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M. Artner:
"High-Quality Volume Rendering with Resampling in the Frequency Domain";
Supervisor: T. Möller, I. Viola; Institut für Computergraphik und Algorithmen, 2005.

This thesis introduces a volume rendering technique that is conceptually based on the shearwarp factorization. The novelty in our approach is that we perform the shear transformation entirely in the frequency domain. A compensation for the direction dependent sampling distance along the viewing rays, which is present in the standard shear-warp approach, is developed. This compensation is also carried out in the frequency domain and is capable of producing freely selectable sampling distances. The accurate scaling of the volume slices is achieved by using the zero padding interpolation property. Finally, a high quality gradient estimation scheme is presented which uses the derivative theorem of the Fourier transform. Experimental trials have shown that the presented method can outperform established algorithms in the quality of the resulting images. Especially in the case when the dataset was acquired according to the sampling theorem, the presented method is capable of a perfect reconstruction of the original function.