A geometric investigation of reach
A geometric investigation of reach
Image Analysis Using Mathematical Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
A mathematical model for shape description using Minkowski operators
Computer Vision, Graphics, and Image Processing
Threshold Decomposition of Gray-Scale Morphology into Binary Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Sweeping of three-dimensional objects
Computer-Aided Design
A generalized sweeping method for SGC modeling
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Computing Minkowski sums
Boundary representation deformation in parametric solid modeling
ACM Transactions on Graphics (TOG)
CSG-BRep duality and compression
Proceedings of the seventh ACM symposium on Solid modeling and applications
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Information Sciences: an International Journal
From theoretical graphic objects to real free-form solids
Information Sciences: an International Journal
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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.