A Planar-Reflective Symmetry Transform for 3D Shapes

ACM Transactions on Graphics (Proc. SIGGRAPH), July 2006

Abstract

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
a continuous measure of the reflectional 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.

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Citation

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

"A Planar-Reflective Symmetry Transform for 3D Shapes."

*ACM Transactions on Graphics (Proc. SIGGRAPH) 25(3)*, July 2006.

BibTeX

@article{Podolak:2006:APS, author = "Joshua Podolak and Philip Shilane and Aleksey Golovinskiy and Szymon Rusinkiewicz and Thomas Funkhouser", title = "A Planar-Reflective Symmetry Transform for {3D} Shapes", journal = "ACM Transactions on Graphics (Proc. SIGGRAPH)", year = "2006", month = jul, volume = "25", number = "3" }