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Weak-Perspective and Scaled-Orthographic Structure from Motion with Missing Data

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Computer Vision, Imaging and Computer Graphics – Theory and Applications (VISIGRAPP 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 983))

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Abstract

Perspective n-Point (PnP) problem is in focus of 3D computer vision community since the late 80’s. Standard solutions deal with the pinhole camera model, the problem is challenging due to the perspectivity. The well-known PnP algorithms assume that the intrinsic camera parameters are known, therefore, only extrinsic ones are needed to estimate. It is carried out by a rough estimation, usually given in closed forms, then the accurate camera parameters are obtained via numerical optimization. In this paper, we show that both the weak-perspective and scaled orthographic camera models can be optimally calibrated including the intrinsic camera parameters. Moreover, the latter one is done without iteration if the \(L_2\) norm is used. It is also shown that the calibration can be inserted into a structure from motion algorithm. We also show that the scaled orthographic version can be powered by GPUs, yielding real-time performance.

Supported by EFOP-3.6.3-VEKOP-16-2017-00001: Talent Management in Autonomous Vehicle Control Technologies – The Project is supported by the Hungarian Government and co-financed by the European Social Fund.

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Notes

  1. 1.

    The transpose of the adjoint is also called the matrix of cofactors.

  2. 2.

    Available at http://thehuwaldtfamily.org/java/Packages/MathTools/MathTools.html.

  3. 3.

    \(A \odot B = C\) if \(c_{ij}=a_{ij} \cdot b_{ij}\).

  4. 4.

    This task is usually called triangulation. This term comes from stereo vision where the camera centers and the 3D position of the point form a triangle.

  5. 5.

    We tried the orthographic projection model with/without scale as well, the results had similar characteristics. Only the fully perspective test generation is contained in this paper due to the page limit.

  6. 6.

    http://users.ics.forth.gr/~lourakis/sba/.

  7. 7.

    http://math.nist.gov/javanumerics/jama/.

  8. 8.

    http://www.robots.ox.ac.uk/~amb/.

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Author information

Authors and Affiliations

  1. Department of Algorithms and Their Applications, Eötvös Loránd University, Pázmány Péter sétány 1/c, Budapest, 1111, Hungary

    Levente Hajder

  2. Machine Perception Laboratory, MTA SZTAKI, Budapest, Hungary

    Levente Hajder

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  1. Levente Hajder
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Correspondence to Levente Hajder .

Editor information

Editors and Affiliations

  1. University of Lisbon, Lisbon, Portugal

    Ana Paula Cláudio

  2. University of Strasbourg, Strasbourg, France

    Dominique Bechmann

  3. University of Angers, Angers, France

    Paul Richard

  4. Tokyo University of Science, Tokyo, Japan

    Takehiko Yamaguchi

  5. University of Münster, Münster, Nordrhein-Westfalen, Germany

    Lars Linsen

  6. University of Groningen, Groningen, The Netherlands

    Alexandru Telea

  7. Apple Inc., Cupertino, CA, USA

    Francisco Imai

  8. Jean Monnet University, Saint-Etienne, France

    Alain Tremeau

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Hajder, L. (2019). Weak-Perspective and Scaled-Orthographic Structure from Motion with Missing Data. In: Cláudio, A., et al. Computer Vision, Imaging and Computer Graphics – Theory and Applications. VISIGRAPP 2017. Communications in Computer and Information Science, vol 983. Springer, Cham. https://doi.org/10.1007/978-3-030-12209-6_7

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  • DOI: https://doi.org/10.1007/978-3-030-12209-6_7

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  • Online ISBN: 978-3-030-12209-6

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