A Transport for imaging process

TL;DR

This paper introduces a novel algorithm for computing a transport process between two images using a fixed point and least squares approach, with applications in medical imaging and motion analysis.

Contribution

It proposes a new algorithm based on a fixed point and space-time least squares formulation for image transport, with existence results and comparison to existing methods.

Findings

Algorithm successfully computes image transport in 2D

Numerical results demonstrate efficiency of the proposed method

Comparison shows advantages over Dacorogna-Moser transport

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 $\rho_0$ 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.