Three-dimensional object recognition from single two-dimensional images
Artificial Intelligence
A survey of the Hough transform
Computer Vision, Graphics, and Image Processing
Geometric reasoning
CVGIP: Image Understanding
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Preserving Topology by a Digitization Process
Journal of Mathematical Imaging and Vision
Geometric Constructions in the Digital Plane
Journal of Mathematical Imaging and Vision
Discretization in Hausdorff Space
Journal of Mathematical Imaging and Vision
Introductory Techniques for 3-D Computer Vision
Introductory Techniques for 3-D Computer Vision
Consensus sets for affine transformation uncertainty polytopes
Computers and Graphics
Reconstruction of concurrent lines from leaning points
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
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 propose different graph-theoretical algorithms to partition a set of digitized lines into parallel groups, i.e., subsets in which each line is parallel to the other lines in the subset. The slope of a digitized line is not a fixed real number, but is represented by an interval. Likewise, the parallel relations of a collection of lines are represented by an interval graph. The extraction of parallel groups is then equivalent to the detection of cliques in the interval graph. We also consider other partitioning methods, for example, methods based on minimum dominating sets, and on simplicial elimination orderings. In addition, we compute the number of ways in which we can divide a set into parallel groups.