Date on Master's Thesis/Doctoral Dissertation
5-2009
Document Type
Doctoral Dissertation
Degree Name
Ph. D.
Department
Mathematics
Committee Chair
Xu, Yongzhi Steve
Author's Keywords
Image segmentation; Active contours
Subject
Imaging systems; Mathematical models
Abstract
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.
Recommended Citation
Cochran, John Marion, "Model extensions and applications in mathematical imaging." (2009). Electronic Theses and Dissertations. Paper 261.
https://doi.org/10.18297/etd/261
