

Computational Strategies for Meshfree Nonrigid Registration
Ph.D. thesis
  

Area Biomedicine, Optimization 
Author(s)
Eliezer Kahn

Year 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 Bspline 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 noncompact, 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. 
AD Tools ADOLC, Treeverse / Revolve 
AD Theory and Techniques Checkpointing, Reverse Mode 
BibTeX
@PHDTHESIS{
Kahn2006CSf,
author = "Eliezer Kahn",
title = "Computational Strategies for Meshfree Nonrigid Registration",
school = "Yale University",
month = "December",
year = "2006",
ad_tools = "ADOLC, Treeverse / Revolve",
ad_area = "Biomedicine, Optimization",
ad_theotech = "Checkpointing, Reverse Mode",
url = "http://noodle.med.yale.edu/~kahn/",
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 Bspline 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 noncompact, 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."
}
 
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