Abstract
This paper deals with the problem of self-calibrating a moving camera with constant parameters. We propose a new set of quartic trivariate polynomial equations in the unknown coordinates of the plane at infinity derived under the no-skew assumption. Our new equations allow to further enforce the constancy of the principal point across all images while retrieving the plane at infinity. Six such polynomials, four of which are independent, are obtained for each triplet of images. The proposed equations can be solved along with the so-called modulus constraints and allow to improve the performance of existing methods.
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Sturm, P.: Critical Motion Sequences for Monocular Self-calibration and Uncalibrated Euclidean Reconstruction. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1100–1105 (1997)
Luong, Q.: Self-calibration of a Moving Camera from Point Correspondences and Fundamental Matrices. International Journal of Computer Vision 22, 261–289 (1997)
Nistér, D.: Untwisting a Projective Reconstruction. International Journal of Computer Vision 60, 165–183 (2004)
Triggs, B.: Autocalibration and the Absolute Quadric. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 609–614 (1997)
Heyden, A., Åström, K.: Euclidean Reconstruction from Constant Intrinsic Parameters. In: International Conference on Pattern Recognition, vol. 1, pp. 339–343. IEEE (1996)
Valdés, A., Ronda, J.I., Gallego, G.: The Absolute Line Quadric and Camera Autocalibration. International Journal of Computer Vision 66, 283–303 (2006)
Ponce, J., Mc Henry, K., Papadopoulo, T., Teillaud, M., Triggs, B.: On the Absolute Quadratic Complex and its Application to Autocalibration. In: IEEE Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 780–787 (2005)
Hartley, R., Hayman, E., Agapito, L., Reid, I.: Camera Calibration and the Search for Infinity. In: IEEE International Conference on Computer Vision, pp. 510–517 (1999)
Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press (2004)
Gherardi, R., Fusiello, A.: Practical Autocalibration. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part I. LNCS, vol. 6311, pp. 790–801. Springer, Heidelberg (2010)
Pollefeys, M., van Gool, L.: Stratified Self-calibration with the Modulus Constraint. IEEE Transactions on Pattern Analysis and Machine Intelligence 21, 707–724 (1999)
Chandraker, M., Agarwal, S., Kriegman, D., Belongie, S.: Globally Optimal Algorithms for Stratified Autocalibration. International Journal of Computer Vision 90, 236–254 (2010)
Pollefeys, M., Koch, R., van Gool, L.: Self-calibration and Metric Reconstruction in spite of Varying and Unknown Internal Camera Parameters. International Journal of Computer Vision 32, 7–25 (1999)
Gurdjos, P., Bartoli, A., Sturm, P.F.: Is Dual Linear Self-calibration Artificially Ambiguous? In: IEEE International Conference on Computer Vision, pp. 88–95 (2009)
Chandraker, M., Agarwal, S., Kahl, F., Kriegman, D., Nister, D.: Autocalibration via Rank-Constrained Estimation of the Absolute Quadric. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2007)
Schaffalitzky, F.: Direct Solution of Modulus Constraints. In: Indian Conference on Computer Vision, Graphics and Image Processing, pp. 314–321 (2000)
Heyden, A., Astrom, K.: Flexible Calibration: Minimal Cases for Auto-calibration. In: IEEE International Conference on Computer Vision, vol. 1, pp. 350–355 (1999)
Rothwell, C.A., Faugeras, O.D., Csurka, G.: Different Paths towards Projective Reconstruction. In: Europe-China Workshop on Geometrical Modelling and Invariants for Computer Vision. Xidan University Press (1995)
Verschelde, J.: Polynomial Homotopy Continuation with PhcPack. ACM Communications in Computer Algebra 44, 217–220 (2011)
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Habed, A., Ismaeil, K.A., Fofi, D. (2012). A New Set of Quartic Trivariate Polynomial Equations for Stratified Camera Self-calibration under Zero-Skew and Constant Parameters Assumptions. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds) Computer Vision – ECCV 2012. ECCV 2012. Lecture Notes in Computer Science, vol 7577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33783-3_51
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DOI: https://doi.org/10.1007/978-3-642-33783-3_51
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