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Diffeomorphic Surface Registration with Atrophy Constraints.

Sylvain Arguillère¹, Michael I Miller¹, Laurent Younes¹

¹Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218.

SIAM Journal on Imaging Sciences

|June 1, 2022

Summary

This summary is machine-generated.

This study introduces a novel algorithm for estimating surface deformations, specifically allowing for atrophy, using inequality constraints within the large deformation diffeomorphic metric mapping framework. The method proves the existence of solutions and demonstrates consistency through numerical experiments.

Keywords:

49N90 49Q10 58D05 68E10 constrained optimization diffeomorphic registration medical imaging optimal control

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Area of Science:

Medical image analysis
Computational anatomy
Differential geometry

Background:

Large deformation diffeomorphic metric mapping (LDDMM) is a standard for shape analysis.
Recent advancements incorporate sub-Riemannian constraints for deformation modeling.
Existing methods lack the ability to enforce specific deformation types, like atrophy.

Purpose of the Study:

To develop a novel algorithm for estimating surface deformations with inequality constraints.
To specifically enable the modeling of atrophy (tissue wasting).
To extend the LDDMM framework with augmented Lagrangian methods.

Main Methods:

Optimal control on diffeomorphism and shape spaces.
Introduction of inequality constraints for atrophy.
Augmented Lagrangian method for solving the constrained optimal control problem.
Mathematical proofs for existence of solutions and approximation scheme consistency.

Main Results:

Successful estimation of surface deformations allowing only atrophy.
Demonstrated existence of solutions for the constrained optimal control problem.
Validated the approximation scheme's consistency with numerical experiments on simulated and real data.

Conclusions:

The developed algorithm effectively models surface atrophy using inequality constraints.
This work extends LDDMM by incorporating inequality constraints for specific deformation modeling.
The approach is robust, as shown by successful application to diverse datasets.