Fast Eigenspace Decomposition of Correlated Images

Fast Eigenspace Decomposition of Correlated Images

C-Y. Chang, A. A. Maciejewski, and V. Balakrishnan

In IEEE Trans. Image Processing, , vol. 9, no. 11, pp 1937-1949, November 2000


Abstract: 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. In addition, the theory of circulant matrices yields very good approximations to the eigendecomposition for images that result when objects are translated and scaled. We use these observations 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 number test cases ranging from images of three-dimensional objects rotated about a single axis to arbitrary video sequences.
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