%0 Generic
%9 ['eprint_fieldopt_thesis_type_Master' not defined]
%A Scherr, Tim
%D 2017
%F heidok:23979
%K surface normal integration, gradient-based surface reconstruction, surface reconstruction from a gradient field, imaging slope gauge
%R 10.11588/heidok.00023979
%T Gradient-Based Surface Reconstruction and the Application to Wind Waves
%U https://archiv.ub.uni-heidelberg.de/volltextserver/23979/
%X New gradient-based surface reconstruction techniques are presented: regularized least absolute deviations based methods using common discrete differential operators, and spline based methods. All new methods are formulated in the same mathematical framework as convex optimization problems and can handle non-rectangular domains. For the spline based methods, either common P-splines or P1-splines can be used. Extensive reconstruction error analysis shows that the new P1-spline based method is superior to conventional methods in the case of gradient fields corrupted with outliers. In the analysis, both spline based methods provide the lowest reconstruction errors for reconstructions from incomplete gradient fields. Furthermore, the pre-processing of gradient fields is investigated. Median filter pre-processing offers a computationally efficient method that is robust  to outliers. After the reconstruction error analysis, selected reconstruction methods are applied to imaging slope gauge data measured in the wind-wave facility  Aeolotron in Heidelberg. Using newly developed segmentation methods, it is possible to detect different coordinate system orientations of gradient field data  and reconstruction algorithms. In addition, the use of a zero slope correction for reconstructions from the provided imaging slope gauge data is justified. The impact of light refracting bubbles on reconstructions from this data is part of this thesis as well. Finally, some water surface reconstructions for measurement conditions with different fetch lengths at the same wind speed in the Aeolotron are shown.