Contour Estimation on Piecewise Homogeneous Random Fields

Contour Estimation, Bayesian Estimation, Random Fields, Dynamic Programming, Multigrid Methods. This paper addresses contour estimation on images modeled as piecewise homogeneous random elds. It is therefore assumed that images are samples of random elds composed of a set of homogeneous, in a statistical sense, regions; pixels within each region are assumed to be independent samples of a given random variable. Particular attention is given to Gaussian, Rayleigh, and Poisson densities. The model just described accurately ts many class of problems on image modalities such as optical, ultrasound, X-rays, emission tomography, and confocal microscopy, only to name a few. The followed approach is Bayesian: contours are assumed to be non-causal Markov random elds. This description is appropriate to include a priori information such as continuity, smoothness, elasticity, and rigidity. The selected estimation criterion is the maximum a posteriori (MAP). In the present context, MAP estimation, although simpler than others (e.g., minimum mean square error or minimum absolute error), leads to a huge non-linear optimization problem. By using dynamic programming associated to a multigrid resolution technique, quasi-optimal contour estimates are computed with an acceptable complexity. A set of tests using synthetic and real images illustrates the appropriateness of the proposed methodology.