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 spatiotemporal 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.