A new boundary-based morphological model

Abstract

Mathematical morphology addresses the problem of describing shapes in an n-dimensional space using the concepts of set theory. A series of standardized morphological operations are defined, and they are applied to the shapes to transform them using another shape called the structuring element. In an industrial environment, the process of manufacturing a piece is based on the manipulation of a primitive object via contact with a tool that transforms the object progressively to obtain the desired design. The analogy with the morphological operation of erosion is obvious. Nevertheless, few references about the relation between the morphological operations and the process of design and manufacturing can be found. The non-deterministic nature of classic mathematical morphology makes it very difficult to adapt their basic operations to the dynamics of concepts such as the ordered trajectory. A new geometric model is presented, inspired by the classic morphological paradigm, which can define objects and apply morphological operations that transform these objects. The model specializes in classic morphological operations, providing them with the determinism inherent in dynamic processes that require an order of application, as is the case for designing and manufacturing objects in professional computer-aided design and manufacturing (CAD/CAM) environments. The operators are boundary-based so that only the points in the frontier are handled. As a consequence, the process is more efficient and more suitable for use in CAD/CAM systems.