A Likelihood-based Triangulation Method for Uncertainties in Through-Water Depth Mapping

Coastal environments, of major economic, social, and strategic importance, rely heavily on bathymetry for navigation safety, harbor development, and resource monitoring. Innovations in bathymetry include optical alternatives for shallower waters, as traditional acoustic solutions are less efficient. Recent studies demonstrated airborne imagery is an efficient option to frequently map shallow waters at synoptic scales and has the capacity to retrieve the Water Column Depth (WCD). Geometric approaches allow to obtain 3D reconstruction from images by triangulating a set of pixels that are located on more than one image (feature points). They demonstrate great potential for WCD assessment, achieving a penetration depth of over 5 meters with an accuracy in the decimeter range when creating high resolution maps of clear shallow water bodies as long as there is sufficient bottom texture with identifiable features. As the navigation safety of vessels relies on WCD accuracy, it is of utmost importance to quantify the uncertainty associated with the derived product. Studies on bathymetry estimation using geometric approaches tend to focus on the estimation accuracy, rather than the assessment of uncertainty, despite the fact that there are many sources of uncertainty. As a result, here is a lack of robust uncertainty modeling methods, crucial for assessing the quality of bathymetric charts, especially in shallow waters. In response, this research introduces a novel likelihood-based approach for through-water photogrammetry with a focus on the uncertainties associated with camera pose, a key factor affecting through-water depth mapping. Our methodology incorporates probabilistic modeling and stereo-photogrammetric triangulation. In addition to providing a realistic estimate of the uncertainty, this approach allows to handle complex cases involving noisy camera poses in addition to retrieving the water interface height. The results proposed in this paper reveal the significant influence of viewing geometry and camera pose quality on the resulting uncertainties, overshadowing the impact of depth. In addition, they demonstrate the superior performance of the likelihood ratio statistic in scenarios involving high attitude noise, high flight altitude, and complex viewing geometries. Also, we highlight the transformative potential of drone-based applications in underwater surveying, leveraging high-precision and efficient data collection to contribute to more accurate bathymetric charts.