In murky water, the light interaction with the medium particles results in a complex image formation model that is hard to use effectively with a shape estimation framework like Photometric Stereo. All previous approaches have resorted to necessary model simplifications that were though used arbitrarily, without describing how their validity can be estimated in an unknown underwater situation. In this work, we evaluate the effectiveness of such simplified models and we show that this varies strongly with the imaging conditions. For this reason, we propose a novel framework that can predict the effectiveness of a photometric model when the scene is unknown. To achieve this we use a dynamic lighting framework where a robotic platform is able to probe the scene with varying light positions, and the respective change in estimated surface normals serves as a faithful proxy of the true reconstruction error. This creates important benefits over traditional Photometric Stereo frameworks, as our system can adapt some critical factors to an underwater scenario, such as the camera-scene distance and the light position or the photometric model, in order to minimize the reconstruction error. Our work is evaluated through both numerical simulations and real experiments for different distances, underwater visibilities and light source baselines. 
Model effectiveness prediction and system adaptation for photometric stereo in murky water