Three-dimensional reconstruction of a point immersed in water and application to a single rising bubble

The ability to reconstruct an object submerged in water is instrumental in scenarios such as the study of a rising bubble trajectory, and subsequently, its motion and force balance. In this paper, we propose a method that can reconstruct the three-dimensional position of a scene point immersed in water, while taking into account the refraction-induced distortion at the air-water interface between the point and camera. The scene point is captured by two orthogonally placed high-speed cameras, providing a pair of images through which the point's image coordinates are obtained. With pre-calibrated camera matrices, the world coordinates of the point's position can be correctly calculated using a triangulation method, provided the scene point is in air. However, because of refraction, triangulating the image pairs of the point submerged in water results in erroneous world coordinates. Thus, we propose a method to correct the point's image coordinates to account for refraction induced distortion during reconstruction. The method was first verified by reconstructing the coordinates of square corners on a checkerboard, which produced results that deviated from the real value by 0.18%, as opposed to the 5.15% false enlargement prior to correction. Then, we applied the method to the reconstruction of the three-dimensional trajectories of single rising spherical bubbles, whose results were in favorable agreement with previous studies. (C) 2019 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.