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Constance de largeur et désocclusion dans les images digitales

Emmanuel Villéger 1, 2
2 ARIANA - Inverse problems in earth monitoring
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : Gestaltists study vision, they think that we put objects together
using rules to make bigger objects, Gestalts.

The first part of this thesis deals with the constant width Gestalt,
it puts together points between parallel borders. We seek in images
``parallel'' curves. We use an a contrario model: we therefore
introduce a quantification of the ``no parallelism'' of two curves in
three ways. First we compute a probability using a model to generate
regular curves. Then we estimate this probability by a Monte-Carlo
method. Finaly a taylor expansion in the first computation leads to a
partial differential equation (PDE). The Monte-Carlo method is fastest
and most robust of the three.

Our PDE is very similar to the PDE used in image disocclusion, thus
the second part is about image disocclusion. We talk of the existing
methods and then present a new one based on two PDEs. We introduce the
probability of the image gradient orientation. We take into account
the uncertainty upon the orientation due to its computation. This
uncertainty is quantified with respect to the gradient norm.

The futur developments of this work are for the first part to use the
computed probability to detect constant width, and for the second one
to tune the parameters in order to have good results on natural images.
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Submitted on : Saturday, December 17, 2005 - 12:47:19 AM
Last modification on : Monday, October 12, 2020 - 10:30:13 AM
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Emmanuel Villéger. Constance de largeur et désocclusion dans les images digitales. Mathématiques [math]. Université Nice Sophia Antipolis, 2005. Français. ⟨tel-00011229⟩

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