A Markov Random Field Approach to Edge Detection

This contribution is focused on the design of a Markov random field (MRF) for the edge detection problem using a Bayesian formulation. The likelihood and the a priors knowledge are dearly separated and the MRF is designed upon the potentials derived from both sources of information. The likelihood function, which characterizes the contrast likelihood at a site, is obtained using the Holladay´s principle. The edge maps obtained using this likelihood function solely to model the MRF are similar to the ones found using the classical gradient based edge detectors, with an appropriate threshold. To refine the edge snaps, a priors knowledge is introduced. Potentials, related to the a priors knowledge are built heuristically to favor edge maps with continuous and thin edges. It will be shown that it is possible to build each of the potentials from specific pdfs. The experiments show the results obtained with the model designated with this methodology; the performance of the edge detector is shown and the advantages of the model and the methodology proposed are outlined