Partial and approximate symmetry detection for 3D geometry

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

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

367 Scopus citations


"Symmetry is a complexity-reducing concept [...]; seek it every-where." - Alan J. Perlis Many 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)
Pages (from-to)560-568
Number of pages9
JournalACM transactions on graphics
Issue number3
StatePublished - Jul 2006
Externally publishedYes
EventACM SIGGRAPH 2006 - Boston, MA, United States
Duration: Jul 30 2006Aug 3 2006


  • Geometric modeling
  • Sampling guarantees
  • Shape analysis
  • Shape descriptor
  • Symmetry detection

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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