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# Rigorous computing in computer vision

Institute of Mathematics and its Applications - Vision, Video and Graphics 2005, VVG 2005 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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Available from: Andrea Fusiello
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• "The idea is to formalize this as a Constraint Satisfaction Problem, to use Constraint Logic Programming (CLP) to narrow the intervals as much as possible and then to pick one solution, i.e., to select a point inside each interval such that it satisfies all constraints. This work builds on [4], where interval-based triangulation is described. The novel contribution of this paper is the use of CLP(Intervals) to impose geometrical constraints on an interval reconstruction. "
##### Article: Reconstruction with Interval Constraints Propagation
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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.
Full-text · Article · Jun 2006 · Proceedings / CVPR, IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society Conference on Computer Vision and Pattern Recognition
• Source
• "The idea is to formalize this as a Constraint Satisfaction Problem, to use Constraint Logic Programming (CLP) to narrow the intervals as much as possible and then to pick one solution, i.e., to select a point inside each interval such that it satisfies all constraints. This work builds on [4], where interval-based triangulation is described. The novel contribution of this paper is the use of CLP(Intervals) to impose geometrical constraints on an interval reconstruction. "
##### Conference Paper: Reconstruction with Interval Constraints Propagation.
[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.
Full-text · Conference Paper · Jan 2006
• ##### Article: Covariance Propagation for the Uncertainty Estimation in Stereo Vision
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ABSTRACT: Stereo vision has emerged as an effective approach for contactless 3-D measurements. This paper presents a methodology for the propagation of the measurement uncertainty through stereo-vision calibration and measurement algorithms, according to international standards. The proposed procedure is compared to the reference statistical procedure for uncertainty evaluation, and the results are presented and discussed. The results proved that the proposed procedure was able to estimate the standard uncertainty even at considerable working distances from the calibrated volume with negligible processing times and far more accurately than the theoretical simplified models commonly adopted.
No preview · Article · May 2011 · IEEE Transactions on Instrumentation and Measurement