Patent ID: 8712185
Filing Date: 2014-04-29
Classification: G06K,G06T

Abstract:
1. A method for numerically generating a centered discrete fractional Fourier transform matrix on a computer for use in processing an image, the centered discrete fractional Fourier transform matrix of size N by N where N is an odd integer, the method comprising: numerically calculating the N eigenvectors of an N by N discrete fractional Fourier transform matrix from a closed-form mathematical formula, the calculation performed on a computer; performing a barrel shift operation on each of the N eigenvectors to produce N shifted eigenvectors; performing a Gram-Schmidt orthogonalization procedure on the N shifted eigenvectors to produce a first set of improved-orthogonal shifted eigenvectors, the Gram-Schmidt orthogonalization procedure; testing the resulting first set of improved-orthogonal shifted eigenvectors for mutually orthogonality performed on the computer; if the first set of improved-orthogonal shifted eigenvectors does not possess enough mutually orthogonality, applying another Gram-Schmidt orthogonalization procedure on the first set of improved-orthogonal shifted eigenvectors to produce a second set of improved-orthogonal shifted eigenvectors, and testing the resulting second set of improved-orthogonal shifted eigenvectors for mutually orthogonality; wherein if the first set of improved-orthogonal shifted eigenvectors does not possess enough mutually orthogonality, applying another Gram-Schmidt orthogonalization procedure, and testing the resulting improved-orthogonal shifted eigenvectors for mutually orthogonality, continuing until a resulting set of improved-orthogonal shifted eigenvectors is sufficiently orthogonal, and wherein the resulting set of improved-orthogonal shifted eigenvectors that is sufficiently orthogonal is used to create a centered discrete fractional Fourier transform matrix for use in processing the image.