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

NTNU: Norges Teknisk-Naturvitenskapelige Universitet


This work presents a camera model for refractive media such as water and its application in underwater visual-inertial odometry. The model is self-calibrating in real-time and is free of known correspondences or calibration targets. It is separable as a distortion model (dependent on refractive index and radial pixel coordinate) and a virtual pinhole model (as a function of refractive index). We derive the self-calibration formulation leveraging epipolar constraints to estimate the refractive index and subsequently correct for distortion. Through experimental studies using an underwater robot integrating cameras and inertial sensing, the model is validated regarding the accurate estimation of the refractive index and its benefits for robust odometry estimation in an extended envelope of conditions. Lastly, we show the transition between media and the estimation of the varying refractive index online, thus allowing computer vision tasks across refractive media.



Figure Detailed results of one of the trajectories in from the Trajectory Group 1 of the dataset. The ambient lighting was set to the lowest level whereas the onboard lighting was at the highest level. Sub-figure (a) shows a qualitative comparison between the odometry solution estimated using the proposed \ac{rcm} and the baseline ROVIO solution. The locations of the tag-sets are shown each time that set is detected and the error in these locations is used to measure the quality of the odometry. This and the visible skewing of the path clearly show that odometry estimated using the proposed model is more accurate than the common approach of calibrating an otherwise conventional camera model directly underwater (which is also more laborious). Sub-figure (b) shows pixels in the input image the features from which were used to calculate the refractive index n colorized based on the error in the calculated n versus the true value for water (1.33). Finally, sub-figure (c) shows the estimated n over the duration of the mission.


      title={An Online Self-calibrating Refractive Camera Model with Application to Underwater Odometry}, 
      author={Mohit Singh and Mihir Dharmadhikari and Kostas Alexis},