A Deterministic Algorithm for Reconstructing Images with Interacting Discontinuities

The most common approach for incorporating discontinuities in visual reconstruction problems makes use of Bayesian techniques, based on Markov random field models, coupled with stochastic relaxation and simulated annealing. Despite their convergence properties and flexibility in exploiting a priori knowledge on physical and geometric features of discontinuities, stochastic relaxation algorithms often present insurmountable computational complexity. Recently, considerable attention has been given to suboptimal deterministic algorithms, which can provide solutions with much lower computational costs. These algorithms consider the discontinuities implicitly rather than explicitly and have been mostly derived when there are no interactions between two or more discontinuities in the image model. In this paper we propose an algorithm that allows for interacting discontinuities, in order to exploit the constraint that discontinuities must be connected and thin. The algorithm, called E-GNC, can be considered an extension of the graduated nonconvexity (GNC), first proposed by Blake and Zisserman for noninteracting discontinuities. When applied to the problem of image reconstruction from sparse and noisy data, the method is shown to give satisfactory results with a low number of iterations.