基于双正交小波变换的矩不变量

寻找相对于尺度、平移、旋转不变的小波不变量是多尺度分析在模式识别中的关键问题.矩是一种理论和应用上比较成熟的方法，本文将矩与多尺度小波分解的近似系数联系起来，利用空间基函数的双正交性推导得到了双正交小波矩不变量，并用实验验证了结果的正确性.同时以Haar小波为例对结论中的限制条件进行了理论分析和实验验证，结果表明可以计算高于平滑阶数的小波矩，且计算精度符合要求.由此获得了比较完善的理论和实验结果，最后指出了它在实际应用中所需注意的问题.

Moment Invariants Based on Biorthogonal Wavelet Transform

It's a key problem to find wavelet invariants to the transformation of scale,translation and rotation in pattern recognition using multi-resolution analysis.Moment invariant is a mature method on theory and applications.This paper links the moment invariants with the approximation coefficients of image wavelet decomposition.A novel biorthogonal wavelet moment invariant is derived from the biorthogonality of the spatial basis functions.The experimental results are also provided to confirm the correctness of the theoretical derivation.After that,the limiting condition of the conclusion is analyzed by taking Haar wavelet as an example.Both theoretical analysis and experimental verification show that the wavelet moments of higher order than smoothness can be calculated within required accuracy.And the complete theoretical and experimental results are obtained.Finally,some problems to be paid attention to in practical application are pointed out.