Fast and exact primal-dual iterations for variational problems in computer vision

Abstract

The saddle point framework provides a convenient way to formulate many convex variational problems that occur in computer vision. The framework unifies a broad range of data and regularization terms, and is particularly suited for nonsmooth problems such as Total Variation-based approaches to image labeling. However, for many interesting problems the constraint sets involved are difficult to handle numerically. State-of-the-art methods rely on using nested iterative projections, which induces both theoretical and practical convergence issues. We present a dual multiple-constraint Douglas-Rachford splitting approach that is globally convergent, avoids inner iterative loops, enforces the constraints exactly, and requires only basic operations that can be easily parallelized. The method outperforms existing methods by a factor of 4-20 while considerably increasing the numerical robustness. © 2010 Springer-Verlag.