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This work presents a system for 3D reconstruction from underwater images or video. Aside from a camera in an underwater housing, no special equipment is required. However, if navigational data is available, it is utilized in the algorithm. The algorithm is in essence a classical structure from motion approach, which is adapted to account for the special imaging conditions. Hence, there is no need for the camera to follow a specialized trajectory. Adaptions to the underwater imaging environment include a special filtering of background and floating particles, which allows a robust estimation of the camera poses and a sparse set of 3D points. Based on the estimated camera track, dense image correspondence computation enables building a detailed 3D surface model. Once the 3D surface model is completed, the colors of the texture are corrected by a physical model for underwater light propagation, allowing to view the model without the effects of scattering and attenuation or to simulate the effects of water on light in a 3D viewer.