The Misty Three Point Algorithm for Relative Pose

There is a significant interest in scene reconstruction from underwater images given its utility for oceanic research and for recreational image manipulation. In this paper we propose a novel algorithm for two view camera motion estimation for underwater imagery. Our method leverages the constraints provided by the attenuation properties of water and its effects on the appearance of the color to determine the depth difference of a point with respect to the two observing views of the underwater cameras. Additionally, we propose an algorithm, leveraging the depth differences of three such observed points, to estimate the relative pose of the cameras. Given the unknown underwater attenuation coefficients, our method estimates the relative motion up to scale. The results are represented as a generalized camera. We evaluate our method on both real data and simulated data.