A Variational Wave Acquisition Stereo System for the 3-D Reconstruction of Oceanic Sea States

Abstract

We propose a novel remote sensing technique that infers the three-dimensional wave form and radiance of oceanic sea states via a variational stereo imagery formulation. In this setting, the shape and radiance of the wave surface are minimizers of a composite cost functional which combines a data fidelity term and smoothness priors on the unknowns. The solution of a system of coupled partial differential equations derived from the cost functional yields the desired ocean surface shape and radiance. The proposed method is naturally extended to study the spatio-temporal dynamics of ocean waves, and applied to three sets of video data. Statistical and spectral analysis are carried out. The results shows evidence of the fact that the omni-directional wavenumber spectrum S(k) of the reconstructed waves decays as k^{-2.5} in agreement with Zakharov's theory (1999). Further, the three-dimensional spectrum of the reconstructed wave surface is exploited to estimate wave dispersion and currents.