Efficient Numerical Methods for Initial Value Control Problems for Diffeomorphic Image Registration

We discuss numerical algorithms for diffeomorphic image registration. We present extensions for a framework for diffeomorphic image registration termed CLAIRE. In diffeomorphic image registration, we seek a diffeomorphic map that establishes spatial correspondence between two views (images) of the same scene or object. In the continuum, this represents an infinite-dimensional, inverse problem. We formulate diffeomorphic image registration as a partial differential equation constrained optimization problem. The partial differential equations enter the formulation as equality constraints. We consider hyperbolic transport equations as well as Euler Poincaré equations associated with the group of diffeomorphisms. The contributions of this thesis are three-fold: (i) We study the performance of the graphics processing unit implementation of CLAIRE for (large-scale) biomedical imaging studies. (ii) We develop numerical algorithms for the solution of a variational optimization problem for diffeomorphic image registration governed by a hyperbolic transport equation and the Euler Poincaré equations associated with the group of diffeomorphisms. This represents the main contribution of this thesis. (iii) We present preliminary results for a computational framework for uncertainty quantification for the latter formulation that exploits the numerical algorithms developed in this thesis.. We report results to assess the rate of convergence, computational performance, reconstruction accuracy, and scalability of our methods.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Houston

Year dc:date.issued

2023

Author dc:creator

• Kim, Jae Youn

Advisor dc:contributor.advisor

• Mang, Andreas

Committee members dc:contributor.committeemember

• Azencott, Robert
• He, Jiwen
• Biros, George

• diffeomorphic image registration
• optimization

Statement dc:rights

• The author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. UH Libraries has secured permission to reproduce any and all previously published materials contained in the work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/10657/15999

OAI identifier oai:identifier

oai:uh-ir.tdl.org:10657/15999