Convergence of the robust Gaussian regression filter applied to sanded wood surfaces

The quality of a sanded wood surface is represented by its roughness, which can be separated from the originally measured data by a procedure of filtering. Past experience has shown that the robust Gaussian regression filter (RGRF) is suitable for wood surfaces because it does not introduce distortions into the roughness profiles. The filter works iteratively until a user-defined convergence condition is met. The iterations stop when the difference between two consecutive profile median values becomes smaller than a given tolerance. This paper examines the convergence of RGRF when applied to wood surfaces sanded with various grit sizes in order to establish the tolerance value, which leads to convergence with the minimum number of iterations. This study was based on monitoring the variation of roughness parameters with the number of iterations for a range of tolerance values. A tolerance of 0.01 μm was found acceptable for filtering sanded wood surfaces.