Computing 3D Medial Axis Transform via Restricted Power Diagram
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| Publicado no: | ProQuest Dissertations and Theses (2025) |
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ProQuest Dissertations & Theses
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| Acesso em linha: | Citation/Abstract Full Text - PDF |
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| 045 | 2 | |b d20250101 |b d20251231 | |
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| 100 | 1 | |a Wang, Ningna | |
| 245 | 1 | |a Computing 3D Medial Axis Transform via Restricted Power Diagram | |
| 260 | |b ProQuest Dissertations & Theses |c 2025 | ||
| 513 | |a Dissertation/Thesis | ||
| 520 | 3 | |a This thesis investigates the theory and practice of computing the 3D medial axis transform (MAT) through the lens of the restricted power diagram (RPD). As geometric data becomes increasingly central to applications in scientific computing, computer-aided design, and machine learning, there is a pressing need for robust and efficient algorithms that support compression, analysis, and synthesis of 3D shapes. The 3D MAT offers a compact, structure-aware representation well-suited to these challenges, capturing both geometric and topological information critical to downstream tasks.The contributions of this work begin with a generalization of existing medial sphere classifications to accommodate non-smooth geometries—such as Computer-Aided Design (CAD) models—in addition to traditional organic shapes. This generalization enables a suite of new operations that retain key medial properties while ensuring computational robustness. Building on this foundation, we present MATFP, a complete RPD-based framework for computing the MAT of 3D shapes. MATFP effectively preserves external features, including sharp edges and corners, as well as internal medial structures that enable natural shape decomposition. We further extend this framework with MATTopo, a volumetric variant that computes the 3D MAT while explicitly preserving homotopy equivalence—a property crucial for topology-aware shape processing. Finally, we propose MATStruct, which integrates the strengths of MATFP and MATTopo to generate medial meshes that simultaneously preserve medial structure and achieve high geometric quality.Together, these contributions establish a unified, RPD-based approach for high-fidelity 3D medial axis computation, offering a practical and theoretically grounded foundation for future applications in shape analysis, reconstruction, and geometric learning. | |
| 653 | |a Computer engineering | ||
| 653 | |a Computer science | ||
| 653 | |a Information science | ||
| 773 | 0 | |t ProQuest Dissertations and Theses |g (2025) | |
| 786 | 0 | |d ProQuest |t ProQuest Dissertations & Theses Global | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3279253130/abstract/embedded/H09TXR3UUZB2ISDL?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3279253130/fulltextPDF/embedded/H09TXR3UUZB2ISDL?source=fedsrch |