Journal article
Geometric Optimization via Composite Majorization
ACM Transactions on Graphics, Vol.36(4), 38
Jul/2017
Abstract
Many algorithms on meshes require the minimization of composite objectives, i.e., energies that are compositions of simpler parts. Canonical examples include mesh parameterization and deformation. We propose a second order optimization approach that exploits this composite structure to efficiently converge to a local minimum. Our main observation is that a convex-concave decomposition of the energy constituents is simple and readily available in many cases of practical relevance in graphics. We utilize such convex-concave decompositions to define a tight convex majorizer of the energy, which we employ as a convex second order approximation of the objective function. In contrast to existing approaches that largely use only local convexification, our method is able to take advantage of a more global view on the energy landscape. Our experiments on triangular meshes demonstrate that our approach outperforms the state of the art on standard problems in geometry processing, and potentially provide a unified framework for developing efficient geometric optimization algorithms.
Details
- Title
- Geometric Optimization via Composite Majorization
- Creators
- Anna Shtengel (null) - 972WIS_INST___83Roi Poranne (null) - 972WIS_INST___83Olga Sorkine-Hornung (null)Shahar Z. Kovalsky (null)Yaron Lipman (null) - 972WIS_INST___83
- Resource Type
- Journal article
- Publication Details
- ACM Transactions on Graphics, Vol.36(4), 38; Jul/2017
- Number of pages
- 11
- Language
- English
- DOI
- https://doi.org/10.1145/3072959.3073618
- Grant note
- European Research Council starting grant Surf-Comp [307754]; European Research Council starting grant iModel [306877]; I-CORE program of the Israel PBC [4/11]; I-CORE program of the ISF [4/11]; Simons Foundation Math+X Investigator award_ALMAME_DELIMITER_
- Record Identifier
- 993262047303596
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