Geometric multigrid for high-order regularizations of early vision problems

The surface estimation problem is used as a model to demonstrate a framework for solving early vision problems by high-order regularization with natural boundary conditions. Because the application of algebraic multigrid is usually constrained by an M-matrix condition which does not hold for discretizations of high-order problems, a geometric multigrid framework is developed for the efficient solution of the associated optimality systems. It is shown that the convergence criteria of [5] are met, and in particular the general elliptic regularity required is proved. Further, the Galerkin formalism is used together with a multi-colored ordering of unknowns to permit vectorization of a symmetric Gauss-Seidel relaxation in image processing systems. The implementation is analyzed computationally and inaccuracies are corrected by lumping and by proper floating point representations. Direct one-dimensional calculations are used to estimate the effect of regularization order, regularization s...

• Type: Journal
• Year: 2007
• Where: AMC
• Authors: Stephen L. Keeling, Gundolf Haase
• Keywords: AMC 2007, Geometric Multigrid Framework, Multigrid, Surface Estimation Problem