A Lattice-Preserving Multigrid Method for Solving the Inhomogeneous Poisson Equations Used in Image Analysis

Abstract. The inhomogeneous Poisson (Laplace) equation with internal Dirichlet boundary conditions has recently appeared in several applications ranging from image segmentation [1, 2, 3] to image colorization [4], digital photo matting [5, 6] and image filtering [7, 8]. In addition, the problem we address may also be considered as the generalized eigenvector problem associated with Normalized Cuts [9], the linearized anisotropic diffusion problem [10, 11, 8] solved with a backward Euler method, visual surface reconstruction with discontinuities [12, 13] or optical flow [14]. Although these approaches have demonstrated quality results, the computational burden of finding a solution requires an efficient solver. Design of an efficient multigrid solver is difficult for these problems due to unpredictable inhomogeneity in the equation coefficients and internal Dirichlet boundary conditions with unpredictable location and value. Previous approaches to multigrid solvers have typically employ...

• Type: Conference
• Year: 2008
• Where: ECCV
• Authors: Leo Grady
• Keywords: Coarse Levels, Computer Vision, Data-driven Coarse Operator, Dirichlet Boundary Conditions, ECCV 2008, Efficient Multigrid Solver, Low Memory Overhead