A fast and adaptive bi-dimensional empirical mode decomposition approach for filtering of workpiece surfaces using high definition metrology

The surface topography of workpieces has an important influence on the final performances of the product. The digital filtering is a critical step to analyze the surface topography of workpieces. Bi-dimensional empirical mode decomposition (BEMD) approach is superior to conventional filtering approaches in the analysis of non-stationary and non-linear data. High definition metrology (HDM) can generate massive point cloud data to represent the three-dimensional (3D) surface topography of workpieces, which provides a new opportunity for surface topography analysis. This paper develops a fast and adaptive bi-dimensional empirical mode decomposition (FABEMD) approach for filtering of workpiece surfaces using HDM. Firstly, the neighboring window algorithm is presented to extract local extrema and draw the extrema spectrum. Secondly, the adaptive window algorithm is developed to automatically select the optimal window size of the order statistics filter, and plot the envelope spectrum. Finally, the average smoothing filter is presented for smooth filtering and generating of the mean envelope. The performance of the proposed FABEMD-based filter is validated by a simulated surface data and three real-world surface data. Compared with Gaussian filter (ISO 11562:1996, ASME B46.1-2002), the BEMD-based filter and the recent shearlet-based filter in the qualitative and quantitative analysis, the proposed FABEMD-based filter is superior for the separation and extraction of different surface components.