A Fast Algorithm for Morphological Filters

In surface metrology, M-system (Mean-line filtering system) and E-system (Envelope filtering system) are two filtering approaches. Although M-system has been the dominant choice and played an important role in manufacturing control, Morphological filters, that evolved from the E-system, are believed to give better results in function prediction of surface finish in the analysis of surfaces in contact.
The naïve way of computing morphological filter is described in ISO 16610. It is time consuming,
especially for areal data. The presented fast algorithm employs alpha shape as the basis of the
computation. The boundary of the hull obtained by rolling the alpha ball over the point set is identical to the closing/opening envelope in theory. Spikes in the data set are detected and points interpolated to prevent singularities. Edge distortion is corrected by reflective padding for open profiles/surfaces. This algorithm directly generates the closing and opening envelope in comparison with combining
dilation and erosion in the naïve algorithm.