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On the Global Self-calibration of Central Cameras Using Two Infinitesimal Rotations

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Computer Vision – ACCV 2012 (ACCV 2012)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7727))

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Abstract

The calibration of a generic central camera can be described non-parametrically by a map assigning to each image pixel a 3D projection ray. We address the determination of this map and the motion of a camera that performs two infinitesimal rotations about linearly independent axes. A complex closed-form solution exists, which in practice allows to visually identify the geometry of a range of sensors, but it only works at the center of the image domain and not accurately.

We present a new two-step method to solve the stated self-calibration problem that overcomes these drawbacks. Firstly, the Gram matrix of the camera rotation velocities is estimated jointly with the Lie bracket of the two rotational flows computed from the data images. Secondly, the knowledge that such Lie bracket is also a rotational flow is exploited to provide a solution for the calibration map which is defined on the whole image domain. Both steps are essentially linear, being robust to the noise inherent to the computation of optical flow from images.

The accuracy of the proposed method is quantitatively demonstrated for different noise levels, rotation pairs, and imaging geometries. Several applications are exemplified, and possible extensions and improvements are also considered.

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Author information

Authors and Affiliations

  1. Laboratoire MAP5 (CNRS UMR 8145), Université Paris Descartes, France

    Ferran Espuny

Authors
  1. Ferran Espuny
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, 151-744, Seoul, Korea

    Kyoung Mu Lee

  2. Microsoft Research Asia, No. 5, Danling st., Haidian district, 100080, Beijing, P.R. China

    Yasuyuki Matsushita

  3. School of Interactive Computing, Georgia Institute of Technology, 801 Atlantic Drive, CCB 315, 30332, Atlanta, GA, USA

    James M. Rehg

  4. Institute of Automation, National Laboratory of Pattern Recognition, Chinese Academy of Sciences, Zhong Quan Cun East Road 95, Haidian District,, 100 190, Beijing, P.R. China

    Zhanyi Hu

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Espuny, F. (2013). On the Global Self-calibration of Central Cameras Using Two Infinitesimal Rotations. In: Lee, K.M., Matsushita, Y., Rehg, J.M., Hu, Z. (eds) Computer Vision – ACCV 2012. ACCV 2012. Lecture Notes in Computer Science, vol 7727. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37447-0_19

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  • DOI: https://doi.org/10.1007/978-3-642-37447-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37446-3

  • Online ISBN: 978-3-642-37447-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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