a functional analysis model for natural images permitting structured compression

Jacques Froment

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 4, page 473-495
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Froment, Jacques. "a functional analysis model for natural images permitting structured compression ." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 473-495. <http://eudml.org/doc/197315>.

@article{Froment2010,
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. },
author = {Froment, Jacques},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Perceptual image model; total variation; mathematical morphology; segmentation; image compression.; perceptual image model; total vatiation; mathematical morphology; image compression},
language = {eng},
month = {3},
pages = {473-495},
publisher = {EDP Sciences},
title = {a functional analysis model for natural images permitting structured compression },
url = {http://eudml.org/doc/197315},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Froment, Jacques
TI - a functional analysis model for natural images permitting structured compression
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 473
EP - 495
AB - 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.
LA - eng
KW - Perceptual image model; total variation; mathematical morphology; segmentation; image compression.; perceptual image model; total vatiation; mathematical morphology; image compression
UR - http://eudml.org/doc/197315
ER -

References

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