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**1 - 1**of**1**### Fourier Volume Rendering final version

, 1995

"... 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 3 �. FVR has a complexity of O�N 2 logN � and thus can be computed muc ..."

Abstract
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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 3 �. FVR has a complexity of O�N 2 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 implemention in hardware is discussed. The last chapter handles about a completely different subject. It is about coronary artery extraction out of a three dimensional dataset of the heart obtained by MRI. 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 of a three dimensional dataset in 150 ns. This chip should use a resampling filter of size 5 � 5 � 5, which needs 64 voxels to compute one sample point. i