基于投影的多尺度小波矩快速算法

多尺度小波变换矩采用几何矩定义，由信号在某一尺度下的小波逼近系数计算得到，它反映的是信号在该尺度下小波分解对应的视觉不变量。由于受到矩本身计算量的限制，小波矩的计算很难实时实现。本文提出了一种基于投影变换的二维多尺度小波变换矩快速算法。该快速算法通过投影变换将二维图像小波变换低频分量信息投影到一维空间中，从而降低了多尺度小波变换矩的计算复杂度，保证了计算精度。

Fast Algorithm for Multiresolution Wavelet Moments Based on Projection

Multiresolution wavelet moments, relating wavelet analysis with theory of moment invariants, are perfect representations of moments in multiresolution wavelet transform. Wavelet moments calculated by approximation components at certain scale level correspond to the visual invariants at multiresolution wavelet spaces. But because of its computation complexity, it is difficult to be implemented in real time. A fast projection-based algorithm for two-dimensional wavelet moments is presented. In the approach, the computation of a two-dimensional wavelet transform moment can be performed in several one-dimensional spaces, thus reducing the computational complexity without introducing extra error.