Fast Hermite Projection Method
Fast Hermite projection scheme for image processing and analysis is introduced. It is based on an expansion of image intensity function into a Fourier series using full orthonormal system of Hermite functions instead of trigonometric basis. Hermite functions are the eigenfunctions of the Fourier transform and they are computationally localized both in frequency and spatial domains in the contrast to the trigonometric functions. The acceleration of this expansion procedure is based on Gauss-Hermite quadrature scheme simplified by the replacement of Hermite associated weights and Hermite polynomials by an array of associated constants. This array of associated constants depends on the values of Hermite functions. Image database retrieval and image foveation applications based on 2D fast Hermite projection method have been considered. The proposed acceleration algorithm can be also efficiently used in Hermite transform method.
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