HP Labs Technical Reports

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Fourier Volume Rendering

Lichtenbelt, Barthold



Abstract: In this report a direct volume rendering technique called Fourier Volume Rendering (FVR) is explored in depth. FVR computes projection of a three dimensional dataset. Conventional volume rendering methods have a complexity of O(N to the 3rd power). FVR has a complexity of O(N to the 2nd power logN) and thus can be computed much faster. The mathematical theory behind FVR is explained first. Then FVR itself is discussed, and an example is given. The reason why the Hartley transform was chosen instead of the Fourier transform is explained. Finally a possible real time implementation in hardware is discussed. Images computed using FVR look like X-ray pictures. FVR is a fast method for computing projections. A hardware implementation mainly concerns a resampling chip that can resample a plane out a three dimensional dataset in 150 ns. This chip should use a resampling filter of size 5x5x5, which needs 64 voxels to compute one sample point.

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