# a functional analysis model for natural images permitting structured compression

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

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

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topFroment, 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 -

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