Rendering using the Fourier Projection - Slice Theorem

The Fourier projection-slice theorem states that the inverse transform of a slice extracted from the frequency domain representation of a volume yields a projection of the volume in a direction perpendicular to the slice. This theorem allows the generation of attenuation-only renderings of volume data in 0 (N2 log N) time for a volume of size N 3 • In this paper, we show how more realistic renderings can be generated using a class of shading models whose terms are Fourier projections. Models are derived for rendering depth cueing by linear attenuation of variable energy emitters and for rendering directional shading by Lambertian reflection with hemispherical illumination. While the resulting images do not exhibit the occlusion that is characteristic of conventional volume rendering, they provide sufficient depth and shape cues to give a strong illusion that occlusion exists.