Edge detection by 2D recursive least squares and Markov random fields

Abstract

Summary form only given, as follows. An algorithm is presented for smoothing and segmenting images with regions characterized by constant intensity levels and/or textures. It is based on a doubly stochastic model of the data, where the local behavior is modeled by autoregressive equations with piecewise constant parameters, while the regions are modeled by a Markov random field (MRF). The edges of the image, in terms of boundaries between regions, are associated with the reinitialization of the covariance matrix of the recursive-least-squares (RLS) estimator. With this approach it is shown that for any given set of edges gamma a likelihood function P( gamma mod gamma ) can be computed, with gamma denoting the noisy observations. Using this fact, a suboptimal algorithm for edge detection is devised which locally maximizes the likelihood function by operating sequentially on the observations. The main Advantage seems to be that the algorithm is robust with respect to the observation noise, in the sense that the edges of very small regions (unlikely in the MRF model) are not detected.<>