Two-View Underwater Structure and Motion for Cameras under Flat Refractive Interfaces

Lai Kang, Lingda Wu, Yee-Hong Yang

Abstract: In an underwater imaging system, a refractive interface is introduced when a camera looks into the water-based environment, resulting in distorted images due to refraction. Simply ignoring the refraction effect or using the lens radial distortion model causes erroneous 3D reconstruction. This paper deals with a general underwater imaging setup using two cameras, of which each camera is placed in a separate waterproof housing with a flat window. The impact of refraction is explicitly modeled in the refractive camera model. Based on two new concepts, namely the Ellipse of Refrax (EoR) and Refractive Depth (RD) of a scene point, we show that provably optimal underwater structure and motion under L  ∞ -norm can be estimated given known rotation. The constraint of known rotation is further relaxed by incorporating two-view geometry estimation into a new hybrid optimization framework. The experimental results using both synthetic and real images demonstrate that the proposed method can significantly improve the accuracy of camera motion and 3D structure estimation for underwater applications.