Abstract
Estimating the shape of transparent and refractive objects is one of the few open problems in 3D reconstruction. Under the assumption that the rays refract only twice when traveling through the object, we present the first approach to simultaneously reconstructing the 3D positions and normals of the object's surface at both refraction locations. Our acquisition setup requires only two cameras and one monitor, which serves as the light source. After acquiring the ray-ray correspondences between each camera and the monitor, we solve an optimization function which enforces a new position-normal consistency constraint. That is, the 3D positions of surface points shall agree with the normals required to refract the rays under Snell's law. Experimental results using both synthetic and real data demonstrate the robustness and accuracy of the proposed approach.