraction identifies a subset of these fragments and connects them sequentially to form a closed boundary with the largest saliency. We encode the Gestalt laws of proximity and continuity in a novel boundary-saliency measure based on the relative gap length and average curvature when connecting fragments to form a closed boundary. This new measure attempts to remove a possible bias toward short boundaries. We present a polynomial-time algorithm for finding the most-salient closed boundary. We also present supplementary preprocessing steps that facilitate the application of ratio contour to real images. We compare ratio contour to two closely related methods for extracting closed boundaries: Elder and Zucker's method based on the shortest-path algorithm and Williams and Thornber's method based on spectral analysis and a strongly-connected-components algorithm. This comparison involves both theoretic analysis and experimental evaluation on both synthesized data and real images.

[1]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[2]  Lawrence G. Roberts,et al.  Machine Perception of Three-Dimensional Solids , 1963, Outstanding Dissertations in the Computer Sciences.

[3]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[4]  Irwin Edward Sobel,et al.  Camera Models and Machine Perception , 1970 .

[5]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Harold N. Gabow,et al.  A scaling algorithm for weighted matching on general graphs , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[7]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Shimon Ullman,et al.  Structural Saliency: The Detection Of Globally Salient Structures using A Locally Connected Network , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[9]  Stuart German,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1988 .

[10]  Laurent D. Cohen,et al.  A finite element method applied to new active contour models and 3D reconstruction from cross sections , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[11]  Ramesh C. Jain,et al.  Using Dynamic Programming for Solving Variational Problems in Vision , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Mubarak Shah,et al.  A fast algorithm for active contours , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[13]  Tai Sing Lee,et al.  Texture Segmentation by Minimizing Vector-Valued Energy Functionals: The Coupled-Membrane Model , 1992, ECCV.

[14]  James S. Duncan,et al.  Boundary Finding with Parametrically Deformable Models , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Richard M. Leahy,et al.  An Optimal Graph Theoretic Approach to Data Clustering: Theory and Its Application to Image Segmentation , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[17]  Gérard G. Medioni,et al.  Inferring global perceptual contours from local features , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[18]  V. Caselles,et al.  A geometric model for active contours in image processing , 1993 .

[19]  I Kovács,et al.  A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[20]  David W. Jacobs.  Robust and efficient detection of convex groups , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[21]  David Mumford,et al.  Filtering, Segmentation and Depth , 1993, Lecture Notes in Computer Science.

[22]  Radu Horaud,et al.  Figure-Ground Discrimination: A Combinatorial Optimization Approach , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  Kim L. Boyer,et al.  Hypothesizing structures in edge-focused cerebral magnetic resonance images using graph-theoretic cycle enumeration , 1993 .

[24]  K. Raghunath Rao,et al.  Optimal Edge Detection using Expansion Matching and Restoration , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  David Mumford,et al.  Bayesian Rationale for the Variational Formulation , 1994, Geometry-Driven Diffusion in Computer Vision.

[26]  Bart M. ter Haar Romeny,et al.  Geometry-Driven Diffusion in Computer Vision , 1994, Computational Imaging and Vision.

[27]  Steven W. Zucker,et al.  Logical/Linear Operators for Image Curves , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Timothy F. Cootes,et al.  Active Shape Models-Their Training and Application , 1995, Comput. Vis. Image Underst..

[29]  Steven W. Zucker,et al.  Computing Contour Closure , 1996, ECCV.

[30]  Lance R. Williams,et al.  Analytic solution of stochastic completion fields , 1995, Biological Cybernetics.

[31]  Ingemar J. Cox,et al.  "Ratio regions": a technique for image segmentation , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[32]  Ronen Basri,et al.  Extracting Salient Curves from Images: An Analysis of the Saliency Network , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[33]  Kim L. Boyer,et al.  Quantitative measures of change based on feature organization: eigenvalues and eigenvectors , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[34]  Alan L. Yuille,et al.  Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[35]  Anil K. Jain,et al.  Object Matching Using Deformable Templates , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[36]  David W. Jacobs,et al.  Robust and Efficient Detection of Salient Convex Groups , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[37]  Lance R. Williams,et al.  Stochastic Completion Fields: A Neural Model of Illusory Contour Shape and Salience , 1997, Neural Computation.

[38]  Sudeep Sarkar,et al.  Robust Visual Method for Assessing the Relative Performance of Edge-Detection Algorithms , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[39]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[40]  Daniel Rueckert,et al.  Geometrically Deformable Templates for Shape-Based Segmentation and Tracking in Cardiac MR Images , 1997, EMMCVPR.

[41]  Pietro Perona,et al.  A Factorization Approach to Grouping , 1998, ECCV.

[42]  Jerry L. Prince,et al.  Snakes, shapes, and gradient vector flow , 1998, IEEE Trans. Image Process..

[43]  Michael Lindenbaum,et al.  A Generic Grouping Algorithm and Its Quantitative Analysis , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[44]  Sean Dougherty,et al.  Edge detector evaluation using empirical ROC curves , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[45]  Michael Werman,et al.  Stochastic image segmentation by typical cuts , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[46]  William J. Cook,et al.  Computing Minimum-Weight Perfect Matchings , 1999, INFORMS J. Comput..

[47]  Olivier D. Faugeras,et al.  Statistical shape influence in geodesic active contours , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[48]  Ronen Basri,et al.  Fast multiscale image segmentation , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[49]  Olga Veksler,et al.  Image segmentation by nested cuts , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[50]  Sudeep Sarkar,et al.  Supervised Learning of Large Perceptual Organization: Graph Spectral Partitioning and Learning Automata , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[51]  Ronen Basri,et al.  Completion Energies and Scale , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[52]  Ronen Basri,et al.  Segmentation and boundary detection using multiscale intensity measurements , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[53]  Ian H. Jermyn,et al.  Globally Optimal Regions and Boundaries as Minimum Ratio Weight Cycles , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[54]  Xiao Han,et al.  A topology preserving deformable model using level sets , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[55]  Jitendra Malik,et al.  A Probabilistic Multi-scale Model for Contour Completion Based on Image Statistics , 2002, ECCV.

[56]  Toshiro Kubota,et al.  Salient Boundary Detection using Ratio Contour , 2003, NIPS.

[57]  Alan L. Yuille,et al.  Statistical Edge Detection: Learning and Evaluating Edge Cues , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[58]  Sudeep Sarkar,et al.  An In-Depth Study of Graph Partitioning Measures for Perceptual Organization , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[59]  Adrian Barbu,et al.  Graph partition by Swendsen-Wang cuts , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[60]  Toshiro Kubota,et al.  Contextual and Non-combinatorial Approach to Feature Extraction , 2003, EMMCVPR.

[61]  Ronen Basri,et al.  Texture segmentation by multiscale aggregation of filter responses and shape elements , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[62]  Lance R. Williams,et al.  Segmentation of Multiple Salient Closed Contours from Real Images , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[63]  Jeffrey Mark Siskind,et al.  Image Segmentation with Ratio Cut , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[64]  Benjamin B. Kimia,et al.  Euler Spiral for Shape Completion , 2003, International Journal of Computer Vision.

[65]  Ronen Basri,et al.  Extracting Salient Curves from Images: An Analysis of the Saliency Network , 2004, International Journal of Computer Vision.

[66]  Lance R. Williams,et al.  A Comparison of Measures for Detecting Natural Shapes in Cluttered Backgrounds , 1998, International Journal of Computer Vision.

[67]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[68]  Song Wang,et al.  From fragments to salient closed boundaries: an in-depth study , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..