Bregman Iteration for Correspondence Problems: A Study of Optical Flow

Abstract

Bregman iterations are known to yield excellent results for denoising, deblurring and compressed sensing tasks, but so far this technique has rarely been used for other image processing problems. In this paper we give a thorough description of the Bregman iteration, unifying thereby results of different authors within a common framework. Then we show how to adapt the split Bregman iteration, originally developed by Goldstein and Osher for image restoration purposes, to optical flow which is a fundamental correspondence problem in computer vision. We consider some classic and modern optical flow models and present detailed algorithms that exhibit the benefits of the Bregman iteration. By making use of the results of the Bregman framework, we address the issues of convergence and error estimation for the algorithms. Numerical examples complement the theoretical part.

Inverse Scale Space Iterations for Non-Convex Variational Problems: The Continuous and Discrete Case

“…In [25], the Bregman iteration was used to solve a nonconvex optical flow problem, however, the approach relies on an iterative reduction to a convex problem using first-order Taylor approximations.…”

Inverse Scale Space Iterations for Non-Convex Variational Problems: The Continuous and Discrete Case

“…However, applying the Bregman iteration to variational problems with non-convex data term H is not trivial since the well-definedness of the iterations, the use of subgradients, as well as the convergence results in [34] rely on the convexity of the data term. In [27], the Bregman iteration was used to solve a non-convex optical flow problem, however, the approach relies on an iterative reduction to a convex problem using first-order Taylor approximations. In [46], the Bregman iteration is applied to the relaxed and convexified segmentation problem suggested in [17].…”

Scale Space and Variational Methods in Computer Vision

“…However, applying the Bregman iteration to variational problems with nonconvex data term H is not trivial since the well-definedness of the iterations as well as the convergence results in [21] rely on the convexity of the data term. In [14], the Bregman iteration was used to solve a non-convex optical flow problem, however, the approach relies on an iterative reduction to a convex problem using first-order Taylor approximations.…”