Please use this identifier to cite or link to this item: http://hdl.handle.net/10553/46205
Title: Recursivity and PDE's in image processing
Authors: Alvarez, Luis 
Deriche, Rachid
Santana Pérez, Francisco J 
UNESCO Clasification: 120601 Construcción de algoritmos
120602 Ecuaciones diferenciales
120326 Simulación
220990 Tratamiento digital. Imágenes
120304 Inteligencia artificial
Keywords: Image processing
Nonlinear filters
Nonlinear equations
Computer vision
Filtering, et al
Issue Date: 2000
Project: "Proyecto no ULPGC[Acciones Integradas Proyect HF1998 0098–Projet Action Int´egr´ee PICASSO 99050.]"
Conference: 15th International Conference on Pattern Recognition (ICPR-2000) 
Abstract: Recursive filtering structures reduce drastically the computational effort required for different tasks in image processing. These operations are done with a fixed number of operations per output point independently of the size of the neighbourhood considered. In this paper we show that implicit numerical implementations of some partial differential equations (PDEs) provide algorithms that can be interpreted in terms of recursive filters. We show, in particular, that the classical second order recursive filter introduced by Deriche (1987, 1990) is in fact a particular implementation of the heat equation. Using the well-known Neumann boundary condition for the heat equation, we propose some new implementation of the filter. We extend this linear filter to a nonlinear recursive smoothing filter, following the general idea of anisotropic diffusion. We present some comparison results with the classical Perona-Malik model.
URI: http://hdl.handle.net/10553/46205
ISBN: 0-7695-0751-4
ISSN: 1051-4651
DOI: 10.1109/ICPR.2000.905312
Source: Proceedings - International Conference on Pattern Recognition [ISSN 1051-4651], v. 15 (1), p. 242-248
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