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A Transport for imaging process

Olivier Besson 1, Martine Picq 2, Jerome Pousin (  Corresponding author ) 2

For the Multimodal quantification and validation of 3D regional myocardial function ANR-11-TECSAN-002-003 collaboration(s)

(2012-06-13)

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 $\rho_0$ and $\rho_1$, we calculate an evolution process $\rho(t,\cdot)$ which transports $\rho_0$ to $\rho_1$ 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.

1:	Institut de Mathématiques (UNINE)
	Université de Neuchatel
2:	Institut Camille Jordan (ICJ)
	CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) : - LYON – Université Jean Monnet - Saint-Etienne

Research team: MMCS

Subject

:

Mathematics/Analysis of PDEs Mathematics/Numerical Analysis

Keyword(s): Images transport – least squares solutions

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From: Jerome Pousin <>

Submitted on: Thursday, 14 June 2012 09:27:07

Updated on: Thursday, 14 June 2012 09:51:46