New approaches of handling waves in photo-bathymetry

Abstract

Stereo-photogrammetric measurements under water with a camera placed outside the water require modelling refraction. In the case of a wavy, non-stationary natural water surface, this requires spatio-temporal modelling, which may become rather complex. This paper gives an overview on novel methods for consideration of non-stationary water surfaces in photogrammetric approaches recently developed in a joint research project between TU Dresden and TU Wien. We first introduce a comprehensive and rigorous model, which reconstructs the water surface from multi-view imagery with cubic splines in a simultaneous bundle block adjustment, allowing us to introduce water bottom point coordinates together with camera orientation parameters and water surface model parameters as unknowns. The model is then extended to spatio-temporal water surface modelling based on short multi-view image sequences. As an alternative approach, we introduce pixel-wise median filtering of short image sequences on the time axis to handle dynamic, wavy water surfaces, which allows to largely mitigate the distortions of underwater objects caused by the wavy water surface. In the resulting image, the water surface appears smoothed, and the 3D reconstruction underwater can be performed as if the water surface was horizontal. Such a sequence-based approach can either be formulated in image space or in object space. Both approaches, the image sequence median filtering and the simultaneous bundle block adjustment, are then combined into a two-step procedure for water bottom point and water surface parameter determination, avoiding effects of over-parametrization in practical applications with a rather large number of unknowns. First results obtained in several practical tests of the developed approaches indicate a substantial accuracy increase in underwater 3D point coordinate determination by about one order of magnitude, compared to processing the data under the assumption of a flat horizontal water surface.