Fast eigenspace decomposition of images of objects with variation in illumination and pose

Many appearance-based classification problems such as principal component analysis, linear discriminant analysis, and locally preserving projections involve computing the principal components (eigenspace) of a large set of images. Although the online expense associated with appearance-based techniques is small, the offline computational burden becomes prohibitive for practical applications. This paper presents a method to reduce the expense of computing the eigenspace decomposition of a set of images when variations in both illumination and pose are present. In particular, it is shown that the set of images of an object under a wide range of illumination conditions and a fixed pose can be significantly reduced by projecting these data onto 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 at different poses can be further reduced by utilizing the fast Fourier transform. An eigenspace decomposition is then applied in the spectral domain at a much lower dimension, thereby significantly reducing the computational expense. An analysis is also provided, showing that the principal eigenimages computed assuming a single illumination source are capable of recovering a significant amount of information from images of objects when multiple illumination sources exist.