基于双树复小波变换的三维粗糙表面评定方法研究

针对目前用于提取三维粗糙表面基准面的第一和第二代小波存在的平移变动性与方向性差等缺点，以及最优小波基的选取和小波分解次数的确定等难点，提出将第三代小波变换--双树复小波变换（DT-CWT）用于三维粗糙表面的评定。通过比较三代小波实际重构图像以及仿真三维粗糙表面的误差和最大重构误差，得出了DT-CWT最优的结论；采用频带能量法确定DT-CWT的分解次数，并用仿真三维表面表征参数均方差S来验证得出的分解次数的正确性。最后用DT-CWT对具有分形特征的三维非平稳随机粗糙表面进行基准面的提取，结果验证了所提出方法的有效性。

Evaluation Method of Three-dimensional Rough Surface Based on Dual-tree Complex Wavelet Transform Methods

At present, wavelet transform applied to the establishment of three-dimensional rough surface datum was mainly the first and the second-generation wavelet. However, they had some defects such as the shift variation and poor directional selectivity and so on, especially the selection of optimum wavelet base and the determination of the times of wavelet decomposition, which was always the difficult points of surface evaluation. Now the third generation wavelet DT-CWT was used for valuation of three-dimensional rough surfaces, by comparing the datum errors and maximum reconstruction error of the actual reconstruction images of the three wavelets as well as simulation of three-dimensional rough surface, the optimality of DT-CWT was obtained. Band energy method was employed to ascertain the times of wavelet decomposition and then mean square error S which was the characterization parameter of three dimensional simulation surfaces was used to check the correctness of decomposition times. Finally, the reference surface of the three dimensional nonstationary random rough surface with fractal properties was extracted by DT-CWT transform. The results prove the effectiveness.