Date of Award

Summer 8-2020

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computer Science

Committee Director

Andrey Chernikov

Committee Member

Danella Zhao

Committee Member

Jiangwen Sun

Committee Member

Nail Yamaleev

Abstract

Image-based geometric modeling and mesh generation play a critical role in computational biology and medicine. In this dissertation, a comprehensive computational framework for both guaranteed quality linear and high-order automatic mesh generation is presented. Starting from segmented images, a quality 2D/3D linear mesh is constructed. The boundary of the constructed mesh is proved to be homeomorphic to the object surface. In addition, a guaranteed dihedral angle bound of up to 19:47o for the output tetrahedra is provided. Moreover, user-specified guaranteed bounds on the distance between the boundaries of the mesh and the boundaries of the materials are allowed. The mesh contains a small number of mesh elements that comply with these guarantees, and the runtime is compatible in performance with other software. Then the curvilinear mesh generator allows for a transformation of straight-sided meshes to curvilinear meshes with C1 or C2 smooth boundaries while keeping all elements valid and with good quality as measured by their Jacobians. The mathematical proof shows that the meshes generated by our algorithm are guaranteed to be homeomorphic to the input images, and all the elements inside the meshes are guaranteed to be with good quality. Experimental results show that the mesh boundaries represent the objects' shapes faithfully, and the accuracy of the representation is improved compared to the corresponding linear mesh.

DOI

10.25777/31kp-az96

ISBN

9798678109002

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