Author

John Montalbo

ORCID Identifier(s)

0000-0001-8384-9680

Graduation Semester and Year

2020

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Gaik Ambartsoumian

Second Advisor

Souvik Roy

Abstract

Optical flow is a concept originally introduced in computer vision that quantifies, and aids in the presentation of, motion (flow field) between two or more images. In essence, it is a solution of an inverse problem recovering a vector field between images through optimization techniques. This work studies the possibility of using optical flow and various techniques of forward propagation of the recovered flow field for a pair of image processing tasks in magnetic resonance imaging (MRI). It is shown that the proposed framework can be efficient in approximating missing image layers, as well as in generation of deliberately modified synthetic MRI images. We present the underlying mathematical hypotheses necessary for the applicability of the method, practical limitations associated with it, and potential mechanisms for its future improvements.

Keywords

Optical flow, Data generation

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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