Ein Skalenraumverfahren zur Orts/Wellenzahl-Raum-Analyse winderzeugter Wasserwellen

The following thesis describes a new technique for the calculation of local wave numbers and the creation of a combined space/wave number-representation of images. The design of a steerable and separable smoothing filter and a corresponding Hilbert filter makes it possible to create a logarithmic scale-space of the local amplitude. An oversampled multigrid structure (pyramid) is used for the Implementierung. An additional decomposition of the orientation is carried out. As the method's response to a wave with a delta-shaped spectra is known, a superposition of partial waves can be separated and their individual absolute values, orientations and amplitudes be calculated. A calibration using test images shows the accuracy of the described technique and its robustness to noise. The scale-space method is applied to wave slope images and the results on single images are visualised. Saturation spectra of image sequences are calculated and and shown to match those computed by a discrete Fourier transform. Further possibilities of the technique are demonstrated by calculating spectra showing the distribution of the amplitudes as a function of the wave number.