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3D to 2D bijection for spherical objects under equidistant fisheye projection

2014

Article

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The core problem addressed in this article is the 3D position detection of a spherical object of known-radius in a single image frame, obtained by a dioptric vision system consisting of only one fisheye lens camera that follows equidistant projection model. The central contribution is a bijection principle between a known-radius spherical object’s 3D world position and its 2D projected image curve, that we prove, thus establishing that for every possible 3D world position of the spherical object, there exists a unique curve on the image plane if the object is projected through a fisheye lens that follows equidistant projection model. Additionally, we present a setup for the experimental verification of the principle’s correctness. In previously published works we have applied this principle to detect and subsequently track a known-radius spherical object.

Author(s): Ahmad, A and Xavier, J and Santos-Victor, J and Lima, P
Journal: Computer Vision and Image Understanding
Volume: 125
Pages: 172--183
Year: 2014
Month: August

Department(s): Perceiving Systems
Bibtex Type: Article (article)

DOI: 10.1016/j.cviu.2014.04.004

BibTex

@article{AhmadXSL2014,
  title = {3D to 2D bijection for spherical objects under equidistant fisheye projection},
  author = {Ahmad, A and Xavier, J and Santos-Victor, J and Lima, P},
  journal = {Computer Vision and Image Understanding},
  volume = {125},
  pages = {172--183},
  month = aug,
  year = {2014},
  month_numeric = {8}
}