Exact and fast algorithm for two-dimensional image wavelet moments via the projection transform

Wavelet moments are perfect representations of moments in multiresolution wavelet domain, which integrates the theory of moment invariants into wavelet analysis. However, the calculations of moments are very complicated in terms of computational complexity, so it is difficult to implement them in real time. An exact and fast projection-based algorithm for two-dimensional wavelet moments is presented in this paper. In our approach, the computation of a two-dimensional wavelet moment of order of r is performed in (r+1) different one-dimensional spaces. Since only additions are required to perform the projection transform, the total computational complexity can be greatly reduced.