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 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.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2023

Author dc:creator

• Palmer, David R.

Advisor dc:contributor.advisor

• Solomon, Justin M.

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/152846

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/152846