Three-dimensional object recognition from single two-dimensional images
Artificial Intelligence
Geometric reasoning
CVGIP: Image Understanding
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
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]
Concurrency of Line Segments in Uncertain Geometry
DGCI '02 Proceedings of the 10th 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 use an interval graph to model the uncertainty of line slopes in a digital image. We propose two different algorithms that group lines into classes of lines that are parallel, or almost parallel. This grouping is strongly based on the Helly-type property of parallelism in the digital plane: a group of lines is digitally parallel if and only if each pair of lines is digitally parallel. As a result, the extraction of parallel groups is reduced to the extraction of cliques in the interval graph generated by the slope intervals. Likewise, the extraction of lines that are almost parallel becomes equivalent to the detection of subgraphs that resemble cliques.