Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper, we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D model for all planes through the model’s center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. We show how to obtain a voxel grid from arbitrary 3D shapes and, using Fourier methods, we present an algorithm that computes the symmetry descriptor in O(N4 logN) time for an N  N  N voxel grid and computes a multiresolution approximation in O(N3 logN) time. In our initial experiments, we have found that the symmetry descriptor is insensitive to noise and stable under point sampling. We have also found that it performs well in shape matching tasks, providing a measure of shape similarity that is orthogonal to existing methods.

@article{Kazhdan:2003:ARS,
   author = "Michael Kazhdan and Bernard Chazelle and David Dobkin and Thomas
      Funkhouser and Szymon Rusinkiewicz",
   title = "A Reflective Symmetry Descriptor for {3D} Models",
   journal = "Algorithmica",
   year = "2003",
   month = oct,
   volume = "38",
   number = "1"
}