Refractive two-view reconstruction for underwater 3D vision

Recovering 3D geometry from cameras in underwater applications involves the Refractive Structure-from-Motion problem where the non-linear distortion of light induced by a change of medium density invalidates the single viewpoint assumption. The pinhole-plus-distortion camera projection model suffers from a systematic geometric bias since refractive distortion depends on object distance. This leads to inaccurate camera pose and 3D shape estimation. To account for refraction, it is possible to use the axial camera model or to explicitly consider one or multiple parallel refractive interfaces whose orientations and positions with respect to the camera can be calibrated. Although it has been demonstrated that the refractive camera model is well-suited for underwater imaging, Refractive Structure-from-Motion remains particularly difficult to use in practice when considering the seldom studied case of a camera with a flat refractive interface. Our method applies to the case of underwater imaging systems whose entrance lens is in direct contact with the external medium. By adopting the refractive camera model, we provide a succinct derivation and expression for the refractive fundamental matrix and use this as the basis for a novel two-view reconstruction method for underwater imaging. For validation we use synthetic data to show the numerical properties of our method and we provide results on real data to demonstrate its practical application within laboratory settings and for medical applications in fluid-immersed endoscopy. We demonstrate our approach outperforms classic two-view Structure-from-Motion method relying on the pinhole-plus-distortion camera model.

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.