Abstract
This paper considers and solves the problem of estimating camera pose given a pair of point-tangent correspondences between the 3D scene and the projected image. The problem arises when considering curve geometry as the basis of forming correspondences, computation of structure and calibration, which in its simplest form is a point augmented with the curve tangent. We show that while the standard resectioning problem is solved with a minimum of three points given the intrinsic parameters, when points are augmented with tangent information only two points are required, leading to substantial computational savings, e.g., when used as a minimal engine within ransac. In addition, computational algorithms are developed to find a practical and efficient solution shown to effectively recover camera pose using both synthetic and realistic datasets. The resolution of this problem is intended as a basic building block of future curve-based structure from motion systems, allowing new views to be incrementally registered to a core set of views for which relative pose has already been computed.
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Agarwal, S., Snavely, N., Simon, I., Seitz, S.M., Szeliski, R.: Building Rome in a day. In: ICCV 2009 (2009)
Ayache, N., Lustman, L.: Fast and reliable passive trinocular stereovision. In: ICCV 1987 (1987)
Bujnak, M., Kukelova, Z., Pajdla, T.: A general solution to the p4p problem for camera with unknown focal length. In: CVPR 2008 (2008)
Fabbri, R., Kimia, B.B.: High-Order Differential Geometry of Curves for Multiview Reconstruction and Matching. In: Rangarajan, A., Vemuri, B.C., Yuille, A.L. (eds.) EMMCVPR 2005. LNCS, vol. 3757, pp. 645–660. Springer, Heidelberg (2005)
Fabbri, R., Kimia, B.B.: 3D curve sketch: Flexible curve-based stereo reconstruction and calibration. In: CVPR 2010 (2010)
Finsterwalder, S., Scheufele, W.: Das ruckwartseinschneiden im raum. Sebastian Finsterwalder zum 75, 86–100 (1937)
Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24(6), 381–395 (1981)
Grunert, J.A.: Das pothenotische problem in erweiterter gestalt nebst Über seine anwendungen in der geodäsie. Archiv der für Mathematik and Physik 1, 238–248 (1841)
Haralick, R.M., Lee, C.-N., Ottenberg, K., Nölle, M.: Review and analysis of solutions of the three point perspective pose estimation problem. IJCV 13(3), 331–356 (1994)
Harris, C., Stephens, M.: A combined edge and corner detector. In: Alvey Vision Conference (1988)
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press (2000)
Horaud, R., Conio, B., Leboulleux, O., Lacolle, B.: An analytic solution for the p4p problem. CVGIP 47(1), 33–44 (1989)
Hu, Z.Y., Wu, F.C.: A note on the number of solutions of the noncoplanar p4p problem. PAMI 24(4), 550–555 (2002)
Kahl, F., Heyden, A.: Using conic correspondence in two images to estimate the epipolar geometry. In: ICCV 1998 (1998)
Kaminski, J.Y., Shashua, A.: Multiple view geometry of general algebraic curves. IJCV 56(3), 195–219 (2004)
Longuet-Higgins, H.C.: A computer algorithm for reconstructing a scene from two projections. Nature 293, 133–135 (1981)
Lowe, D.G.: Distinctive image features from scale-invariant keypoints. IJCV 60(2), 91–110 (2004)
Moreels, P., Perona, P.: Evaluation of features detectors and descriptors based on 3D objects. IJCV 73(3), 263–284 (2007)
Porrill, J., Pollard, S.: Curve matching and stereo calibration. IVC 9(1), 45–50 (1991)
Robert, L., Faugeras, O.D.: Curve-based stereo: figural continuity and curvature. In: CVPR 1991 (1991)
Sinha, S.N., Pollefeys, M., McMillan, L.: Camera network calibration from dynamic silhouettes. In: CVPR 2004 (2004)
Tamrakar, A., Kimia, B.B.: No grouping left behind: From edges to curve fragments. In: ICCV 2007 (2007)
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Fabbri, R., Kimia, B.B., Giblin, P.J. (2012). Camera Pose Estimation Using First-Order Curve Differential Geometry. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds) Computer Vision – ECCV 2012. ECCV 2012. Lecture Notes in Computer Science, vol 7575. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33765-9_17
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DOI: https://doi.org/10.1007/978-3-642-33765-9_17
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