Photometric Stereo is a popular method for 3D reconstruction from images due to its high level of details handling. However, when it is used in a scattering medium such as lakes and oceans, the recovery result will be negatively impacted by the light absorption, light scattering and the impurities in the water. In this paper, we present a new method to solve the problem of better 3D reconstruction via Low-Rank Matrix Completion and Recovery. First, we use the dark points, like shadows and darkness in the water to fit the scattering effect distribution and then remove the scattering from the image. Next, we use the Robust Principal Component Analysis method (RPCA) to recover the image by removing the sparse noise including shadows, impurities and some corrupted points caused by backscatter compensation. Finally, we combine the RPCA results and the least-squares (LS) results to get the surface normal and accomplish the 3D reconstruction. Extensive experimental results demonstrate that our method achieves more accurate estimates of surface normal and 3D reconstruction than previous techniques.
