A fast scalable algorithm for discontinuous optical flow estimation

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

“…Ghosal and Vanȇk [14] proposed using a smoothed aggregate restriction/prolongation operator inspired by the algebraic multigrid concept introduced by Ruge of strongly coupled nodes [29]. Although similar to the technique that we present here in the sense that a data-driven aggregation operator is proposed, an important difference between our work and [14] is that their aggregation technique will not preserve a lattice structure at coarse levels. Additionally, our method is parameterfree.…”

“…Problems with this structure have become increasingly important in image pro-cessing applications such as segmentation [1][2][3], colorization [4], matting [5,6] and filtering [7,8]. Similar systems have also been studied in the context of visual reconstruction [12] and optical flow [14].…”

“…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 on highresolution 2D or 3D images demands an efficient solver that is not currently available in the literature.…”

“…The inhomogeneous Poisson (Laplace) equation with internal Dirichlet boundary conditions has recently appeared in several applications ranging from image segmentation [1-3] 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.…”

A Survey on Variational Optic Flow Methods for Small Displacements

“…Performance evaluations such as [9,35] showed that variational methods belong to the best performing techniques for computing the optic flow field. It is thus not surprising that a lot of research has been carried out in order to improve these techniques even further: These amendments include refined model assumptions with discontinuity-preserving constraints [2,28,42,62,65,73,91] or spatiotemporal regularisation [11,61,92], improved data terms with modified constraints [3,26,62,74] or nonquadratic penalisation [11,43,56,26], and efficient multigrid algorithms [15,22,39,38,78,95] for minimising these energy functionals. The goal of the present chapter is to analyse the data term and the smoothness term in detail and to survey some of our recent results on variational optic flow computation.…”