中文摘要：

刻线尺寸的器件表面存在着大量的如槽、台阶等不连续特征,当提取其基准面来做质量评定时,ISO规定最小二乘拟合法来实现,但其鲁棒性远远差于滤波法。而若直接采用传统滤波法（如高斯滤波、小波滤波等）在不连续特征处会产生波动。基于此,提出一种新的滤波稳健算法,通过对双树复小波变换（Dual-tree complex wavelet transform,DT-CWT）进行全变分最小化理论（Total variation minimization,TVM）梯度处理,即对每层的小波系数运用阈值方法进行初始化,借助投影次梯度法将TVM理论与DT-CWT相结合,不断迭代,最终增强DT-CWT在提取几何结构特征基准面的鲁棒性。仿真结果表明,所提算法与传统滤波方法相比,整个表征精度（最大重构误差和均方差）具有最优性,且评定高度也最接近理想高度。对一实测标块,无论从直观三维视图还是侧面对比图,其在阶跃处能很好地抑制波动,与标块实际加工的理论高度偏差只有0.040 3μm,保证了产品的几何特征,为实际的工程应用提供了一种有效的基准提取方法。

英文摘要：

There are a lot of discontinuous characteristics such as grooves and the steps in the device surface with the groove size. The least squares fitting method is required by ISO regulation when the datum is extracted for its quality evaluation,but its robustness is far worse than filtering method. Fluctuations which are called the pseudo Gibbs phenomenon will be generated in the discontinuous surface if the traditional filtering method（such as Gaussian filtering,wavelet filtering,etc.） is used directly. A new filtering algorithm is proposed. By gradient processing the dual tree complex wavelet transform（DT-CWT） though the total variation minimization theory（TVM）,which means initializing the wavelet coefficients of each layer by using the threshold value method; combining the idea of TVM with DT-CWT with projected subgradient method; continuous iteration; and finally the robustness of the DT-CWT transform in extracting the datum which has plane geometry characteristic is enhanced. The simulation results show that compared with the traditional filtering methods,the algorithm has the optimality in the characterization of precision（maximum reconstruction error and the mean square error）,and its assess height is the closest to the ideal height. Assessment carried out on a real convex sticker block,fluctuations can be well restrained at steps whether from the intuitive 3D view or side contrast figure,and the geometrical characteristics of the product are ensured as the theoretical height deviation with the actual processed standard block is only 0.0403 μm,and an effective reference extraction method is provided for practical engineering application.