A Transport for imaging process

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

1 UNINE - Institut de Mathématiques
2 MMCS - Modélisation mathématique, calcul scientifique

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.

Mots clés: Images transport; least squares solutions

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Olivier Besson, Martine Picq, Jerome Pousin. A Transport for imaging process. 2012. ⟨hal-00708089⟩