A spectral approach to statistical polar shape modeling

Accounting for uncertainty in three-dimensional (3D) shapes is important in a large number of scientific and engineering areas including: biometrics, biomedical imaging, and multimodality image registration. It is well known that 3D star-shaped objects can be represented by Fourier descriptors such as spherical harmonics and double Fourier series. However, the statistics of these spectral shape models have not been widely explored. This article presents a spectral theory and its applications in 3D shape modeling. Spherical harmonic (SH) expansions over the unit sphere not only provide a low dimensional polarimetric parameterization of stochastic shape, but also correspond to Karhunen-Loéve (K-L) expansion of any isotropic random field on the unit sphere. Spherical harmonic expansions permit estimation and detection tasks, such as optimal shape filtering, object registration, and shape classification, which can be performed directly in the spectral domain with low computational complexity.