Title: *Computational Strategies for Meshfree Nonrigid Registration*

Advisor: Lawrence Hamilton Staib

December 2006

#### Abstract

*
*Biological shapes such as the brain are difficult to register due to their
complicated geometry. To deal with this, registration methods often rely on a
transformation model consisting of a dense regular grid such as a free form
deformation or B-spline grid. However, very dense grids or meshes are usually
needed to register images with convoluted shapes, and a regular mesh structure
is not well suited for the irregular structure of the brain. What is therefore
needed is a meshfree approach such as a radial basis function transformation
model. Unfortunately, because radial basis functions are typically
non-compact, using them with large numbers of points is fraught with numerical
difficulties and, as a result, their use in image registration is not
prevalent.

The goal of this work is to overcome these computational difficulties so that
radial basis function transformations can be used efficiently, even with large
numbers of points. To achieve this, a new registration framework was developed
based on automatic differentiation and the fast multipole method. Automatic
differentiation is useful since an important component of registration is
computing the gradient of the similarity metric which is to be
optimized. Automatic differentiation allows one to efficiently calculate
gradients without having to write any gradient code explicitly. Although the
technique of automatic differentiation is well established, it does not appear
to be used for image registration. The fast multipole method was developed to
efficiently evaluate large sums such as radial basis functions but its use in
image registration is still minimal. With the integration of these algorithms
within a complete registration framework, it should be possible to obtain a
truly meshfree registration.

Download the complete dissertation here.

#### BibTeX Entry

@PhDthesis(KahnThesis,
author = "Eliezer Kahn",
title = "Computational Strategies for Meshfree Nonrigid Registration",
school = "Yale University",
month = "December",
year = "2006")