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Rigorous computing in computer vision

01/2005;

ABSTRACT In this paper we discuss how Interval Analysis can be used to solve some problems in Computer Vision, namely autocalibration and triangulation. The crucial property of Interval Analysis is its ability to rigorously bound the range of a function over a given domain. This allows to propagate input errors with guaranteed results (used in multi-views triangulation) and to search for solution in non-linear minimisation problems with provably correct branch-and-bound algorithms (used in autocalibration). Experiments with real calibrated images illustrate the interval approach.

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    ABSTRACT: In this paper we demonstrate how Interval Analysis and Constraint Logic Programming can be used to obtain an accurate geometric model of a scene that rigorously takes into account the propagation of data errors and roundoff. Image points are represented as small rectangles: As a result, the output of the n-views triangulation is not a single point in space, but a polyhedron that contains all the possible solutions. Interval Analysis is used to bound this polyhedron with a box. Geometrical constraints such as orthogonality, parallelism, and coplanarity are subsequently enforced in order to reduce the size of those boxes, using Constraint Logic Programming. Experiments with real calibrated images illustrate the approach.
    Proceedings / CVPR, IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society Conference on Computer Vision and Pattern Recognition 06/2006; 1:1185-1190.
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    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper we demonstrate how Interval Analysis and Constraint Logic Programming can be used to obtain an ac- curate geometric model of a scene that rigorously takes into account the propagation of data errors and roundoff. Image points are represented as small rectangles: As a result, the output of the n-views triangulation is not a single point in space, but a polyhedron that contains all the possible so- lutions. Interval Analysis is used to bound this polyhedron with a box. Geometrical constraints such as orthogonal- ity, parallelism, and coplanarity are subsequently enforced in order to reduce the size of those boxes, using Constraint Logic Programming. Experiments with real calibrated im- ages illustrate the approach.
    2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2006), 17-22 June 2006, New York, NY, USA; 01/2006

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