Elastic image registration with exact mass preservation

TL;DR

This paper introduces a novel image registration framework combining linear elasticity and optimal mass transportation, solved via PDE-constrained optimization with finite difference discretization and an inexact SQP algorithm, demonstrating robustness on real-world examples.

Contribution

It develops a new PDE-constrained optimization approach for image registration that integrates elasticity and mass preservation, with a stable discretization scheme and efficient solver.

Findings

Robust numerical performance on artificial and real images.

Stable discretization using a fully staggered grid.

Effective solution of large sparse saddle point systems.

Abstract

We establish a new framework for image registration, which is based on linear elasticity and optimal mass transportation theory. We combine these two arguments in order to obtain a PDE constrained optimization problem that is analytically investigated and further discretized with the finite difference method and solved by an inexact SQP algorithm. This requires to solve in each step a large sparse linear system, which has a saddle point form. Motivated by stability arguments we use a fully staggered grid for the discretization of the displacement vector field. Artificial and real world examples are presented to underline the numerical robustness of the method.