Frequency domain volume rendering

The Fourier projection-slice theorem allos projections of volume data to be generated in O(nsquare log n) time for a volumbe of size ncube. 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]  Ronald N. Bracewell,et al.  The Fourier Transform and Its Applications , 1966 .

[2]  Donald P. Greenberg,et al.  The hemi-cube: a radiosity solution for complex environments , 1985, SIGGRAPH.

[3]  Tomoyuki Nishita,et al.  Continuous tone representation of three-dimensional objects illuminated by sky light , 1986, SIGGRAPH.

[4]  Ronald N. Bracewell.  The Hartley transform , 1986 .

[5]  Pat Hanrahan,et al.  Volume Rendering , 2020, Definitions.

[6]  Marc Levoy,et al.  Display of surfaces from volume data , 1988, IEEE Computer Graphics and Applications.

[7]  Marc Levoy,et al.  Efficient ray tracing of volume data , 1990, TOGS.

[8]  Kalpathi R. Subramanian,et al.  Applying space subdivision techniques to volume rendering , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.

[9]  Brian K. Rutt,et al.  Fast reprojection of volume data , 1990, [1990] Proceedings of the First Conference on Visualization in Biomedical Computing.

[10]  John E. Howland,et al.  Computer graphics , 1990, IEEE Potentials.

[11]  Lee Westover,et al.  Footprint evaluation for volume rendering , 1990, SIGGRAPH.

[12]  S Dunne,et al.  Fast Fourier projection for MR angiography , 1991, Magnetic resonance in medicine.

[13]  Max A. Viergever,et al.  Acceleration of ray-casting using 3-D distance transforms , 1992, Other Conferences.

[14]  Marc Levoy,et al.  Volume rendering using the Fourier projection-slice theorem , 1992 .

[15]  Thomas Malzbender,et al.  Fourier volume rendering , 1993, TOGS.