Fitting of robust reference surface based on least absolute deviations

Engineering surfaces comprise shape deviations namely form, waviness and roughness. For characterization of roughness, form and waviness are separated from the measured surface by establishing a reference surface that represents these deviations. This paper presents a new approach of simultaneously separating form and waviness deviations by fitting a reference surface that remains robust against the outliers such as deep grooves. A second degree polynomial and a set of sinusoidal functions are taken as basis functions to represent form and waviness respectively. A criterion of minimization of sum of absolute deviations (L1-norm) is considered as against the commonly used least squares (L2-norm) criterion and the reference surface obtained is found to be robust against outliers such as deep valleys in the measured surface. The superiority of the proposed fitting scheme is brought out by testing on different surfaces and comparing with the least squares method of fitting and the robust Gaussian regression filtering.