An efficient algorithm for areal morphological filter

This article discusses morphological filtering for assessing a areal parameters of a texture of engineering products. A data organization structure has been proposed that makes it possible to increase the efficiency of an iterative algorithm for enumerating a surface coordinates. Morphological filters complement the standard Gaussian filter to evaluate the functional properties of a surface. The widespread use of the areal morphological filtering in metrological practice is currently hampered by the lack of an effective algorithm. An algorithm based on a matrix representation of morphological operations on the surface coordinates is presented. For this purpose, different indexing of points on a primary surface and a structuring element has been introduced. A sphere or flat segment is used as the structuring element. The high performance of the developed algorithm is ensured due to the fact that all calculations are carried out by enumerating the surface coordinates in one pass, without nested loops, as in some other algorithms. Algorithms for morphological operations of dilation and erosion are presented, on the basis of which a closing and opening filters are constructed. Simulations carried out for various data sets and comparison with known morphological filtering algorithms confirmed the high efficiency of the designed algorithm. The results obtained can be used to analyze the functional properties of product surfaces.