Discrete algorithm for disk morphological filter based on piecewise linear interpolation

Abstract

The use of six-axis coordinate measuring machines “Lapik” for measuring the roughness of complex surfaces has a feature that consists in non-uniform discretization along the coordinate axes. One of the elements of the applied software should be a morphological filtering algorithm that takes into account this specificity. Compared to linear and regression Gaussian filters, morphological filters have a number of advantages. The main ones are the absence of edge effects and the not need to first apply a form filter. The well-known basic discrete algorithm for the morphological filter provides for a constant profile discretization step. Another limitation is related to the error from the discretization of the structural element. This article presents a discrete algorithm that takes into account the indicated features of measurement on coordinate measuring machines. To do this, the primary roughness profile is subjected to piecewise linear interpolation, and the disk structural element is described continuously. This makes it possible to determine the center of the disc with less error during morphological operations. Checking the accuracy of the algorithm on real and model examples showed that the filtering error in measuring the parameters Ra and Rqs about 3 %. The advantage of the developed algorithm is realized with a high unevenness of the initial data. The comparison of the performance of the proposed algorithm with the known ones showed its sufficient efficiency. The calculation time for 10000 points of the roughness profile does not exceed 0.05 sec.