R. Manduchi, P. Perona, and D. Shy, "Efficient implementation of deformable filter banks," California Institute of Technology, 1997, Tech. Rep. CNS-TR-97-04; also available at http://www.vision.caltech.edu/manduchi/deformable.ps.Z. Home/Search Document Details and Download
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Efficient Recovery of Low-dimensional Structure from.. - Shyjan Mahamud Martial (Correct)
....matrix constructed from the frame sequence. Even though the shape that is to be recovered has low dimension, the direct computation of the SVD of the measurement matrix depends on the dimensions of the matrix hence does not scale well. Another example is in the construction of steerable filters [5, 3, 4]. Given a filter OE(x; y) and a set of transformations T , the task is to find a set of basis filters Phi = fOE 1 ; OE k g such that the response of the original filter OE under any transformation from T is some linear combination of the responses of the basis filters in Phi. For ....
....reducing the run time cost, we would like to keep the number of basis filters in Phi as small as possible. Analytical solutions are known only for some filters under a restricted set of transformations. One straight forward technique that was recently proposed for numerically constructing Phi [4, 5] is to sample OE under various transformations from T and then sample the transformed filter spatially upto some required resolution. The most significant left eigenvectors of the SVD of the matrix of such samples provide a basis set for steering OE. The cost of directly computing such an SVD can ....
Perona, P., "Efficient Implementation of Deformable Filter Banks", Tech Rept. CNS-TR-97-04, California Institute of Technology, 1997.
Efficient Deformable Filter Banks - Roberto Manduchi Pietro (1998) (1 citation) Self-citation (Manduchi Perona Shy) (Correct)
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R. Manduchi, P. Perona, and D. Shy, "Efficient implementation of deformable filter banks," California Institute of Technology, 1997, Tech. Rep. CNS-TR-97-04; also available at http://www.vision.caltech.edu/manduchi/deformable.ps.Z.
Efficient Deformable Filter Banks - Roberto Manduchi (1998) (1 citation) Self-citation (Manduchi Shy) (Correct)
....X r=0 d r (x)t r ( 1) We will call the filters d r (x) basis filters and the functions t r ( recombination functions. Term R is called the rank of the decomposition. Perona [4] studied the conditions for a kernel d(x; with continuous x and ) to be exactly steerable. One easily shows [7] that steerable filters are formally equivalent to multistage X Y separable structures, introduced by Treitel and Shanks [6] As in the case of multistage X Y separable filters, the least squares design of steerable filter banks [4] is performed by computing the SVD of a matrix built from the ....
....observation suggests the following iterative procedure: keep two variables fixed and minimize for the third one; then, cycle for the other variables. The approximation error is guaranteed to lower at each step, and since it is bounded from below by zero, the algorithm converges to a minimum. In [7] we use the formalism of hypermatrix algebra [8] and Kronecker algebra to translate the approximation task into a sequence of simple matrix operations. Unfortunately, one cannot be sure that the minimum found this way will be global (the error surface being in general not convex) and the solution ....
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Perona P. Manduchi, R. and Shy D. Efficient implementation of deformable filter banks. Technical Report CNS-TR-97-04, California Institute of Technology, 1997. Also available at http://www.vision.caltech.edu/manduchi/deformable.ps.Z.
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