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On the Camera Placement Problem

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Algorithms and Computation (ISAAC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5878))

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Abstract

We introduce a new probing problem: what is the minimum number of cameras at fixed positions necessary and sufficient to reconstruct any strictly convex polygon contained in a disk of radius 1 if cameras only see the silhouette of the polygon? The optimal number only depends on the largest angle α of the polygon. If no two camera tangents overlap, \(\lceil \frac{3\pi}{\pi-\alpha} \rceil\) cameras are necessary and sufficient. Otherwise, approximately \(\lceil \frac{4\pi}{\pi-\alpha} \rceil\) cameras are sufficient. Reconstruction only takes time linear in the number of cameras. We also give results for the 3D case.

This work was supported by a grant from the National High Technology Research and Development Program of China (863 Program) (No. 2007AA01Z176) and the Shanghai Leading Academic Discipline Project (project number B114). The authors are ordered alphabetically by family name; otherwise, Y. Wang would be first author.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, IIPL, Fudan University, Shanghai, China

    Rudolf Fleischer & Yihui Wang

Authors
  1. Rudolf Fleischer
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  2. Yihui Wang
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Editor information

Editors and Affiliations

  1. Dept. of Electrical and Computer Engineering, University of Hawaii, Holmes Hall 483, 2540 Dole Street, 96822, Honolulu, HI, USA

    Yingfei Dong

  2. Department of Computer Science, University of Texas at Dallas, 75083, Dallas, TX, USA

    Ding-Zhu Du

  3. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar Ibarra

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© 2009 Springer-Verlag Berlin Heidelberg

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Fleischer, R., Wang, Y. (2009). On the Camera Placement Problem. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_27

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  • DOI: https://doi.org/10.1007/978-3-642-10631-6_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10630-9

  • Online ISBN: 978-3-642-10631-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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