Image representation using vector wavelets

A new layered representation of images is proposed using, what one may call, vector wavelets defined by generalized Hermite polynomials. This representation has some special properties: it is distinct from and superior to the other wavelet schemes of the literature; it is stable; it transforms the image into matrices of coefficients in the same manner as the standard transforms (Fourier, Hadamard and others), but at the specified `scales´; the zero-crossings of the signal at various scales can be directly obtained from the coefficients; and the size of the resolution cell in the `phase-space´ is variable even at a specified scale, depending on the image being analysed. This representation has been successfully applied to different types of images, both synthetic and natural