Abstract
In this paper we present methods for triangulation of infinite cylinders from image line silhouettes. We show numerically that linear estimation of a general quadric surface is inherently a badly posed problem. Instead we propose to constrain the conic section to a circle, and give algebraic constraints on the dual conic, that models this manifold. Using these constraints we derive a fast minimal solver based on three image silhouette lines, that can be used to bootstrap robust estimation schemes such as RANSAC. We also present a constrained least squares solver that can incorporate all available image lines for accurate estimation. The algorithms are tested on both synthetic and real data, where they are shown to give accurate results, compared to previous methods.
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References
Åström, K., Cipolla, R., Giblin, P.J.: Generalised Epipolar constraints. Int. J. Comput. Vis. 33, 51–72 (1999)
Åström, K., Kahl, F.: Motion estimation in image sequences using the deformation of apparent contours. IEEE Trans. Pattern Anal. Mach. Intell. 21(2), 114–127 (1999)
Bartoli, A., Sturm, P.: Structure-from-motion using lines: Representation, triangulation, and bundle adjustment. Comput. Vis. Image Underst. 100(3), 416–441 (2005)
Biederman, I.: Human image understanding: recent research and a theory. Comput. Vis. Graph. Image Process. 32(1), 29–73 (1985)
Cox, D., Little, J., OShea, D.: Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra. Springer Science & Business Media (2013)
Dai, X., Yuan, X., Gong, H., Ma, Y.: Fully convolutional line parsing. arXiv preprint arXiv:2104.11207 (2021)
De Ma, S.: Conics-based stereo, motion estimation, and pose determination. Int. J. Comput. Vision 10(1), 7–25 (1993)
Frosio, I., Alzati, A., Bertolini, M., Turrini, C., Borghese, N.A.: Linear pose estimate from corresponding conics. Pattern Recogn. 45(12), 4169–4181 (2012)
Frosio, I., Turrini, C., Alzati, A.: Camera re-calibration after zooming based on sets of conics. Vis. Comput. 32(5), 663–674 (2016)
Gummeson, A., Engman, J., Åström, K., Oskarsson, M.: Fast and efficient minimal solvers for quadric based camera pose estimation. In: Proceedings of the International Conference on Pattern Recognition (2022)
Josephson, K., Kahl, F.: Triangulation of points, lines and conics. J. Math. Imag. Vis. 32(2), 215–225 (2008)
Kahl, F., Heyden, A.: Using conic correspondences in two images to estimate the epipolar geometry. In: Sixth International Conference on Computer Vision (IEEE Cat. No. 98CH36271), pp. 761–766. IEEE (1998)
Kaminski, J., Shashua, A.: Multiple view geometry of algebraic curves. Int. J. Comput. Vis. 56, 195–219 (2003)
Keppel, E.: Approximating complex surfaces by triangulation of contour lines. IBM J. Res. Dev. 19(1), 2–11 (1975)
Larsson, V., Åström, K., Oskarsson, M.: Efficient solvers for minimal problems by syzygy-based reduction. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 820–829 (2017)
Ma, S., Li, L.: Ellipsoid reconstruction from three perspective views. In: Proceedings of 13th International Conference on Pattern Recognition, vol. 1, pp. 344–348. IEEE (1996)
Marr, D., Nishihara, H.K.: Representation and recognition of the spatial organization of three-dimensional shapes. Proceed. Royal Soc. London. Ser. B. Biol. Sci. 200(1140), 269–294 (1978)
Mei, J., Zhang, D., Ding, Y.: Monocular vision for pose estimation in space based on cone projection. Opt. Eng. 56(10), 103108 (2017)
Mudigonda, P.K., Jawahar, C., Narayanan, P.: Geometric structure computation from conics. In: ICVGIP, pp. 9–14. CiteSeer (2004)
Mur-Artal, R., Montiel, J.M.M., Tardos, J.D.: ORB-SLAM: a versatile and accurate monocular slam system. IEEE Trans. Rob. 31(5), 1147–1163 (2015)
Navab, N., Appel, M.: Canonical representation and multi-view geometry of cylinders. Int. J. Comput. Vision 70(2), 133–149 (2006)
Pautrat, R., Lin, J.T., Larsson, V., Oswald, M.R., Pollefeys, M.: Sold2: self-supervised occlusion-aware line description and detection. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 11368–11378 (2021)
Quan, L.: Conic reconstruction and correspondence from two views. IEEE Trans. Pattern Anal. Mach. Intell. 18(2), 151–160 (1996)
Sattler, T., et al.: Benchmarking 6DoF outdoor visual localization in changing conditions. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 8601–8610 (2018)
Schönberger, J.L., Frahm, J.M.: Structure-from-motion revisited. In: Conference on Computer Vision and Pattern Recognition (CVPR) (2016)
Schönberger, J.L., Zheng, E., Frahm, J.-M., Pollefeys, M.: Pixelwise view selection for unstructured multi-view stereo. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9907, pp. 501–518. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46487-9_31
Semple, J.G., Kneebone, G.T.: Algebraic projective geometry. Clarendon Press (1979)
Sun, J., Cheng, X., Fan, Q.: Camera calibration based on two-cylinder target. Opt. Express 27(20), 29319–29331 (2019)
Von Gioi, R.G., Jakubowicz, J., Morel, J.M., Randall, G.: LSD: a line segment detector. Image Process. Line 2, 35–55 (2012)
Winkler, A., Zagar, B.: A curve fitting method for extrinsic camera calibration from a single image of a cylindrical object. Meas. Sci. Technol. 24(8), 084001 (2013)
Xu, Y., Xu, W., Cheung, D., Tu, Z.: Line segment detection using transformers without edges. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 4257–4266 (2021)
Acknowledgements
This work was partially supported by the ADACORSA project with funding from ECSEL JU in the H2020 Framework Programme (H2020/2014-2020) and National Authorities, under GA 876019, and the strategic research project ELLIIT.
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Gummeson, A., Oskarsson, M. (2023). Robust and Accurate Cylinder Triangulation. In: Gade, R., Felsberg, M., Kämäräinen, JK. (eds) Image Analysis. SCIA 2023. Lecture Notes in Computer Science, vol 13886. Springer, Cham. https://doi.org/10.1007/978-3-031-31438-4_30
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