Document Type


Date of Degree

Fall 2016

Degree Name

MS (Master of Science)

Degree In

Electrical and Computer Engineering

First Advisor

Christensen, Gary E.

First Committee Member

Christensen, Gary E.

Second Committee Member

Saha, Punam K.

Third Committee Member

Durumeric, Oguz C.

Fourth Committee Member

Hugo, Geoffrey D.


This thesis compares and contrasts currents- and varifolds-based diffeomorphic image registration approaches for registering tree-like structures in the lung and surface of the lung. In these approaches, curve-like structures in the lung—for example, the skeletons of vessels and airways segmentation—and surface of the lung are represented by currents or varifolds in the dual space of a Reproducing Kernel Hilbert Space (RKHS). Currents and varifolds representations are discretized and are parameterized via of a collection of momenta. A momenta corresponds to a line segment via the coordinates of the center of the line segment and the tangent direction of the line segment at the center. A momentum corresponds to a mesh via the coordinates of the center of the mesh and the normal direction of the mesh at the center. The magnitude of the tangent vector for the line segment and the normal vector for the mesh are the length of the line segment and the area of the mesh respectively.

A varifolds-based registration approach is similar to currents except that two varifolds representations are aligned independent of the tangent (normal) vector orientation. An advantage of varifolds over currents is that the orientation of the tangent vectors can be difficult to determine

especially when the vessel and airway trees are not connected. In this thesis, we examine the image registration sensitivity and accuracy of currents- and varifolds-based registration as a function of the number and location of momenta used to represent tree like-structures in the lung and the surface of the lung. The registrations presented in this thesis were generated using the Deformetrica software package, which is publicly available at

Public Abstract

Registration of lung CT images is important for many radiation oncology applications including assessing and adapting to anatomical changes, accumulating radiation dose for planning or assessment, and managing respiratory motion. For example, variation in the anatomy during radiotherapy introduces uncertainty between the planned and delivered radiation dose and may impact the appropriateness of the originally-designed treatment plan. Frequent imaging during radiotherapy accompanied by accurate longitudinal image registration facilitates measurement of such variation and its effect on the treatment plan. The cumulative dose to the target and normal tissue can be assessed by mapping delivered dose to a common reference anatomy and comparing to the prescribed dose. The treatment plan can then be adapted periodically during therapy to help mitigate the impact of these changes by ensuring the cumulative delivered dose is concordant with the prescribed dose[16, 10, 18]. Furthermore, image registration can also help measure how the tumor changes during or after treatment, which can potentially assist in predicting early response to therapy. These applications all rely on accurate tracking of lung motion over the breathing cycle and anatomical and functional changes over time.

The main contribution of this thesis is a sensitivity analysis of the feature-based (currents- and varifolds-based) image registration methods to learn how to choose good parameters for the algorithm and parametrize lung features in the lung, such as the centerline of the pulmonary vessel and airway trees, and surface of the lung.


currents, Diffeomorphic Image Registration, Reproducing Kernel Hilbert Space (RKHS), varifolds


xi, 46 pages


Includes bibliographical references (pages 45-46).


Copyright © 2016 Yue Pan