Relaxing Topological Barriers in Geometry Processing
Name
palmer-drp-phd-eecs-2023-thesis.pdf
Description
Thesis PDF
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255.07 MB
Format
Adobe PDF
Checksum (MD5)
e79dbf834b8504c00c5d46f7f55b5900
Author(s)
Palmer, David R.
Advisor(s)
Solomon, Justin M.
Date Issued
September 2023
Publisher
Massachusetts Institute of Technology
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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