3D-pose estimation from a quadratic-curved feature in two perspective views

Safaee-Rad, R.; Tchoukanov, I.; Benhabib, B.; Smith, K.C.

doi:10.1109/icpr.1992.201571

Cited by 10 publications

(13 citation statements)

References 10 publications

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“…Intersecting two volumes, instead of a volume and a surface, seems more complicated to derive closed-formed expressions (and therefore robust estimations) in the case of complex primitives. For a circle for example, the discrete method proposed in [13] is based on the resolution of a complex non linear system, whereas our method is based on the simple resolution of two linear systems.…”

Section: I-imentioning

confidence: 99%

Optimal estimation of 3D structures using visual servoing

Chaumette

Boukir

Bouthemy

et al. 1994

Proceedings of IEEE Conference on Computer Vision and Pattern Recognition CVPR-94

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This paper deals with the recovery of 3D information using a single mobile camera in the context of active vision. W e propo.se a general revisited formulation of the structure-from-motion issue, and we determine adequate camerti configurations and motions which lead to a robust and accurate estimation of the 3D structure parameters. W e apply the visual servoing approach. to perform these camera motions. Real-time experaments dealing ,with the 3 0 structure estimation of points and cylinders are reported, and demonstrate that this active vision strategy can very significantly improve the estimation accuracy.

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Section: I-imentioning

confidence: 99%

Optimal estimation of 3D structures using visual servoing

Chaumette

Boukir

Bouthemy

et al. 1994

Proceedings of IEEE Conference on Computer Vision and Pattern Recognition CVPR-94

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“…its geometric multiplicity 3 ) equal its algebraic multiplicity. When the algebraic multiplicity exceeds the geometric multiplicity, the matrix pencil is defective 4 . Otherwise, the matrix pencils are simple, non-defective.…”

Section: Polynomial Conditions For Correspondencementioning

confidence: 99%

“…The number of linearly independent eigenvectors associated with this multiple eigenvalue 4. Or as being derogatory, they are non-diagonalizable.…”

mentioning

confidence: 99%

Conic reconstruction and correspondence from two views

Quan

1996

IEEE Trans. Pattern Anal. Machine Intell.

102

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| Conics are widely accepted as one of the most fundamental image features together with points and line segments. The problem of space reconstruction and correspondence of two conics from two views is addressed in this paper. It is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views, given the relative orientation of the two views. These two correspondence conditions are derived algebraically and one of them is shown to be fundamental in establishing the correspondences of conics. A uni ed closed-form solution is also developed for both projective reconstruction of conics in space from two views for uncalibrated cameras and metric reconstruction from calibrated cameras.Experiments are conducted to demonstrate the discriminality of the correspondence conditions and the accuracy and stability of the reconstruction both for simulated and real images.

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“…Though Xie and Thonnet 11,12 give the analytical formulation for the reconstruction of quadratic curves, they have not given any methodology to determine the unique solution from the roots of quadratic equation. The case of reconstruction of conics in 3-D space has been discussed by several authors 3,6,[8][9][10][11][12] in their work. Balasubramanian et.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of quadratic curves in 3D using two or more perspective views: simulation studies

Kumar

Sukavanam

Balasubramanian

2006

Vision Geometry XIV

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The shapes of many natural and man-made objects have planar and curvilinear surfaces. The images of such curves usually do not have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. In this paper, we describe a method of reconstruction of a quadratic curve in 3-D space as an intersection of two cones containing the respective projected curve images. The correspondence between this pair of projections of the curve is assumed to be established in this work. Using least-square curve fitting, the parameters of a curve in 2-D space are found. From this we are reconstructing the 3-D quadratic curve. Relevant mathematical formulations and analytical solutions for obtaining the equation of reconstructed curve are given. The result of the described reconstruction methodology are studied by simulation studies. This reconstruction methodology is applicable to LBW decision in cricket, path of the missile, Robotic Vision, path planning etc.

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3D-pose estimation from a quadratic-curved feature in two perspective views

Cited by 10 publications

References 10 publications

Optimal estimation of 3D structures using visual servoing

Optimal estimation of 3D structures using visual servoing

Conic reconstruction and correspondence from two views

Reconstruction of quadratic curves in 3D using two or more perspective views: simulation studies

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