Discrete Algorithm for a Disk Morphological Filter Based on Piecewise Linear Interpolation

The use of six-axis coordinate measuring machines (Lapik) for measuring the roughness of complex surfaces is characterized by nonuniform discretization along the coordinate axes. One of the elements of the applied software is a morphological filtering algorithm that takes into account such non-uniform discretization. In the discrete algorithm, the primary roughness profile was subjected to piecewise linear interpolation, and the disk structural element was described continuously, which reduced the error in determining the disk element center during morphological operations. The algorithm accuracy was tested on real and model examples, and the resulting filtering error in measuring the roughness parameters was approximately 3%. The performance of the proposed basic discrete and alpha forms of the algorithm was compared. The advantage of the algorithm developed with the high unevenness of initial data is presented. The filtration time for 10,000 points of the roughness profile does not exceed 0.05 s.