#### DOI

10.17077/etd.xkr98o74

#### Document Type

Thesis

#### Date of Degree

Fall 2016

#### Degree Name

MS (Master of Science)

#### Degree In

Electrical and Computer Engineering

#### First Advisor

Gary E. Christensen

#### First Committee Member

Gary E Christensen

#### Second Committee Member

Hans J Johnson

#### Third Committee Member

Oguz C Durumeric

#### Abstract

This thesis examines and identifies the problems of shape collapse in large deformation image registration. Shape collapse occurs in image registration when a region in the moving image is transformed into a set of near zero volume in the target image space. Shape collapse may occur when the moving image has a structure that is either missing or does not sufficiently overlap the corresponding structure in the target image. We state that shape collapse is a problem in image registration because it may lead to the following consequences: (1) Incorrect pointwise correspondence between different coordinate systems; (2) Incorrect automatic image segmentation; (3) Loss of functional signal. The above three disadvantages of registration with shape collapse are illustrated in detail using several examples with both real and phantom data. Shape collapse problem is common in image registration algorithms with large degrees of freedom such as many diffeomorphic image registration algorithms. This thesis proposes a shape collapse measurement algorithm to detect the regions of shape collapse after image registration in pairwise and group-wise registrations. We further compute the shape collapse for a whole population of pairwise transformations such as occurs when registering many images to a common atlas coordinate system. Experiments are presented using the SyN diffeomorphic image registration algorithm and diffeomorphic demons algorithm. We show that shape collapse exists in both of the two large deformation registration methods. We demonstrate how changing the input parameters to the SyN registration algorithm can mitigate the collapse image registration artifacts.

#### Public Abstract

Image registration is the process of finding a geometric transformation that defines an optimal pointwise correspondence between a moving image and a target image (fixed image). This correspondence transformation deforms the moving image into the shape of the target image.

This thesis mainly examines the problems of shape collapse in image registration with large degrees of freedom for its transformation function. Shape collapse occurs in image registration when some structure with nonzero volume in the moving image is transformed into a set of near zero volume in the target image space. Shape collapse may occur when the moving image has a structure that is either missing or does not sufficiently overlap the corresponding structure in the target image [6]. We state that shape collapse is a problem in image registration because it may lead to the following consequences: (1) Incorrect pointwise correspondence between moving image and target image, for example, a point in the white matter in the moving image was mapped to a point in the gray matter in the target image; (2) Incorrect automatic image segmentation, which is to deform the label map of the moving image into the target image space using the generated transformation to obtain a segmentation of the target image; (3) Loss of functional signal, which may occur when mapping functional data such as fMRI, PET, SPECT using a transformation with a shape collapse if the functional signal occurs at the collapse region. The above three disadvantages of registration with shape collapse are illustrated in detail using several examples. We demonstrate that shape collapse is common in large deformation image registration. This thesis proposes a shape collapse measurement algorithm to detect regions in the target image space that have shape collapse problem after pairwise image registration. Each pairwise registration may exhibit the collapse problem. We evaluate the percentage of whole population that has a shape collapse at each point in the target image space. By evaluating the shape collapse for a population of pairwise transformations and generating a population shape collapse probability map. We show that shape collapse exists in both the SyN diffeomorphic and the diffeomorphic demons large deformation image registration methods. We demonstrate that changing the input parameters to the SyN registration algorithm can mitigate the collapse image registration artifacts. Finally, we show that reducing the shape collapse may not necessarily solve the poor correspondence problem.

#### Keywords

Diffeomorphic Image Registration, Large Deformation, Shape Collapse

#### Pages

xi, 43 pages

#### Bibliography

Includes bibliographical references (pages 42-43).

#### Copyright

Copyright © 2016 Wei Shao

#### Recommended Citation

Shao, Wei. "Identifying the shape collapse problem in large deformation image registration." MS (Master of Science) thesis, University of Iowa, 2016.

https://doi.org/10.17077/etd.xkr98o74.