Near-lighting Photometric Stereo for unknown scene distance and medium attenuation*

- Shape reconstruction in murky water
- Near-lighting Photometric Stereo optimization
- Murky water attenuation coefficient calibration
- Normals estimation for unknown scene distance and medium attenuation

Photometric Stereo in murky water is subject to light attenuation and near-field illumination, and the resulting image formation model is complex. Apart from the scene normals and albedo, the incident illumination varies per-pixel and it depends on the scene depth and the attenuation coefficient of the medium. When these are unknown, e.g. in a realistic scenario where a robotic platform explores an underwater scene (unknown shape and distance) within the dynamic subsea environment (unknown scattering level), Photometric Stereo becomes ambiguous. Previous approaches have tackled the problem by assuming distant-lighting and resorting to external hardware for estimating the unknown model variables. In our work, we show that the Photometric Stereo problem can be determined as soon as some additional constraints regarding the scene albedo and the presence of pixels with local intensity maxima within the image are incorporated into the optimization framework. Our proposed solution leads to effective Photometric Stereo and yields detailed 3D reconstruction of objects in murky water when the scene distance and the medium attenuation are unknown. We evaluate our work using both numerical simulations and real experiments in the controlled environment of a water tank and real port water using a remotely operated vehicle.