Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Committee Chair

Xu, Yongzhi Steve

Author's Keywords

Image segmentation; Active contours


Imaging systems; Mathematical models


Mathematical imaging consists of many different applications including image segmentation, image classification, and inpainting. This work deals more specifically with image segmentation: the partition of an image into the background and the objects present in the image. The main focus is the active contours without gradient model by Tony Chan and Luminita Vese which deals with fitting a curve imbedded in the plane image. The fitting of the curve comes from an evolutionary partial differential equation. The dissertation contributes three novel ideas: a linearized version of the active contours without gradient model published in [20]; a new procedure using fourth order fitting terms in place of the second order fitting terms which gives faster segmentation and may be used to provide a good initial condition; a novel way of tracking regions present in bulk data in order to gain an understanding of macroscopic details associated with some physical application. Results include images showing the accuracy of the segmentation for the methods, a discussion of the choice of initial condition, and discussion of feasibility for the data tracking. These results compare to those obtained with the nonlinear model and serve as a proof-of-concept for further investigation. The dissertation ends with a discussion of future research.