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What Does One Image of One Ball Tell Us About the Focal Length?

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Advanced Concepts for Intelligent Vision Systems (ACIVS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9386))

Abstract

We reanimate the (sometimes forgotten) Belgian Theorems, and show how the balls of Dandelin can give us elegant proofs for geometric properties of perspective ball projections. As a consequence, we derive a new formula for computing the focal length by means of 1 image of 1 ball. By means of simulations we show the sensitivity of our formula in function of the ratio of the major axis to the minor axis of the elliptic ball image. This provides a measure of reliability and enables us to select the most appropriate ball image.

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Author information

Authors and Affiliations

  1. Faculty of Applied Engineering, University of Antwerp, Salesianenlaan 90, 2660, Antwerp, Belgium

    Rudi Penne, Bart Ribbens, Luc Mertens & Paul Levrie

  2. Department of Mathematics, University of Antwerp, Antwerp, Belgium

    Rudi Penne

Authors
  1. Rudi Penne
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  2. Bart Ribbens
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  3. Luc Mertens
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  4. Paul Levrie
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Corresponding author

Correspondence to Rudi Penne .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Catania, Catania, Catania, Italy

    Sebastiano Battiato

  2. Arcueil CX, France

    Jacques Blanc-Talon

  3. Catania, Italy

    Giovanni Gallo

  4. Gent, Belgium

    Wilfried Philips

  5. CSIRO, Sydney, New South Wales, Australia

    Dan Popescu

  6. Vision Lab., University of Antwerp, Antwerpen, Belgium

    Paul Scheunders

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© 2015 Springer International Publishing Switzerland

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Penne, R., Ribbens, B., Mertens, L., Levrie, P. (2015). What Does One Image of One Ball Tell Us About the Focal Length?. In: Battiato, S., Blanc-Talon, J., Gallo, G., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2015. Lecture Notes in Computer Science(), vol 9386. Springer, Cham. https://doi.org/10.1007/978-3-319-25903-1_43

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  • DOI: https://doi.org/10.1007/978-3-319-25903-1_43

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25902-4

  • Online ISBN: 978-3-319-25903-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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