An illustration of eigenspace decomposition for illumination invariant pose estimation

Determining the pose of a three-dimensional object under unknown lighting conditions is a challenging problem. Eigenspace methods represent one computationally efficient method for doing illumination invariant pose estimation, and have been applied in a variety of application domains. Unfortunately, determining the appropriate eigenspace dimension, as well as the eigenspace itself, is computationally prohibitive for real-world applications. This paper presents a method to reduce this expense by using results from spectral theory. In particular, this paper shows that a set of images of an object under a wide range of illumination conditions and a fixed pose can be significantly reduced by projecting this data on to a few low-frequency spherical harmonics, producing a set of ¿harmonic images¿. It is then shown that the dimensionality of the set of harmonic images can be further reduced by utilizing the fast Fourier transform. An eigendecomposition is then applied in the spectral domain thus relieving the computational burden. Experimental results are presented to compare the proposed algorithm to the true eigendecomposition, as well as assess the computational savings.