  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 compare 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.
