In this paper, we propose a method for accurate 3D reconstruction based on Photometric Stereo. Instead of applying the global least square solution on the entire over-determined system, we randomly sample the images to form a set of overlapping groups and recover the surface normal for each group using the least square method. We then employ fourdimensional Tensor Robust Principal Component Analysis (TenRPCA) to obtain the accurate 3D reconstruction. Our method outperforms global least square in handling sparse noises such as shadows and specular highlights. Experiments demonstrate the reconstruction accuracy of our approach.
Laser triangulation and photometric stereo are commonly used three-dimensional (3-D) reconstruction methods, but they bear limitations in an underwater environment. One important reason is due to the refraction occurring at the interface (usually glass) of the underwater housing. The image formation process does not follow the commonly used pinhole camera model, and the image captured by the camera is a refracted projection of the object. We introduce a flat refraction model to describe the geometric relation between the refracted image and the real object. The model parameters were estimated in a calibration step with a standard chessboard. The proposed geometric relation is used for rebuilding underwater 3-D shapes in laser triangulation and photometric stereo. The experimental results indicate that our method can effectively correct the distortion in underwater 3-D reconstruction.