Geometric modeling and representation based on sweep mathematical morphology

We propose a framework for geometric modeling and representation by sweep mathematical morphology, which is based on set-theoretic concept together with geometric sweep. We use a new class of morphological operations that allows one to select varying shapes and orientations of structuring elements during the sweeping process. The sweep dilation/erosion provides a natural representation of sweep motion in manufacturing processes, and the sweep opening/closing provides variant degrees of smoothing in image filtering and edge linking. A set of grammatical rules that govern the generation of objects belonging to the same group can be defined. Earley's parser serves in the screening process to determine whether a pattern is a part of the language. Sweep mathematical morphology is demonstrated as an intuitive and efficient tool for geometric modeling and representation.