“Frequency domain volume rendering” by Totsuka and Levoy

The Fourier projection-slice theorem allows projections of volume
data to be generated in O(n2 log n) time for a volume of size n3
.
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.

1. Bracewell, Ronald, The Fourier Transform and its Applications, revised second edition, McGraw-Hill, 1986.
2. Bracewell, Ronald, The Hartley Transform, Oxford University Press, 1986.
3. Cohen, Michael and Greenberg, Donald, “The Hemicube: A Radiosity Solution for Complex Environments”, Computer Graphics, Vol. 19, No.3, pp.31-40, 1985.
4. Drebin, Robert, Carpenter, Loren, and Hanrahan, Pat, “Volume Rendering”, Computer Graphics, Vol.22, No.4, pp.65- 74, 1988.
5. Dunne, Shane, Napel, Sandy, and Rutt, Brian, “Fast Reprojection of Volume Data”, Proceedings of the First Conference on Visualization in Biochemical Computing, IEEE Computer Society Press, pp. 11-18, 1990.
6. Hottel, Hoyt, and Sarofim, Adel, “Radiative Transfer”, McGraw-Hill, 1967.
7. Levoy, Marc, “Display of Surfaces from Volume Data”, IEEE Computer Graphics andApplications , Vol.8, No.3, pp.29-37, 1988.
8. Levoy, Marc, “Efficient Ray Tracing of Volume Data”, ACM Transactions on Graphics, Vol.9, No.3, pp.245-261, 1990.
9. Levoy, Marc, “Volume Rendering using the Fourier Projection-Slice Theorem”, Proceedings of Graphics Interface ’92, Canadian Information Processing Society, pp.61- 69, 1992.
10. Malzbender, Tom, “Fourier Volume Rendering”,ACM Transactions on Graphics, Vo1.12, No.3, July 1993.
11. Napel, Sandy, Dunne, Shane, and Rutt, Brian, “Fast Fourier Projection for MR Angiography”, Magnetic Resonance in Medicine, Vo1.19, pp.393-405, 1991.
12. Nishita, Tomoyuki and Nakamae, Eihachiro, “Continuous Tone Representation of Three-Dimensional Objects”, Computer Graphics, Vol.20, No.4, pp.125-132, 1986.
13. Pentland, Alex, “Linear Shape from Shading”, International Journal of Computer Vision, Vol.4, pp.153-162, 1990.
14. Subramanian, K.R. and Fussel, Donald, “Applying space subdivision techniques to volume rendering”, Proceedings of the First IEEE Conference on Visualization. (Visualization ‘ 90), IEEE Computer Society Press, pp. 150-159, 1990.
15. Westover, Lee, “Footprint Evaluation for Volume Rendering”, Computer Graphics, Vol.24, No.4, pp.367-376, 1990.
16. Zuiderveld, Karel, Koning, Anton, and Viergever, Max, “Acceleration of ray-casting using 3D distance transforms”, Proceedings of the SPIE- Visualization in Biomedical Computing 1992, Vo1.1808, pp.324-335, 1992.