Computational algebraic topology-based video restoration
A. Rochel, Djemel Ziou, M.-F. Auclair-Fortier · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2005
This paper presents a scheme for video denoising by diffusion of gray levels, based on the Computational Algebraic Topology (CAT) image model. The diffusion approach is similar to the one used to denoise static images. Rather than using the heat transfer partial differential equation, discretizing it and solving it by a purely mathematical process, the CAT approach considers the global expression of the heat transfer and decomposes it into elementary physical laws. Some of these laws describe conservative relations, leading to error-free expressions, whereas others depend on metric quantities and require approximation. This scheme allows for a physical interpretation for each step of the resolution process. We propose a nonlinear and an anisotropic diffusion algorithms based on the extension to video of an existing 2D algorithm thanks to the flexibility of the topological support. Finally it is validated with experimental results. Keywords: Physics-based methods, computational algebraic topology, heat transfer problem, video denoising 1.