3D object representation using spherical harmonic functions

The authors provide an object representation method that describes 3-D shape and pose using a set of covariant quantities based on a group theoretical approach. These covariant quantities can produce coordinate-invariant features that represent an object´s shape and coordinate variant features that represent its pose. First they formulate covariant quantities that are linearly transformed when the coordinate system is changed. Then they show that the invariant features capture coordinate-independent shape information and provide descriptors for indexing into a database of stored models. The variant features are obtained from the covariant quantities in terms of pose equations. A sufficient number of equations (at least three) can determine the object pose. The authors describe two pose estimation algorithms that use these equations, and present numerical simulation results which demonstrate that the algorithms yield close approximations of the object poses