Toward real-time optical estimation of ocean waves’ space-time fields

Stereo 3D reconstruction is continuously increasing its popularity in the study of mid-to small-scale sea waves. In the recent past, different approaches have been proposed to reconstruct the space-time sea surface elevation field from synchronized stereo frames. Usually, the reconstruction is performed by first recovering a dense and sparse 3D point cloud from stereo pairs and then by interpolating it into a regular grid. Even considering state-of-the-art methods, with typical image resolutions, it's unlikely to perform the first step in less than dozens of seconds (without paralellization), that can easily doubled if we include the subsequent interpolation step. This will limit the applicability of stereo based wave analysis for all the approaches (like monitoring or data assimilation) in which the time between the raw acquisition and the output of processed data is critical. In this paper, we propose a new method to directly estimate the sea surface spectrum over time from a sequence of stereo frames. We exploit the frequency dispersion relation of gravity waves and the (Non-uniform) Fast Fourier Transform to continuously update the 3D surface and 2D wavenumber spectrum estimations given a sparse set of matching features between the two frames. This effectively combines the two aforementioned steps with a performance gain of more than an order of magnitude while keeping a reconstruction accuracy that is extremely close to the current state-of-the-art approaches. Code is available at https://gitlab.com/fibe/wassfast.