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This work presents a camera model for refractive media such as water and itsapplication in underwater visual-inertial odometry. The model isself-calibrating in real-time and is free of known correspondences orcalibration targets. It is separable as a distortion model (dependent onrefractive index $n$ and radial pixel coordinate) and a virtual pinhole model(as a function of $n$). We derive the self-calibration formulation leveragingepipolar constraints to estimate the refractive index and subsequently correctfor distortion. Through experimental studies using an underwater robotintegrating cameras and inertial sensing, the model is validated regarding theaccurate estimation of the refractive index and its benefits for robustodometry estimation in an extended envelope of conditions. Lastly, we show thetransition between media and the estimation of the varying refractive indexonline, thus allowing computer vision tasks across refractive media.

An Online Self-calibrating Refractive Camera Model with Application to Underwater Odometry