A planar-reflective symmetry transform for 3D shapes

Joshua Podolak, Philip Shilane, Aleksey Golovinskiy, Szymon Rusinkiewicz, Thomas Funkhouser

Research output: Contribution to journalConference articlepeer-review

139 Scopus citations


Symmetry is an important cue for many applications, including object alignment, recognition, and segmentation. In this paper, we describe a planar reflective symmetry transform (PRST) that captures u continuous measure of the refiectional symmetry of a shape with respect to all possible planes. This transform combines and extends previous work that has focused on global symmetries with respect to the center of mass in 3D meshes and local symmetries with respect to points in 2D images. We provide an efficient Monte Carlo sampling algorithm for computing the transform for surfaces and show that it is stable under common transformations. We also provide an iterative refinement algorithm to find local maxima of the transform precisely. We use the transform to define two new geometric properties, center of symmetry and principal symmetry axes, and show that they are useful for aligning objects in a canonical coordinate system. Finally, we demonstrate that the symmetry transform is useful for several applications in computer graphics, including shape matching, segmentation of meshes into parts, and automatic viewpoint selection.

Original languageEnglish (US)
Pages (from-to)549-559
Number of pages11
JournalACM Transactions on Graphics
Issue number3
StatePublished - Jul 2006
EventACM SIGGRAPH 2006 - Boston, MA, United States
Duration: Jul 30 2006Aug 3 2006

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design


  • Matching
  • Registration
  • Segmentation
  • Shape analysis
  • Symmetry
  • Viewpoint selection


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