LDDMM Surface Registration with Atrophy Constraints

TL;DR

This paper introduces a novel LDDMM surface registration method with inequality constraints to model atrophy, using augmented Lagrangian optimization, demonstrated on brain data with volume reduction constraints.

Contribution

It extends LDDMM surface registration by incorporating inequality constraints for atrophy, including a volume-decreasing variant, with an augmented Lagrangian algorithm.

Findings

Successfully estimated atrophy-constrained surface deformations

Demonstrated effectiveness on brain imaging data

Provided a new framework for atrophy modeling in shape analysis

Abstract

Diffeomorphic registration using optimal control on the diffeomorphism group and on shape spaces has become widely used since the development of the Large Deformation Diffeomorphic Metric Mapping (LDDMM) algorithm. More recently, a series of algorithms involving sub-riemannian constraints have been introduced, in which the velocity fields that control the shapes in the LDDMM framework are constrained in accordance with a specific deformation model. Here, we extend this setting by considering, for the first time, inequality constraints, in order to estimate surface deformations that only allow for atrophy, introducing for this purpose an algorithm that uses the augmented lagrangian method. We also provide a version of our approach that uses a weaker constraint in which only the total volume is forced to decrease. These developments are illustrated by numerical experiments on brain data.