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 voxel 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. Using Fourier methods, our algorithm computes the symmetry descriptor in O(N⁴ log N) time for an N×N×N voxel grid, and computes a multiresolution approximation in O(N³ log N) time. In our initial experiments, we have found the symmetry descriptor to be useful for registration, matching, and classification of shapes.

@inproceedings{Kazhdan:2002:ARS,
   author = "Michael Kazhdan and Bernard Chazelle and David Dobkin and Adam
      Finkelstein and Thomas Funkhouser",
   title = "A Reflective Symmetry Descriptor",
   booktitle = "7th European Conference on Computer Vision (ECCV 2002)",
   year = "2002",
   month = may,
   pages = "642--656"
}