Bispectral analysis and recovery of images distorted by a moving water surface

Abstract

We propose a new algorithm to recover a geometrically correct image of an object or scene from a set of images distorted by the wave motion of a water surface. Under mild conditions where the wavy surface normals weakly satisfy a Gaussian distribution, we demonstrate that the geometric distortion can be removed and a corrected image can be recovered. Our method is based on higher-order spectra analysis-in particular, the bispectrum, similar to its use in astronomical speckle imaging. In adapting this technique to imaging through or over a moving water surface, special care must be taken, and specifically tailored techniques are discussed in this paper. Our algorithm has been tested under two different scenarios: the refraction of light through a water surface (the underwater case) and the reflection of light from a water surface (the reflection case). Results in both cases have been encouraging.