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
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Montalbo, John, "INVERSE PROBLEMS AND FORWARD PROPAGATION OF OPTICAL FLOW" (2020). Mathematics Dissertations. 241.
https://mavmatrix.uta.edu/math_dissertations/241
Comments
Degree granted by The University of Texas at Arlington