An efficient algorithm for areal morphological filtering

The present article considers the estimation of functional product surface properties using the results of measuring areal surface texture parameters via morphological filtering. Under this method, a form of measurement data representation is proposed to improve the efficiency of an algorithm for iterating over surface coordinates. It is shown that for wide implementation of areal morphological filtering in metrological practice, it is necessary to create an efficient filtering algorithm. In the work, an algorithm was developed relying on a matrix representation of morphological operations on surface coordinates. Different indexing of the primary surface and structuring element points was introduced. A sphere or flat segment was used as the structuring element. The performance of the developed algorithm is higher than that of some other algorithms due to the fact that all computations are performed by iterating over surface coordinates in a single pass without nested loops. The diagrams of algorithms for the morphological operations of dilation and erosion are given; these operations were used to construct closing and opening filters. Simulations performed for different datasets and a comparison with known morphological filtering algorithms confirmed the high efficiency of the developed algorithm. The obtained results can be applied in the analysis of the functional properties of product surfaces.