A Closed-Form Solution to Single Underwater Camera Calibration Using Triple Wavelength Dispersion and Its Application to Single Camera 3D Reconstruction

In this paper, we present a new method to estimate the housing parameters of an underwater camera by making full use of triple wavelength dispersion. Our method is based on an important finding that there is a closed-form solution to the distance from the camera center to the refractive interface once the refractive normal is known. The correctness of this finding is mathematically proved in this paper. To the best of our knowledge, such a finding has not been studied or reported, and hence is never proved theoretically. As well, the refractive normal can be estimated by solving a set of linear equations using wavelength dispersion. Our method does not require any calibration target, such as a checkerboard pattern, which may be difficult to manipulate when the camera is deployed deep undersea. Extensive experiments have been carried out which include simulations to verify the correctness and robustness to noise of our method and real experiments. The results of real experiments show that our method works as expected. The accuracy of our results is evaluated against the ground truth in both simulated and real experiments. Finally, we also show how we can apply dispersion to compute the 3D shape of an object using one single camera.