The development of a robust 3D imaging system for underwater applications is a crucial process in underwater imaging where the physical properties of the underwater environment make the implementation of such systems challenging. Calibration is an essential step in the application of such imaging systems and is performed to acquire the parameters of the image formation model and to enable 3D reconstruction. We present a novel calibration method for an underwater 3D imaging system comprising a pair of cameras, of a projector, and of a single glass interface that is shared between cameras and projector(s). The image formation model is based on the axial camera model. The proposed calibration uses a numerical optimization of a 3D cost function to determine all system parameters, thus avoiding the minimization of re-projection errors which require numerically solving a 12th order polynomial equation multiple times for each observed point. We also propose a novel stable approach to estimate the axis of the axial camera model. The proposed calibration was experimentally evaluated on four different glass interfaces, wherein several quantitative results were reported, including the re-projection error. The achieved mean angular error of the system's axis was under 6∘, and the mean absolute errors for the reconstruction of a flat surface were 1.38 mm for normal glass interfaces and 2.82 mm for the laminated glass interface, which is more than sufficient for application.
Keywords: calibration; flat refractive geometry; structured light; underwater imaging.