Partial and approximate symmetry detection for 3D geometry

Niloy J. Mitra, Leonidas J. Guibas, Mark Pauly

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

111 Scopus citations

Abstract

"Symmetry is a complexity-reducing concept [...]; seek it every-where." - Alan J. PerlisMany natural and man-made objects exhibit significant symmetries or contain repeated substructures. This paper presents a new algorithm that processes geometric models and efficiently discovers and extracts a compact representation of their Euclidean symmetries. These symmetries can be partial, approximate, or both. The method is based on matching simple local shape signatures in pairs and using these matches to accumulate evidence for symmetries in an appropriate transformation space. A clustering stage extracts potential significant symmetries of the object, followed by a verification step. Based on a statistical sampling analysis, we provide theoretical guarantees on the success rate of our algorithm. The extracted symmetry graph representation captures important high-level information about the structure of a geometric model which in turn enables a large set of further processing operations, including shape compression, segmentation, consistent editing, symmetrization, indexing for retrieval, etc.

Original languageEnglish (US)
Title of host publicationACM SIGGRAPH 2006 Papers, SIGGRAPH '06
Pages560-568
Number of pages9
DOIs
StatePublished - Dec 1 2006
EventACM SIGGRAPH 2006 Papers, SIGGRAPH '06 - Boston, MA, United States
Duration: Jul 30 2006Aug 3 2006

Publication series

NameACM SIGGRAPH 2006 Papers, SIGGRAPH '06

Other

OtherACM SIGGRAPH 2006 Papers, SIGGRAPH '06
CountryUnited States
CityBoston, MA
Period07/30/0608/3/06

Keywords

  • geometric modeling
  • sampling guarantees
  • shape analysis
  • shape descriptor
  • symmetry detection

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition
  • Software

Fingerprint

Dive into the research topics of 'Partial and approximate symmetry detection for 3D geometry'. Together they form a unique fingerprint.

Cite this