Medical image registration has received considerable attention in the medical imaging and computer vision communities because of the variety of ways in which it can potentially improve patient care. This application of image registration aligns images of regions of the human body for comparing images of the same patient at different times, for example, when assessing differences in a disease over time; comparing images of the same anatomical structure across different patients, for example, to understand patient variability; and comparing images of the same patient from different modalities that provide complementary information, for example, CT and PET to assess cancer.

The two primary types of registration make use of rigid and nonrigid transformations. Medical images typically contain some regions of bone, which behave rigidly, and some regions of soft tissue, which are able to deform. While a strictly rigid transformation would not account for soft tissue deformations, a strictly nonrigid transformation would not abide by the physical properties of the bone regions. Over the years, many image registration techniques have been developed and refined for particular applications but none of them compute a continuous transformation simultaneously containing both rigid and nonrigid regions.

This thesis focuses on using a sophisticated segmentation algorithm to identify and preserve bone structure in medical image registration while allowing the rest of the image to deform. The registration is performed by minimizing an objective function over a set of transformations that are defined in a piecewise manner: rigid over a portion of the domain, nonrigid over the remainder of the domain, and continuous everywhere. The objective function is minimized via steepest gradient descent, yielding an initial boundary value problem that is discretized in both time and space and solved numerically using multigrid. The registration results are compared to results of strictly rigid and nonrigid registrations.

Library of Congress Subject Headings

Image registration--Mathematics; Imaging systems in medicine--Data processing

Publication Date


Document Type


Student Type


Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)


Nathan D. Cahill

Advisor/Committee Member

Tamas Wiandt

Advisor/Committee Member

Elizabeth M. Cherry


Physical copy available from RIT's Wallace Library at TA1637 .S73 2016


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