Morphological Method for Surface Metrology and Dimensional Metrology Based on Alpha Shape

Morphological filters are useful tools as they are commonly employed in surface metrology and dimensional metrology, serving for surface texture analysis and data smoothing respectively. Compared to the mean-line filtering techniques, such as the Gaussian filter, morphological filters have the merits of compact support, no need to remove form, and being relevant to geometrical properties of surfaces. This paper proposes a novel morphological method based on the alpha shape. The proposed method has the advantages over the traditional methods that it runs relative fast, enables arbitrary large ball radii, and applies to freeform surfaces and nonuniform sampled surfaces. The theory of basic morphological operations and the alpha shape are introduced and the theoretical link between the alpha hull and the morphological closing and opening operation is presented. A practical algorithm is developed that corrects possible singularities caused by data spikes and reduces the amount of calculation for open profiles/surfaces. Computer simulation is used to compare the results from the traditional algorithm and the proposed one. Experimental studies are conducted to demonstrate the feasibility and applicability of using the proposed method.