Eigendecomposition of images correlated on S1, S2, and SO(3) using spectral theory
IEEE Transactions on Image Processing
Designing eigenspace manifolds: with application to object identification and pose estimation
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
An illustration of eigenspace decomposition for illumination invariant pose estimation
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
| Hi-index | 0.01 |
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 (2-D) 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 (3-D) objects rotated about a single axis. In addition, the theory of circulant matrices yields 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 of test cases ranging from images of 3-D objects rotated about a single axis to arbitrary video sequences