Detection of discontinuities in noisy and textured images using weak continuity constraints

This paper presents a new approach for the constrained recovery of discontinuities in noisy and textured images. An objective function using weak continuity and line configuration constraints is proposed to detect the discontinuities. The weak continuity constraints are based on an elastic membrane model. The line configuration constraints are based on a prior defined for the boundary process, with favorable/unfavorable boundary configurations. The weak continuity constraint term in the objective function is particularly suitable for optimization with the Graduated Non-Convexity (GNC) method. To minimize the proposed objective function we merged the GNC algorithm with a deterministic descent approach operating on the state space of the line configurations. A non-stationary Gaussian Markov Random Field (GMRF) model is used to represent a wide class of noisy and textured images. However, this assumption is neither binding nor explicitly used in the discontinuity detection algorithm.