Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Computer Science and Engineering

Major Professor

Paul Rosen, Ph.D.

Committee Member

Les Piegl, Ph.D.

Committee Member

Yicheng Tu, Ph.D.

Committee Member

Zhuo Lu, Ph.D.

Committee Member

Dmytro Savchuk, Ph.D.


Contour Trees, Image Enhancement, Parallel Computing, Persistent Pairing, Reeb Graphs


Topological Data Analysis (TDA) is a new and fast growing research field developed over last two decades. TDA finds many applications in computer vision, computer graphics, scientific visualization, molecular biology, and material science, to name a few. In this dissertation, we make algorithmic and application contributions to three data structures in TDA: contour trees, Reeb graphs, and Mapper. From the algorithmic perspective, we design a parallel algorithm for contour tree construction and implement it in OpenCL. We also design and implement critical point pairing algorithms to compute persistence diagrams directly from contour trees, Reeb graphs, and Mapper. In terms of applications, we apply TDA in the design and implementation of an image enhancement application using contour trees. Lastly, we introduce an application of Mapper and persistent homology in model quality assessment for 3D printing.