This paper introduces single-image 3D scene reconstruction from water reflection photography, i.e., images capturing direct and water-reflected real-world scenes. Water reflection offers an additional viewpoint to the direct sight, collectively forming a stereo pair. The water-reflected scene, however, includes internally scattered and reflected environmental illumination in addition to the scene radiance, which precludes direct stereo matching. We derive a principled iterative method that disentangles this scene radiometry and geometry for reconstructing 3D scene structure as well as its high-dynamic range appearance. In the presence of waves, we simultaneously recover the wave geometry as surface normal perturbations of the water surface. Most important, we show that the water reflection enables calibration of the camera. In other words, we show that capturing a direct and water-reflected scene in a single exposure forms a self-calibrating catadioptric stereo camera. We demonstrate our method on a number of images taken in the wild. The results demonstrate a new means for leveraging this accidental catadioptric camera.
Conventional video cameras have limited fields of view which make them restrictive for certain applications in computational vision. A catadioptric sensor uses a combination of lenses and mirrors placed in a carefully arranged configuration to capture a much wider field of view. One important design goal for catadioptric sensors is choosing the shapes of the mirrors in a way that ensures that the complete catadioptric system has a single effective viewpoint. The reason a single viewpoint is so desirable is that it is a requirement for the generation of pure perspective images from the sensed images. In this paper, we derive the complete class of single-lens single-mirror catadioptric sensors that have a single viewpoint. We describe all of the solutions in detail, including the degenerate ones, with reference to many of the catadioptric systems that have been proposed in the literature. In addition, we derive a simple expression for the spatial resolution of a catadioptric sensor in terms of the resolution of the cameras used to construct it. Moreover, we include detailed analysis of the defocus blur caused by the use of a curved mirror in a catadioptric sensor.