Accurate Detection of Symmetries in 3D Shapes

We propose an automatic method for finding symmetries of 3D shapes, i.e. isometric transforms which leave a shape globally unchanged. These symmetries are deterministically found through the use of an intermediate quantity: the generalized even moments. By examining their extrema and spherical harmonic coefficients we recover the parameters of the symmetries of the shape. The computation for large composite models is made efficient by using this information in an incremental algorithm capable of recovering the symmetries of a whole shape using the symmetries of its sub-parts. Applications of this work range from coherent re-meshing of geometry with respect to the symmetries of a shape, to geometric compression, intelligent mesh editing and automatic instantiation.

@Article\{MSHS06,
  author       = "Martinet, Aur\'elien and Soler, Cyril and Holzschuch, Nicolas and Sillion, Fran\c{c}ois",
  title        = "Accurate Detection of Symmetries in 3D Shapes",
  journal      = "ACM Transactions on Graphics",
  number       = "2",
  volume       = "25",
  pages        = "439 - 464",
  month        = "April",
  year         = "2006",
  url          = "http://maverick.inrialpes.fr/Publications/2006/MSHS06"
}