Laser triangulation and photometric stereo are popular optical 3D reconstruction methods but bear limitations in underwater environment because of the refraction phenomenon. Refraction bends the usually straight rays of light to another directions in the interface of a flat underwater housing. It causes the camera to capture the virtual object points instead of the real ones, so that the commonly used pinhole camera model is invalid. Therefore, in this paper, we introduce a flat refractive model for describing the geometric relation accurately between the virtual object points and the real ones, which can correct the distortions in underwater 3D reconstruction methods. The parameters of model can be estimated in a calibration step with a standard chessboard. Then the proposed geometric relation is used for rebuilding underwater three-dimensional relationship in laser triangulation and photometric stereo. The experimental results indicate the effectiveness of our methods in underwater 3D reconstruction.Index Terms-refractive model, laser triangulation, photometric stereo.

The authors thank Guanying Chen for help in code and Hiroaki Santo for help in providing comparison results. The authors' gratitude also goes to the anonymous reviewers for their careful suggestions and enlightenment that have helped us to improve this paper substantially.

We present an attention-weighted loss in a photometric stereo neural network to improve 3D surface recovery accuracy in complex-structured areas, such as edges and crinkles, where existing learning-based methods often failed. Instead of using a uniform penalty for all pixels, our method employs the attention-weighted loss learned in a self-supervise manner for each pixel, avoiding blurry reconstruction result in such difficult regions. The network first estimates a surface normal map and an adaptive attention map, and then the latter is used to calculate a pixel-wise attention-weighted loss that focuses on complex regions. In these regions, the attention-weighted loss applies higher weights of the detail-preserving gradient loss to produce clear surface reconstructions. Experiments on real datasets show that our approach significantly outperforms traditional photometric stereo algorithms and state-of-the-art learning-based methods.

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