Frequency Domain Volume Rendering

Takashi Totsuka and Marc Levoy, Proc. SIGGRAPH '93, Anaheim, California, August, 1993, pp. 271-278.

Abstract:

The Fourier projection-slice theorem allows projections of volume data to be generated in O(n^2 log n) time for a volume of size n^3. The method operates by extracting and inverse Fourier transforming 2D slices from a 3D frequency domain representation of the volume. Unfortunately, these projections do not exhibit the occlusion that is characteristic of conventional volume renderings. We present a new frequency domain volume rendering algorithm that replaces much of the missing depth and shape cues by performing shading calculations in the frequency domain during slice extraction. In particular, we demonstrate frequency domain methods for computing linear or nonlinear depth cueing and directional diffuse reflection. The resulting images can be generated an order of magnitude faster than volume renderings and may be more useful for many applications.

Additional information available:

Optical scan of paper (from ACM digital library): PDF file
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MPEG movie (99K bytes) of an occluding conventional volume rendering (left) and a non-occluding frequency domain volume rendering (right). The frequency domain rendering includes linear depth cueing and directional diffuse reflection. The dataset is a 96^3 voxel CT scan of a portion of a human skull mounted in a lucite head cast. This movie was generated using the algorithm described in an earlier paper, but would not visibly differ if computed using the algorithm described in the present paper. The present algorithm is simply faster.