An efficient computation of low-dimensional linear subspaces that optimally contain
the set of images that are generated by varying the illumination impinging on the
surface of a three-dimensional object for many different relative positions of
that object and the viewing camera. The matrix elements of the spatial covariance
matrix for an object are calculated for an arbitrary pre-determined distribution
of illumination conditions. The maximum complexity is reduced for the model by
approximating any pair of normal-vector and albedo from the set of all such pairs
of albedo and normals with the centers of the clusters that are the result of the
vector quantization of this set. For an object, a viewpoint-independent covariance
matrix whose complexity is large, but practical, is constructed and diagonalized
off-line. A viewpoint-dependent covariance matrix is computed from the viewpoint-independent
diagonalization results and is diagonalized online in real time.
