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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