Fast eigenspace decomposition of correlated images
Maciejewski, Anthony A.
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We present a computationally efficient algorithm for the eigenspace decomposition of correlated images. Our approach is motivated by the fact that for a planar rotation of a two-dimensional image, analytical expressions can be given for the eigendecomposition, based on the theory of circulant matrices. These analytical expressions turn out to be good first approximations of the eigendecomposition, even for three-dimensional objects rotated about a single axis. We use this observation to automatically determine the dimension of the subspace required to represent an image with a guaranteed user-specified accuracy, as well as to quickly compute a basis for the subspace. Examples show that the algorithm performs very well on a range of test images composed of three-dimensional objects rotated about a single axis.