Variational image processing algorithms for the stereoscopic space-time reconstruction of water waves

A novel video observational method for the space-time stereoscopic reconstruction of dynamic surfaces representable as graphs, such as ocean waves, is developed. Variational optimization algorithms combining image processing, computer vision and partial differential equations are designed to address the problem of the recovery of the shape of an object's surface from sequences of synchronized multi-view images. Several theoretical and numerical paths are discussed to solve the problem. The variational stereo method developed in this thesis has several advantages over existing 3-D reconstruction algorithms. Our method follows a top-down approach or object-centered philosophy in which an explicit model of the target object in the scene is devised and then related to image measurements. The key advantages of our method are the coherence (smoothness) of the reconstructed surface caused by a coherent object-centered design, the robustness to noise due to a generative model of the observed images, the ability to handle surfaces with smooth textures where other methods typically fail to provide a solution, and the higher resolution achieved due to a suitable graph representation of the object's surface. The method provides competitive results with respect to existing variational reconstruction algorithms. However, our method is based upon a simplified but complete physical model of the scene that allows the reconstruction process to include physical properties of the object's surface that are otherwise difficult to take into account with existing reconstruction algorithms. Some initial steps are taken toward incorporating the physics of ocean waves in the stereo reconstruction process. The developed method is applied to empirical data of ocean waves collected at an off-shore oceanographic platform located off the coast of Crimea, Ukraine. An empirically-based physical model founded upon current ocean engineering standards is used to validate the results. Our findings suggest that this remote sensing observational method has a broad impact on off-shore engineering to enrich the understanding of sea states, enabling improved design of off-shore structures. The exploration of ways to incorporate dynamical properties, such as the wave equation, in the reconstruction process is discussed for future research.
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