A statistical model for contours in images

In this paper, we describe a statistical model for the gradient vector field of the gray level in images validated by different experiments. Moreover, we present a global constrained Markov model for contours in images that uses this statistical model for the likelihood. Our model is amenable to an Iterative Conditional Estimation (ICE) procedure for the estimation of the parameters; our model also allows segmentation by means of the Simulated Annealing (SA) algorithm, the Iterated Conditional Modes (ICM) algorithm, or the Modes of Posterior Marginals (MPM) Monte Carlo (MC) algorithm. This yields an original unsupervised statistical method for edge-detection, with three variants. The estimation and the segmentation procedures have been tested on a total of 160 images. Those tests indicate that the model and its estimation are valid for applications that require an energy term based on the log-likelihood ratio. Besides edge-detection, our model can be used for semiautomatic extraction of contours, localization of shapes, non-photo-realistic rendering; more generally, it might be useful in various problems that require a statistical likelihood for contours.