Modeling Hyperhemispherical Points and Calibrating a Dual-Fish-Eye System for Close-Range Applications

Omnidirectional systems composed of two hyperhemispherical lenses (dual-fish-eye systems) are gaining popularity, but only a few works have studied suitable models for hyperhemispherical lenses and dual-fish-eye calibration. In addition, the effects of using points in the hyperhemispherical field of view in photogrammetric procedures have not been addressed. This article presents a comparative analysis of the fish-eye models (equidistant, equisolid-angle, stereographic, and orthogonal) for hyperhemispherical-lens and dual-fish-eye calibration techniques. The effects of adding points beyond 180° field of view in dual-fish-eye calibration using stability constraints of relative orientation parameters are also assessed. The experiments were performed with the Ricoh Theta dual-fish-eye system, which is composed of fish-eye lenses with a field of view of approximately 190° each. The equisolid-angle model presented the best results in the simultaneous calibration experiments. An accuracy of approximately one pixel in the object space units was achieved, showing the potential of the proposed approach for close-range applications.