Effective Backscatter Approximation for Photometry in Murky Water

Shading-based approaches like Photometric Stereo assume that the image formation model can be effectively optimized for the scene normals. However, in murky water this is a very challenging problem. The light from artificial sources is not only reflected by the scene but it is also scattered by the medium particles, yielding the backscatter component. Backscatter corresponds to a complex term with several unknown variables, and makes the problem of normal estimation hard. In this work, we show that instead of trying to optimize the complex backscatter model or use previous unrealistic simplifications, we can approximate the per-pixel backscatter signal directly from the captured images. Our method is based on the observation that backscatter is saturated beyond a certain distance, i.e. it becomes scene-depth independent, and finally corresponds to a smoothly varying signal which depends strongly on the light position with respect to each pixel. Our backscatter approximation method facilitates imaging and scene reconstruction in murky water when the illumination is artificial as in Photometric Stereo. Specifically, we show that it allows accurate scene normal estimation and offers potentials like single image restoration. We evaluate our approach using numerical simulations and real experiments within both the controlled environment of a big water-tank and real murky port-waters.