Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Mathematics



First Advisor

Guojun Liao


Image segmentation and registration are indispensable tools for the aid in medical diagnoses by experts. The current gold-standard for image segmentation is manual labeling of pixels by experts which is cumbersome and inefficient. In a paper by Zhu et. al. grids are generated through the deformation method for grid generation and differential properties of these grids are used in a deep learning algorithm for image segmentation. In this dissertation, we develop a new method for generating grid images based on the Variational Method. This new grid generation method generates grids based on image pixel intensities which improves upon the deformation method for grid generation in constructing such grids. Image registration is used in quantitative analysis based on the grid representation of the registration field, but this is an ill-posed problem. Therefore, many models of regularization are used to regularize the problem. As a result there are many different models that have many different grid representations with large discrepancies. In fact, even the same model with different parameters often result in different deformations with large discrepancies. In this dissertation, we develop a platform for combining different registration fields generated by different methods with the aim of improving robustness.


Grids, Generation, Diffeomorphism, Image, Analysis, Registration, Segmentation


Mathematics | Physical Sciences and Mathematics


Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons