Scale-reconstructable Structure from Motion using refraction with a single camera

Three-dimensional (3D) measurement is an important means for robots to acquire information about their environment. Structure from Motion is one of these 3D measurement methods. The 3D reconstruction of objects in the environment can be obtained from pictures captured with single camera in Structure from Motion. Furthermore, the camera motion can be obtained simultaneously. Because of its simplicity, Structure from Motion has been implemented in various ways. However there is an essential problem in that the scale of the measured objects cannot be computed by Structure from Motion. In order to compute the absolute scale, other information is required. However this is difficult for robots in an unknown situation. In this paper, we propose a method that can reconstruct the absolute scale of objects using refraction. Refraction changes the light ray path between the objects and the camera. This method is implemented using only a refractive plate and single camera. The results of simulations show the effectiveness of the proposed method in both air and other media (e.g., water).