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.
","abstract_html":"<p>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 19:47<sup>o</sup> 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 <em>C<sup>1</sup></em> or<em> C<sup>2</sup></em> 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.</p>","abstract_has_math":false,"creators":["Xu, Jing"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Andrey Chernikov","Danella Zhao","Jiangwen Sun","Nail Yamaleev"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-08-01T07:00:00Z","date_published":"2020-08-01T07:00:00Z","updated_at":"2026-07-24T03:35:38Z","subjects":["Curvilinear","Fidelity","High-order","Homeomorphism","Mesh generation","Tetrahedralization","Computer Sciences"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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"]},{"key":"dc:title","label":"Title","values":["Automatic Linear and Curvilinear Mesh Generation Driven by Validity Fidelity and Topological Guarantees"]}]}],"canonical_facts":{"dc:contributor":["Andrey Chernikov","Danella Zhao","Jiangwen Sun","Nail Yamaleev"],"dc:creator":["Xu, Jing"],"dc:date.available":["2020-09-28T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["9798678109002","https://digitalcommons.odu.edu/computerscience_etds/127"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Curvilinear","Fidelity","High-order","Homeomorphism","Mesh generation","Tetrahedralization","Computer Sciences"],"dc:title":["Automatic Linear and Curvilinear Mesh Generation Driven by Validity Fidelity and Topological Guarantees"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:35:38Z"}