Concrete Math
On Recursive, O(N) Partitioning of a Digitized Curve into Digital Straight Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Applications of Digital Straight Segments to Economical Image Encoding
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Surface digitizations by dilations which are tunnel-free
Discrete Applied Mathematics
Discrete linear objects in dimension n: the standard model
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Discrete Representation of Straight Lines
IEEE Transactions on Pattern Analysis and Machine Intelligence
Discrete surfaces segmentation into discrete planes
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
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
Minimum decomposition of a digital surface into digital plane segments is NP-hard
Discrete Applied Mathematics
Local Non-planarity of Three Dimensional Surfaces for an Invertible Reconstruction: k-Cuspal Cells
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Adaptive Pixel Resizing for Multiscale Recognition and Reconstruction
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
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This paper tackles the problem of the computation of a planar polygonal curve from a digital planar curve, such that the digital data can be exactly retrieved from the polygonal curve. The proposed transformation also provides an analytical modelling of a digital plane segment as a discrete polygon composed of a face, edges and vertices. A dual space representation of lines and planes is used to ensure that the computed curve remains inside the digital curve, and this tool enables to define a very efficient algorithm. Applied on the digital plane segments resulting from the decomposition of a digital surface, this algorithm provides a set of polygons modelling exactly the digital surface.