Computational geometry: an introduction
Computational geometry: an introduction
Efficient algorithms for common transversals
Information Processing Letters
Proof of Gru¨nbaum's conjecture on common transversals for translates
Discrete & Computational Geometry
Determination of the Attitude of 3D Objects from a Single Perspective View
IEEE Transactions on Pattern Analysis and Machine Intelligence
Algorithms for high dimensional stabbing problems
Discrete Applied Mathematics - Computational combinatiorics
A generalization of Hadwiger's transversal theorem to intersecting sets
Discrete & Computational Geometry
Constraints for interpretation of line drawings under perspective projection
CVGIP: Image Understanding
Geometric correction of digitized art
Graphical Models and Image Processing
Discrete analytical hyperplanes
Graphical Models and Image Processing
Collinearity and Weak Collinearity in the Digital Plane
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Parallel Line Grouping Based on Interval Graphs
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Concurrency of Line Segments in Uncertain Geometry
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Collinearity and weak collinearity in the digital plane
Digital and image geometry
Graph-theoretical properties of parallelism in the digital plane
Discrete Applied Mathematics
Gift-wrapping based preimage computation algorithm
Pattern Recognition
Consensus sets for affine transformation uncertainty polytopes
Computers and Graphics
Discrete analytical curve reconstruction without patches
Image and Vision Computing
Reestablishing consistency of uncertain geometric relations in digital images
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Gift-wrapping based preimage computation algorithm
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Duality and geometry straightness, characterization and envelope
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Uncertain geometry in computer vision
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
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We adapt several important properties from affine geometry so that they become applicable in the digital plane. Each affine property is first reformulated as a propertyabout line transversals. Known results abouttransversals are then used to derive Helly typetheorems for the digital plane. The main characteristic of a Helly type theorem isthat it expresses a relation holding fora collection of geometricobjects in terms of simpler relations holding for some of the subcollections. For example, we show that in the digital plane a collection of digital linesis parallel if and only if each of its 2-membered subcollectionsconsists of two parallel digital lines. The derived Helly type theorems lead to many applications in digitalimage processing. For example, they provide an appropriate setting for verifying whetherlines detected in a digital image satisfythe constraints imposed by a perspective projection. The results can be extended to higher dimensions or to other geometric systems, such as projective geometry.