Discrete Combinatorial Surfaces
Graphical Models and Image Processing
On the topology of an arithmetic plane.
Theoretical Computer Science
Geometrical parameters extraction from discrete paths
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Applications of Digital Straight Segments to Economical Image Encoding
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Recognizing arithmetic straight lines and planes
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
SpaMod: Design of a Spatial Modeling Tool
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
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
Recognition of Digital Naive Planes and Polyhedrization
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Defining Discrete Objects for Polygonalization: The Standard Model
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Maximal planes and multiscale tangential cover of 3D digital objects
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
Discrete surfaces segmentation into discrete planes
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Minimal decomposition of a digital surface into digital plane segments is NP-Hard
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Generalized functionality for arithmetic discrete planes
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Reversible polygonalization of a 3d planar discrete curve: application on discrete surfaces
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Computational aspects of digital plane and hyperplane recognition
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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A voxel object (finite set of voxels) is considered in the cuberille approach (more precisely, the 3D cell complex approach). Its boundary is a set of surfels (faces of voxels). We assume, without loss of generality, that this set of surfels is a polyhedron whose faces are surfels. These faces can be agglomerated in such a way that the boundary is a polyhedron whose faces are topological disks of standard arithmetic planes; this new kind of polyhedron is called a discrete standard polyhedron. Thus, these new faces are generally much bigger than one surfel, and a discrete standard polyhedron has generally a less smaller space complexity than the starting set of surfels. This process, called polyhedrization or facetization, is the 3D extension of the known polygonalization of 2D discrete curves. The other main properties of this polyhedrization are the non-uniqueness, and the reversibility, i.e. starting from the discrete standard polyhedron, the boundary can be exactly computed back again. A polyhedrization algorithm is presented in this paper. It uses a recent algorithm for recognizing standard arithmetic planes. Examples of polyhedrizations of synthetic and natural objects are given. Examples of application to the visualization of the boundary of a voxel object are also given.