Study on Effect of Refraction of Light at Water Surface on SfM using Aerial Images

Abstract

With the widespread use of SfM (Structure from Motion) in aerial surveys, it is often applied to images covering shallow water (e.g., rivers, coral reefs). The commonly used SfM softwares ignore the light refraction at the water surface (i.e., enforce one-media collinearity condition). The simplification affects not only the triangulation of submerged points but the estimation of camera parameters by using them. This study examined the latter effect through numerical experiments under simple conditions. As a result, both the intrinsic and extrinsic parameters were found to be affected, depending on water depth and its heterogeneity. The intrinsic parameters did not simply reflect the apparent “magnification” and “pin-cushion distortion” of the bottom image observed from the air. The errors generated in the extrinsic parameters were sometimes large enough to cause a systematic overestimation of water depth by more than 40%. Furthermore, the errors did not diminish even when the intrinsic parameters were fixed to true values. These results show the need for more attention to the effect.