Perceiving Systems, Computer Vision

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

2014

Article

ps


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},
  doi = {10.1016/j.cviu.2014.04.004},
  month_numeric = {8}
}