Classification for Fourier volume rendering

In the last decade, Fourier volume rendering (FVR) has obtained considerable attention due to its O(N²logN) rendering complexity, where O(N³) is the volume size. Although ordinary volume rendering has O(N³) rendering complexity, it is still preferred over FVR for the main reason, that FVR offers bad localization of spatial structures. As a consequence, it was assumed, that it is hardly possible to apply ID transfer functions, which arbitrarily modify voxel values not only in dependence of the position, but also the voxel value. We show that this assumption is not true for threshold operators. Based on the theory of Fourier series, we derive a FVR method, which is capable of integrating all sample points greater (or alternatively, lower) than an iso-value T during rendering, where T can be modified interactively during the rendering session. We compare our method with other approaches and we show examples on well-known datasets to illustrate the quality of the renderings.