Bathymetric Structure-from-Motion: extracting shallow stream bathymetry from multi-view stereo photogrammetry

Stream bathymetry is a critical variable in a number of river science applications. In larger rivers, bathymetry can be measured with instruments such as sonar (single or multi-beam), bathymetric airborne LiDAR (light detection and ranging), or acoustic Doppler current profilers. However, in smaller streams with depths less than 2m, bathymetry is one of the more difficult variables to map at high-resolution. Optical remote sensing techniques offer several potential solutions for collecting high-resolution bathymetry. In this research, I focus on direct photogrammetric measurements of bathymetry using multi-view stereo photogrammetry, specifically Structure-from-Motion (SfM). The main barrier to accurate bathymetric mapping with any photogrammetric technique is correcting for the refraction of light as it passes between the two different media (air and water), which causes water depths to appear shallower than they are. I propose and test an iterative approach that calculates a series of refraction correction equations for every point/camera combination in a SfM point cloud. This new method is meant to address shortcomings of other correction techniques and works within the current preferred method for SfM data collection, oblique and highly convergent photographs. The multi-camera refraction correction presented here produces bathymetric datasets with accuracies of similar to 0.02% of the flying height and precisions of similar to 0.1% of the flying height. This methodology, like many fluvial remote sensing methods, will only work under ideal conditions (e.g. clear water), but it provides an additional tool for collecting high-resolution bathymetric datasets for a variety of river, coastal, and estuary systems. Copyright (c) 2016 John Wiley & Sons, Ltd.