Low-Constraint Ray Optimization for Photogrammetric Shallow Water Bathymetry

Abstract. This paper presents a raytracing-based approach for estimating the depth of shallow water bodies. Based on a calibrated, multi-view camera setup above the water surface, we find correspondences that lie below the surface in pairs of two views. We trace rays from each camera to each triangulated correspondence, as if no interface is present in the scene. Using snell’s law, we then compute refracted rays to optimize an objective function with a theoretical optimum as the Hesse normal form of the water surface. The challenge of our work is to keep the number of constraints in our mathematical model as low as possible. For a practical evaluation, we record images with two different setups: a laboratory setting with a box filled with water at a depth of 14.5 cm and a water roll-of container at 2.2 m, and use both fiducial markers as well as computed features as correspondences. Our results show that with a well-setup optimizer, our method converges towards the true water plane and is usable to estimate the depth of our setups.