In underwater environments, cameras need to be confined in an underwater housing, viewing the scene through a piece of glass. In case of flat port underwater housings, light rays entering the camera housing are refracted twice, due to different medium densities of water, glass, and air. This causes the usually linear rays of light to bend and the commonly used pinhole camera model to be invalid. When using the pinhole camera model without explicitly modeling refraction in Structure-from-Motion (SfM) methods, a systematic model error occurs. Therefore, in this paper, we propose a system for computing camera path and 3D points with explicit incorporation of refraction using new methods for pose estimation. Additionally, a new error function is introduced for non-linear optimization, especially bundle adjustment. The proposed method allows to increase reconstruction accuracy and is evaluated in a set of experiments, where the proposed method's performance is compared to SfM with the perspective camera model.

When using perspective cameras underwater, the underwater housing with its glass interface between water and air causes the light rays to change their direction due to refraction. In applications where geometrical properties of images are exploited without explicitly modeling refraction, i.e. when using the perspective pinhole camera model, this leads to a systematical error. This error is depending on the housing configuration like distance between camera and glass interface and angle between glass interface normal and optical axis. In this paper, we analyze the calibration of those parameters using a camera model explicitly considering refraction. The goal is to determine those parameters without the need of handling a calibration target underwater, which is cumbersome, if not impossible.