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Biologically plausible regularization mechanisms

Thierry Viéville 1
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique - ENS Paris, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS-PSL - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : This study aims at proposing an implementation of regularization mechanisms compatible with biological operators. More precisely, cortical maps code vectorial parametric quantities, computed by network of neurons. In computer vision, similar quantities are efficiently computed using implementations of partial differential equations which define regularization processes allowing to obtain well-defined estimations of these quantities. One of these methods, introduced by Raviat and developed by Degond and Mas-Gallic, is based on an integral approximation of the diffusion operator used in regularization mechanisms. Following this formulation, the present development defines a somehow optimal implementation of such an integral operator with two interesting properties: (i) when used on sampled data such as image pixels or 3D data voxels, it provides an unbiased discrete implementation of such an operator; when used as a model of biological plausible mechanisms, it corresponds to a simple local feedback defined over a small bounded region of any shape inside the parametric space. As such it may be linked to what is processed in a cortical column of the brain and provides an interesting model of general operators corresponding to such a neuronal structure. The present development is illustrated by some experiments of visual motion estimation.
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Submitted on : Tuesday, May 23, 2006 - 7:22:06 PM
Last modification on : Thursday, March 17, 2022 - 10:08:32 AM
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Thierry Viéville. Biologically plausible regularization mechanisms. RR-4625, INRIA. 2002. ⟨inria-00071960⟩

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