Computing the time-continuous Optimal Mass Transport Problem without Lagrangian techniques

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

1 UNINE - Institut de Mathématiques
2 ICJ - Institut Camille Jordan

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, ·} which transports p0 to p1 by using the optimal extended optical flow. In this paper we propose an algorithm based on a fixed point formulation and a time-space least squares formulation of the mass conservation equation for computing the optimal mass transport problem. 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: 35F40; 35L85; 35R05; 62-99

Domaines: Analyse classique [math.CA]; Géométrie différentielle [math.DG]; Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Olivier Besson, Martine Picq, Jérôme Pousin. Computing the time-continuous Optimal Mass Transport Problem without Lagrangian techniques. 2009. ⟨hal-00518572⟩