Publication: Euclidean upgrading from segment lengths
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Publication Date
2010-12
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Springer
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Abstract
We address the problem of the recovery of Euclidean structure of a projectively distorted n-dimensional space from the knowledge of segment lengths. This
problem is relevant, in particular, for Euclidean reconstruction with uncalibrated cameras, extending previously known results in the affine setting. The key concept is the Quadric of Segments (QoS), defined in a higher-dimensional space by the set of segments
of a fixed length from which Euclidean structure can be obtained in closed form. We have intended to make a thorough study of the properties of the QoS, including the
determination of the minimum number of segments of arbitrary length that determine it and its relationship with the standard geometric objects associated to the Euclidean structure of space. Explicit formulas are given to obtain the dual absolute quadric and the absolute quadratic complex from the QoS. Experiments with real and synthetic images evaluate the performance of the techniques.
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Agrawal, M., & Davis, L. S. (2003). Camera calibration using spheres: A semi-definite programming approach. In ICCV ’03: Proceedings of the ninth IEEE international conference on computer vision (p. 782). Washington, DC, USA. Los Alamitos: IEEE Computer Society.
Bayro-Corrochano, E., & Rosenhahn, B. (2002). A geometric approach for the analysis and computation of the intrinsic camera parameters. Pattern Recognition, 35(1), 169–186.
Harris, J. (1995). Algebraic geometry, a first course. Berlin: Springer.
Hartley, R., & Zisserman, A. (2003). Multiple view geometry in computer vision, 2nd edn. Cambridge: Cambridge University Press.
Hartley, R. I. (1992). Estimation of relative camera positions for uncalibrated cameras. In Proc. European Conference on Computer Vision (pp. 579–587). London, UK. Berlin: Springer.
Hartley, R. I., Hayman, E., de Agapito, L., & Reid, I. (1999). Camera calibration and the search for infinity. IEEE International Conference on Computer Vision, 1, 510.
Heyden, A., & Åström, K. (1997). Euclidean reconstruction from image sequences with varying and unknown focal length and principal point. In Proc. IEEE conference on computer vision and pattern recognition, New York, USA.
Kahl, F., Triggs, B., & Åström, K. (2000). Critical motions for autocalibration when some intrinsic parameters can vary. Journal of Mathematical Imaging and Vision, 13(2), 131–146.
Liebowitz, D., & Carlsson, S. (2003). Uncalibrated motion capture exploiting articulated structure constraints. International Journal on Computer Vision, 51(3), 171–187.
Maybank, S. J., & Faugeras, O. D. (1992). A theory of self-calibration of a moving camera. International Journal on Computer Vision, 8(2), 123–151.
Pollefeys, M., & Gool, L. V. (1997). A stratified approach to metric self-calibration. In Proc. of the IEEE conference on computer vision and pattern recognition (pp. 407–412), June 1997.
Ponce, J. (2001). On computing metric upgrades of projective reconstructions under the rectangular pixel assumption. In Second European workshop on 3D structure from multiple images of largescale environments (pp. 52–67). London, UK. Berlin: Springer.
Ponce, J., McHenry, K., Papadopoulo, T., Teillaud, M., & Triggs, B. (2005). On the absolute quadratic complex and its application to autocalibration. In Proc. IEEE conference on computer vision and pattern recognition (Vol. 1, pp. 780–787).Washington, DC, USA.
Pribanic, T., Sturm, P., & Peharec, S. (2009). Wand-based calibration of 3d kinematic system. IET-CV, 3(3), 124–129.
Roe, E. D. Jr. (1897). On the circular points at infinity. The American Mathematical Monthly, 4(5), 132–145.
Ronda, J. I., Gallego, G., & Valdés, A. (2005). Camera autocalibration using Plücker coordinates. In International conference on image processing (Vol. 3, pp. 800–803), Genoa, Italy.
Ronda, J. I., Valdés, A., & Gallego, G. (2008). Line geometry and camera autocalibration. Journal of Mathematical Imaging and Vision, 32(2), 193–214.
Seo, Y., & Heyden, A. (2000). Auto-calibration from the orthogonality constraints. In Proc. international conference on pattern recognition (Vol. 01, pp. 1067–1071), Los Alamitos, CA, USA.
Sturm, P. (1997). Critical motion sequences for monocular selfcalibration and uncalibrated euclidean reconstruction. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 0, 1100.
Tresadern, P. A., & Reid, I. D. (2008). Camera calibration from human motion. Image and Vision Computing, 26(6), 851–862.
Triggs, B. (1997). Autocalibration and the absolute quadric. In Proc. Of the IEEE conference on computer vision and pattern recognition (pp. 609–614), Puerto Rico, USA, June 1997.
Tsai, R. Y. (1992). A versatile camera calibration technique for high accuracy 3d machine vision metrology using off-the-shelf tv cameras and lenses. In Radiometry (pp. 221–244). Boston: Jones and Bartlett.
Valdés, A., & Ronda, J. I. (2005). Camera autocalibration and the calibration pencil. Journal of Mathematical Imaging and Vision, 23(2), 167–174.
Valdés, A., Ronda, J. I., & Gallego, G. (2006). The absolute line quadric and camera autocalibration. International Journal of Computer Vision, 66(3), 283–303.
Wong, K.-Y. K., Mendonça, P. R., & Cipolla, R. (2003). Camera calibration from surfaces of revolution. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25, 147–161.
Zhang, H., Wong, K.-Y. K., & Zhang, G. (2007). Camera calibration from images of spheres. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(3), 499–502.
Zhang, Z. (2000). A flexible new technique for camera calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 1330–1334.
Zhang, Z. (2004). Camera calibration with one-dimensional objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26, 892–899.