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a functional analysis model for natural images permitting structured compression

Published online by Cambridge University Press:  15 August 2002

Jacques Froment
Jacques Froment*
Affiliation:
PRISME, UFR de Math. et Info., Université R. Descartes Paris 5, 45 rue des Saints-Pères, 75270 Paris Cedex 06, France. CMLA, École Normale Supérieure de Cachan, 61 avenue du Président Wilson, 94235 Cachan Cedex, France.
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Abstract

This paper describes a compact perceptual image model intended for morphological representation of the visual information contained in natural images. We explain why the total variation can be a criterion to split the information between the two main visual structures, which are the sketch and the microtextures. We deduce a morphological decomposition scheme, based on a segmentation where the borders of the regions correspond to the location of the topological singularities of a topographic map. This leads to propose a new and morphological definition of edges. The sketch is computed by approximating the image with a piecewise smooth non-oscillating function, using a Lipshitz interpolant given as the solution of a PDE. The data needed to reconstruct the sketch image are very compact, so that an immediate outcome of this image model is the design of a progressive, and artifact-free, image compression scheme.

Keywords

Perceptual image modeltotal variationmathematical morphologysegmentationimage compression.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 4 , 1999 , pp. 473 - 495
Copyright
© EDP Sciences, SMAI, 1999

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