Three-dimensional object recognition from single two-dimensional images
Artificial Intelligence
Efficient algorithms for common transversals
Information Processing Letters
Proof of Gru¨nbaum's conjecture on common transversals for translates
Discrete & Computational Geometry
On finite-precision representations of geometric objects
Journal of Computer and System Sciences
Algorithms for high dimensional stabbing problems
Discrete Applied Mathematics - Computational combinatiorics
A generalization of Hadwiger's transversal theorem to intersecting sets
Discrete & Computational Geometry
Using tolerances to guarantee valid polyhedral modeling results
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Geometric relationships between tolerance features
Geometric reasoning
Geometric reasoning
Helly-type theorems and geometric transversals
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Consistent calculations for solids modeling
SCG '85 Proceedings of the first annual symposium on Computational geometry
Geometric Constructions in the Digital Plane
Journal of Mathematical Imaging and Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Graph-theoretical properties of parallelism in the digital plane
Discrete Applied Mathematics
Digital Straight Line Segments
IEEE Transactions on Computers
Consensus sets for affine transformation uncertainty polytopes
Computers and Graphics
Geometric feature estimators for noisy discrete surfaces
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
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We give an overview of the main ideas and tools that have been employed in uncertain geometry. We show how several recognition problems in computer vision can be translated into combinatorial optimization problems that involve intersection hypergraphs, and how we can obtain approximate solutions for these problems when we replace the hypergraphs by intersection graphs. The statistical properties of these graphs are important when we design algorithms for the extraction of geometric primitives from images. We illustrate the use of uncertain geometry with examples involving the detection of circles and the computation of transformations between images.