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Photometric stereo offers the possibility of object shape reconstruction via reasoning about the amount of light reflected from oriented surfaces. However, in murky media such as sea water, the illuminating light interacts with the medium and some of it is backscattered towards the camera. Due to this additive light component, the standard Photometric Stereo equations lead to poor quality shape estimation. Previous authors have attempted to reformulate the approach but have either neglected backscatter entirely or disregarded its non-uniformity on the sensor when camera and lights are close to each other. We show that by compensating effectively for the backscatter component, a linear formulation of Photometric Stereo is allowed which recovers an accurate normal map using only 3 lights. Our backscatter compensation method for point-sources can be used for estimating the uneven backscatter directly from single images without any prior knowledge about the characteristics of the medium or the scene. We compare our method with previous approaches through extensive experimental results, where a variety of objects are imaged in a big water tank whose turbidity is systematically increased, and show reconstruction quality which degrades little relative to clean water results even with a very significant scattering level.
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