Relaxing Topological Barriers in Geometry Processing
Geometric optimization problems are full of topological barriers that hinder optimization, leading to nonconvexity, initialization-dependence, and local minima. This thesis explores convex relaxation as a powerful guide and tool for reframing such problems. We bring the tools of semidefinite relaxat...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2023
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| Online Access: | https://hdl.handle.net/1721.1/152846 https://orcid.org/0000-0002-1931-5673 |
| _version_ | 1811092848237346816 |
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| author | Palmer, David R. |
| author2 | Solomon, Justin M. |
| author_facet | Solomon, Justin M. Palmer, David R. |
| author_sort | Palmer, David R. |
| collection | MIT |
| description | Geometric optimization problems are full of topological barriers that hinder optimization, leading to nonconvexity, initialization-dependence, and local minima. This thesis explores convex relaxation as a powerful guide and tool for reframing such problems. We bring the tools of semidefinite relaxation to bear on challenging optimization problems in field-based meshing and unlock polynomial geometry kernels for physical simulation. We bring together frame fields with spectral representation of geometry. We use current relaxation to devise a new neural shape representation for surfaces with boundary as well as a convex relaxation of field optimization problems featuring singularities. Unifying these disparate problems is a focus on how the right choice of representation for geometry can simplify optimization algorithms. |
| first_indexed | 2024-09-23T15:30:08Z |
| format | Thesis |
| id | mit-1721.1/152846 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T15:30:08Z |
| publishDate | 2023 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1528462023-11-03T03:10:10Z Relaxing Topological Barriers in Geometry Processing Palmer, David R. Solomon, Justin M. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Geometric optimization problems are full of topological barriers that hinder optimization, leading to nonconvexity, initialization-dependence, and local minima. This thesis explores convex relaxation as a powerful guide and tool for reframing such problems. We bring the tools of semidefinite relaxation to bear on challenging optimization problems in field-based meshing and unlock polynomial geometry kernels for physical simulation. We bring together frame fields with spectral representation of geometry. We use current relaxation to devise a new neural shape representation for surfaces with boundary as well as a convex relaxation of field optimization problems featuring singularities. Unifying these disparate problems is a focus on how the right choice of representation for geometry can simplify optimization algorithms. Ph.D. 2023-11-02T20:21:32Z 2023-11-02T20:21:32Z 2023-09 2023-09-21T14:26:04.813Z Thesis https://hdl.handle.net/1721.1/152846 https://orcid.org/0000-0002-1931-5673 In Copyright - Educational Use Permitted Copyright retained by author(s) https://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Palmer, David R. Relaxing Topological Barriers in Geometry Processing |
| title | Relaxing Topological Barriers in Geometry Processing |
| title_full | Relaxing Topological Barriers in Geometry Processing |
| title_fullStr | Relaxing Topological Barriers in Geometry Processing |
| title_full_unstemmed | Relaxing Topological Barriers in Geometry Processing |
| title_short | Relaxing Topological Barriers in Geometry Processing |
| title_sort | relaxing topological barriers in geometry processing |
| url | https://hdl.handle.net/1721.1/152846 https://orcid.org/0000-0002-1931-5673 |
| work_keys_str_mv | AT palmerdavidr relaxingtopologicalbarriersingeometryprocessing |