A novel video observational method for thespace-time stereoscopic reconstruction ofdynamic surfaces representable as graphs, suchas ocean waves, is developed. Variationaloptimization algorithms combining imageprocessing, computer vision and partialdifferential equations are designed to addressthe problem of the recovery of the shape of anobject's surface from sequences of synchronizedmulti-view images. Several theoretical and numerical paths are discussed to solve theproblem. The variational stereo methoddeveloped in this thesis has several advantagesover existing 3-D reconstruction algorithms.Our method follows a top-down approach orobject-centered philosophy in which an explicitmodel of the target object in the scene isdevised and then related to imagemeasurements. The key advantages of ourmethod are the coherence (smoothness) of thereconstructed surface caused by a coherentobject-centered design, the robustness to noisedue to a generative model of the observedimages, the ability to handle surfaces withsmooth textures where other methods typicallyfail to provide a solution, and the higherresolution achieved due to a suitable graphrepresentation of the object's surface. Themethod provides competitive results withrespect to existing variational reconstructionalgorithms. However, our method is based upona simplified but complete physical model of thescene that allows the reconstruction process toinclude physical properties of the object'ssurface that are otherwise difficult to take intoaccount with existing reconstructionalgorithms. Some initial steps are taken towardincorporating the physics of ocean waves in thestereo reconstruction process. The developedmethod is applied to empirical data of oceanwaves collected at an off-shore oceanographicplatform located off the coast of Crimea,Ukraine. An empirically-based physical modelfounded upon current ocean engineeringstandards is used to validate the results. Ourfindings suggest that this remote sensingobservational method has a broad impact onoff-shore engineering to enrich theunderstanding of sea states, enabling improveddesign of off-shore structures. The explorationof ways to incorporate dynamical properties,such as the wave equation, in thereconstruction process is discussed for futureresearch.
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Variational image processing algorithms for the stereoscopic space-time reconstruction of water waves