3-D shape recovery of planar and curved surfaces from shading cues in underwater images

Automatic construction of high-resolution topographical maps, or determining the shape of man-made objects, targets, and obstacles for localization, identification, and/or recognition is an important capability in the application of autonomous or intelligent underwater vehicles. In this paper, we investigate the application of underwater image models for the reconstruction of three-dimensional object shapes from the shading cues in two-dimensional optical images. We first present the results of a sensitivity analysis in support of a simplified model for a Lambertian surface illuminated by a point source in an attenuating medium, proposed in earlier work. We then generalize a closed-form solution for planar scenes, previously proposed for negligible source-camera baseline, to the case where the baseline may be increased to minimize backscatter effects. For curved surfaces, we propose two techniques based on different iterative updating strategies to recursively improve the recovered surface shape. We study the performance of various methods using synthetic data and real images required under different turbidity conditions.