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

•Detecting the 3D position of a known-radius spherical object with a single camera.•A bijection principle between the spherical object in 3D and its image in 2D.•The core contribution is the formal proof of the bijection principle.•A fish-eye lens-based camera with equidistant projection model is used.•Experimental verification of the bijection principle is provided.