Fourier Based Pre-Processing for Seeing Through Water

Abstract

Consider a scene submerged underneath a fluctuating water surface. Images of such a scene, when acquired from a camera in the air, exhibit significant spatial distortions. In this paper, we present a novel, computationally efficient pre-processing algorithm to correct a significant amount (~ 50%) of apparent distortion present in video sequences of such a scene. We demonstrate that when the partially restored video output from this stage is given as input to other methods, it significantly improves their performance. This algorithm involves (i) tracking a small number N of salient feature points across the T frames to yield point-trajectories \ \boldsymbol q_i \triangleq \ (x_ it ,y_ it )\ _ t=1 ^T\ _ i=1 ^N, and (ii) using the point-trajectories to infer the deformations at other non-tracked points in every frame. A Fourier decomposition of the N trajectories, followed by a novel Fourier phase-interpolation step, is used to infer deformations at all other points. Our method exploits the inherent spatio-temporal characteristics of the fluctuating water surface to correct non-rigid deformations to a very large extent. The source code, datasets and supplemental material can be accessed at [1], [2].