Stochastic Jump-Diffusion Process for Computing Medial Axes in Markov Random Fields

Proposes a statistical framework for computing medial axes of 2D shapes. In the paper, the computation of medial axes is posed as a statistical inference problem not as a mathematical transform. The paper contributes to three aspects in computing medial axes. 1) Prior knowledge is adopted for axes and junctions so that axes around junctions are regularized. 2) Multiple interpretations of axes are possible, each being assigned a probability. 3) A stochastic jump-diffusion process is proposed for estimating both axes and junctions in Markov random fields. We argue that the stochastic algorithm for computing medial axes is compatible with existing algorithms for image segmentation, such as region growing, snake, and region competition. Thus, our method provides a new direction for computing medial axes from texture images. Experiments are demonstrated on both synthetic and real 2D shapes.

[1]  Guillermo Sapiro,et al.  Affine invariant medial axis and skew symmetry , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[2]  Steven W. Zucker,et al.  Region growing: Childhood and adolescence* , 1976 .

[3]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[4]  King-Sun Fu,et al.  Stochastic skeleton modeling of objects , 1984, Comput. Vis. Graph. Image Process..

[5]  Song-Chun Zhu,et al.  Stochastic computation of medial axis in Markov random fields , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[6]  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..

[7]  H. Blum.  Biological shape and visual science (part I) , 1973 .

[8]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[9]  Michael I. Miller,et al.  REPRESENTATIONS OF KNOWLEDGE IN COMPLEX SYSTEMS , 1994 .

[10]  Frederic Fol Leymarie,et al.  Simulating the Grassfire Transform Using an Active Contour Model , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Roberto Cipolla,et al.  Skeletonisation using an Extended Euclidean Distance Transformation , 1994, BMVC.

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

[13]  Roberto Cipolla,et al.  Skeletonization using an extended Euclidean distance transform , 1995, Image Vis. Comput..

[14]  B. Julesz,et al.  Perceptual sensitivity maps within globally defined visual shapes , 1994, Nature.

[15]  Ramakant Nevatia,et al.  Description and Recognition of Curved Objects , 1977, Artif. Intell..

[16]  M. Leyton.  Symmetry, Causality, Mind , 1999 .

[17]  Song-Chun Zhu,et al.  Embedding Gestalt Laws in Markov Random Fields , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Kaleem Siddiqi,et al.  Hyperbolic "Smoothing" of shapes , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[19]  Jayant Shah,et al.  Local symmetries of shapes in arbitrary dimension , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[20]  Robert L. Ogniewicz,et al.  Discrete Voronoi skeletons , 1992 .

[21]  James L. Crowley,et al.  A Representation for Shape Based on Peaks and Ridges in the Difference of Low-Pass Transform , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  M. Brady,et al.  Smoothed Local Symmetries and Their Implementation , 1984 .

[23]  Song-Chun Zhu,et al.  Prior Learning and Gibbs Reaction-Diffusion , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Juneho Yi,et al.  Object recognition from range data , 1994 .

[25]  Stan Z. Li,et al.  Markov Random Field Modeling in Computer Vision , 1995, Computer Science Workbench.

[26]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[27]  Stan Z. Li,et al.  Object recognition from range data prior to segmentation , 1992, Image Vis. Comput..

[28]  Robert Kohn,et al.  Representation and self-similarity of shapes , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).