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

Ahmad, A; Xavier, J; Santos-Victor, J; Lima, P

doi:10.1016/j.cviu.2014.04.004

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

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https://www.sciencedirect.com/science/article/pii/S1077314214000824
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Ahmad, A., Xavier, J., Santos-Victor, J., & Lima, P. (2014). 3D to 2D bijection for spherical objects under equidistant fisheye projection. Computer Vision and Image Understanding, 124, 172-183. doi:10.1016/j.cviu.2014.04.004.

Cite as: https://hdl.handle.net/21.11116/0000-0001-2970-3

Abstract

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.