In the past 20 years, there have been significant advances in the use of medical imaging in patient care. Today, image registration is being used by doctors all over the world to compare computed tomography (CT), Magnetic Resonance Imaging (MRI), X-rays, Ultrasound (US), Positron Emission Tomography (PET), and/or Single Photon Emission Computed Tomography (SPECT) images of their patients from different times to formulate an accurate diagnosis. Mathematically, image registration can be posed as an initial boundary value problem (IBVP). When applied to medical imaging, the current boundary conditions being used are not physically meaningful. We are proposing two new boundary conditions that are more physically meaningful because they were designed as combinations of the current boundary conditions. Therefore the image registration algorithms we employ are slight variations of the current techniques. We show how to apply our boundary conditions to the current image registration techniques and compare the results against the current boundary conditions. By comparing the results, we were able to illustrate the proposed boundary conditions created more visually pleasing and physically realistic results in both two and three dimensions.

Library of Congress Subject Headings

Imaging systems in medicine--Data processing; Image registration--Mathematics; Boundary value problems

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Department, Program, or Center

School of Mathematical Sciences (COS)


Cahill, Nathan


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