Fast Estimation of Mean Curvature on the Surface of a 3D Discrete Object
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Strong Thinning and Polyhedrization of the Surface of a Voxel Object
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Abstraction Pyramids on Discrete Representations
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Simple points and generic axiomatized digital surface-structures
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
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The purpose of this paper is to define the notion of "real" intersection between paths drawn on the 3d digital boundary of a connected object. We consider two kinds of paths for different adjacencies, and define the algebraic number of oriented intersections between these two paths. We show that this intersection number is invariant under any homotopic transformation we apply on the two paths. Already, this intersection number allows us to prove a Jordan curve theorem for some surfels curves which lie on a digital surface, and appears as a good tool for proving theorems in digital topology about surfaces.