Mathematical Morphology in Multi-Dexel Representation

Mathematical morphology provides a set-theoretic approach for spatial structure analysis and is particularly useful for describing the spatial relationship between a tool under motion and the part surface. However, its usage in three-dimension has so far been limited in part due to its computational complexity. This paper presents a multi-dexel based computer implementation of morphology operations. Three dimensional objects (tools and parts) are represented as collections of dexels (depth elements) in multiple directions. Morphology operations such as dilation and erosion are then converted to a series of 1D set operations in each direction. We show that our definition of multi-dexel is formal and our implementation is complete. We present our implementation results on three morphological applications: AFM image simulation, noise removal in 3D mesh, and NC path generation.