Abstract
Morphological filters are E-system-type filters, which are complementary to M-system filters that are based on mathematical morphology. They are the superset of the early envelope filters but offer more tools and capabilities. This chapter first reviews the historical development of morphological filters along with the associated basic theories of morphological operations. The applications of morphological operation in the field of geometrical metrology are illustrated. The chapter then presents two advanced computational algorithms that allow morphological filters to be applied to free-form surfaces. The first algorithm is based on a computational geometry technique, that is, alpha shape theory, which can be further optimized by searching contact points and using the divide and conquer technique. The second algorithm removes the dependence of the alpha shape method on the Delaunay triangulation and recursively searches the contact points of the structuring element and the surface. In conclusion, this chapter will present and evaluate examples of applying morphological filters on precision-machined surfaces and additive manufactured surfaces.
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