Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Xu, Yongzhi Steve

Committee Co-Chair (if applicable)

Sahoo, Prasanna

Committee Member

Sahoo, Prasanna

Committee Member

Hu, Changbing

Committee Member

Lorenz, Douglas

Author's Keywords

partial; differential; equations; image; segmentation


Two hybrid image segmentation models that are able to process a wide variety of images are proposed. The models take advantage of global (region) and local (edge) data of the image to be segmented. The first one is a region-based PDE model that incorporates a combination of global and local statistics. The influence of each statistic is controlled using weights obtained via an asymptotically stable exponential function. Through incorporation of edge information, the second model extends the capabilities of a strictly region-based variational formulation, making it able to process more general images. Several examples are provided showing the improvements of the proposed models over recent methods along with an application to dermoscopy imaging. A number of avenues for future research are also discussed.