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.

[1]  Mehdi Hatamian,et al.  A real-time two-dimensional moment generating algorithm and its single chip implementation , 1986, IEEE Trans. Acoust. Speech Signal Process..

[2]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Wan-Chi Siu,et al.  Fast algorithm for 2-D image moments via the Radon transform , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[4]  Ming-Kuei Hu,et al.  Visual pattern recognition by moment invariants , 1962, IRE Trans. Inf. Theory.

[5]  G. MallatS..  A Theory for Multiresolution Signal Decomposition , 1989 .

[6]  Horst Bunke,et al.  Simple and fast computation of moments , 1991, Pattern Recognit..

[7]  Paul J. Zsombor-Murray,et al.  Fast algorithm for the computation of moment invariants , 1987, Pattern Recognit..

[8]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[9]  Jun Shen,et al.  Fast computation of moment invariants , 1991, Pattern Recognit..

[10]  S. Mallat.  Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .