Metric invariants for unitary transformations and their application in character recognition

摘要

The general case of a unitary discrete one-dimensional transformation is considered and its power spectrum developed. The notion of invariants within this power spectrum is then introduced and the specific cases of the Fourier, Hadamard and Haar transforms as well as the hybrid Hadamard-Haar and Hadamard-Fourier transforms are considered. The results obtained are extended to two-dimensional transformations, and it is shown that, if the number of invariants within the power spectrum of a one-dimensional transformation is an affine function of the transformation order, the number of invariants is a quadratic function of that order in the case of two-dimensional transformations. Finally an application of the results using the invariants thus defined is presented.