Computational geometry: an introduction
Computational geometry: an introduction
Geometric Constructions in the Digital Plane
Journal of Mathematical Imaging and Vision
On Recursive, O(N) Partitioning of a Digitized Curve into Digital Straight Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Discrete Applied Mathematics
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
On digital plane preimage structure
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
An elementary digital plane recognition algorithm
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
A generalized preimage for the standard and supercover digital hyperplane recognition
DGCI'06 Proceedings of the 13th 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
Gift-wrapping based preimage computation algorithm
Pattern Recognition
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The aim of the paper is to define an algorithm for computing preimages - roughly the sets of naive digital planes containing a finite subset S of Z3. The method is based on theoretical results: the preimage is a polytope that vertices can be decomposed in three subsets, the upper vertices, the lower vertices and the intermediary ones (equatorial). We provide a geometrical understanding (as facets on S or S ⊖ S) of each kind of vertices. These properties are used to compute the preimage by gift-wrapping some regions of the convex hull of S or of S⊖S∪{(0, 0, 1)}.