3D Trajectory Reconstruction Under Refraction at a Cylindrical Surface

Abstract

In conventional imaging, the geometry of image formation is described by the pinhole camera model, and it allows multiview reconstruction based on the perspective projection. If a light ray passes through different media, however, the pin-hole camera model becomes invalid due to refraction, causing changes in direction. In this paper, we present a method for 3D trajectory reconstruction under refraction at a cylindrical surface. In the proposed method, the refractive geometry is represented by a geometric mapping from image points to refracted rays, instead of physically modeling it. 3D points inside the cylindrical surface are estimated by computing intersection points between segments of corresponding refracted rays in multiview. In our experiments, we demonstrate that 3D trajectories of multiple moving objects inside a transparent cylinder, which is filled with water, are successfully recovered using multiple cameras.