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.

重建淹没在水中的物体的能力在诸如研究上升的气泡轨迹及其随后的运动和力平衡之类的场景中起着重要作用。在本文中，我们提出了一种方法，该方法可以重构浸入水中的场景点的三维位置，同时考虑到该点与相机之间在空气-水界面处折射引起的畸变。场景点由两个正交放置的高速相机捕获，提供一对图像，通过这些图像可以获得该点的图像坐标。使用预先校准的相机矩阵，只要场景点在空中，就可以使用三角测量法正确计算该点位置的世界坐标。但是，由于折射，对淹没在水中的点的图像对进行三角剖分会导致错误的世界坐标。因此，我们提出了一种校正点的图像坐标的方法，以解决重建过程中折射引起的变形。该方法首先通过在棋盘上重建四角的坐标来进行验证，该结果产生的结果与实际值偏离0.18％，而校正前的错误放大为5.15％。然后，我们将该方法应用于单个上升球形气泡的三维轨迹的重建，其结果与以前的研究相吻合。该方法首先通过在棋盘上重建四角的坐标进行了验证，该结果产生的结果与实际值偏离0.18％，而校正前的错误放大为5.15％。然后，我们将该方法应用于单个上升球形气泡的三维轨迹的重建，其结果与以前的研究相吻合。该方法首先通过在棋盘上重建四角的坐标来进行验证，该结果产生的结果与实际值偏离0.18％，而校正前的错误放大为5.15％。然后，我们将该方法应用于单个上升球形气泡的三维轨迹的重建，其结果与以前的研究相吻合。