Boundary detection through dynamic polygons

A method for the Bayesian restoration of noisy binary images portraying an object with constant grey level on a background is presented. The restoration, performed by fitting a polygon with any number of sides to the object's outline, is driven by a new probabilistic model for the generation of polygons in a compact subset of R2, which is used as a prior distribution for the polygon. Some measurability issues raised by the correct specification of the model are addressed. The simulation from the prior and the calculation of the a posteriori mean of grey levels are carried out through reversible jump Markov chain Monte Carlo computation, whose implementation and convergence properties are also discussed. One example of restoration of a synthetic image is presented and compared with existing pixel‐based methods.

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

[2]  E. Dubois,et al.  Digital picture processing , 1985, Proceedings of the IEEE.

[3]  J. Besag.  On the Statistical Analysis of Dirty Pictures , 1986 .

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

[5]  Ulf Grenander,et al.  Hands: A Pattern Theoretic Study of Biological Shapes , 1990 .

[6]  A. Baddeley,et al.  Stochastic geometry models in high-level vision , 1993 .

[7]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[8]  P. Clifford,et al.  Point-based polygonal models for random graphs , 1993, Advances in Applied Probability.

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

[10]  N. Cressie,et al.  A statistical approach to identifying closed object boundaries in images , 1994, Advances in Applied Probability.

[11]  Geir Storvik,et al.  A Bayesian Approach to Dynamic Contours Through Stochastic Sampling and Simulated Annealing , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[13]  Peter Cliiord,et al.  A Metropolis Sampler for Polygonal Image ReconstructionPeter , 1995 .

[14]  D. M. Titterington,et al.  An Image Analysis Problem in Electron Microscopy , 1996 .

[15]  Kanti V. Mardia,et al.  Deformable Template Recognition of Multiple Occluded Objects , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Håvard Rue,et al.  Bayesian object recognition with baddeley's delta loss , 1998, Advances in Applied Probability.

[17]  Geoff K. Nicholls,et al.  Bayesian image analysis with Markov chain Monte Carlo and coloured continuum triangulation models , 1998 .

[18]  Merrilee Hurn,et al.  Bayesian object identification , 1999 .