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* Corresponding author 1 UNINE - Institut de Mathématiques 2 MMCS ICJ - Institut Camille Jordan Villeurbanne

Abstract : This work originates from a heart-s images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed segmented. Given two images $ ho 0$ and $ ho 1$, we calculate an evolution process $ hot,\cdot$ which transports $ ho 0$ to $ ho 1$ by using the optical flow. In this paper we propose an algorithm based on a fixed point formulation and a space-time least squares formulation of the transport equation for computing a transport problem. Existence results are given for a transport problem with a minimum divergence for a dual norm or a weighted $H^1 0$-semi norm, for the velocity. The proposed transport is compared with the transport introduced by Dacorogna-Moser. The strategy is implemented in a 2D case and numerical results are presented with a first order Lagrange finite element, showing the efficiency of the proposed strategy.

Mots-clés : Images transport least squares solutions

Author: Olivier Besson - Martine Picq - Jerome Pousin -

Source: https://hal.archives-ouvertes.fr/


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