Graduation Semester and Year

2009

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Guojun Liao

Abstract

In this dissertation we present a novel method for the nonrigid registration of 3D images using a well-established mathematical framework mostly known as the deformation based grid generation method. The deformation based grid generation method is able to generate a grid with desired grid density distribution that is free from grid folding. This method gives direct control over the cell size of the adaptive grid and determines the node velocities directly. The adaptive grid system naturally distributes more grids to deprived areas. The positive monitor function disallows grid folding and provides a mean to control the ratio of the areas between the original and transformed domain. Based on these, we have successfully developed a new non-rigid registration method that has many advantages: Firstly, it is based on a solid mathematical foundation. In particular, it accounts for local volume changes through the divergence of the transformation; and it accounts for local rotation through the curl vector of the transformation. Secondly, the method is based on a linear differential system; its numerical implementation is fast, stable, simple and robust. Thirdly, it does not require to use of any regularization term. Finally, the method is general in the sense that it may be used in any optimization problem that involves motion estimation. Thus, it has the potential to be the numerical kernel for a wide range of applications.

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

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