GPUBased Frequency Domain Volume Rendering

1
GPU-Based Frequency Domain Volume Rendering

• Ivan Viola, Armin Kanitsar, and Meister Eduard
  Gröller
• Institute of Computer Graphics and Algorithms
• Vienna University of Technology

2
Motivation

• volume rendering is time consuming
• computational complexity is O(N3)
• our goal fastest volume rendering
• GPUs
• very fast fragment processor
• very fast memory access
• Fourier Volume Rendering (FVR)
• theoretically fastest volume rendering

3
Frequency Domain Volume Rendering
CPU
GPU
4
FVR Characteristics

• Pros
• computational complexity O(N2 log(N))
• renders the whole volume not iso-surfaces
• very fast rendering stage
• slicing in frequency domain
• inverse 2D Fourier transform
• Cons
• rendering results into X-ray images
• time-consuming preprocessing

5
Rendering Stage 1 Slicing

• stage with the highest speed-up
• nearest neighbor interpolation
• supported by GPU
• tri-linear interpolation
• tri-cubic interpolation
• windowed sinc of width four

6
Tri-Linear Interpolation

• not natively supported by graphics hardware
• can be computed using the LRP instruction

1,1
frac(8X)
X,Y
0,0
7
Cubic Interpolation Windowed sinc

• not natively supported by graphics hardware
• no equivalent to LRP instruction
• filter kernel stored in textures Hadwiger et al.
  VMV01
• separability of 3D kernel
• filters of width four ? stored in RGBA

1D texture
8
Rendering Stage 2 Inverse 2D FFT

• 1D FFT consists of two parts
• scrambling
• butterfly operation

9
Fast Fourier Transform in 1D
1 -1 1 -1 1 -1 1 -1
W08 W28 W48 W68 W08 W28 W48 W68
W08 W18 W28 W38 W48 W58 W68 W78

• a0
• a1
• a2
• a3
• a4
• a5
• a6
• a7

a0 a4 a2 a6 a1 a5 a3 a7
A0 A1 A2 A3 A4 A5 A6 A7
WkN
scramble
butterfly
10
Fast Fourier Transform on the GPU

• two buffers ping-pong rendering
• two channels rendering buffers required
• scramble pass
• 1D lookup
• butterfly passes
• log2(N) passes
• texture encodes
• WkN
• p and q coordinate
• butterfly sign

11
Hartley Transform - Alternative to FFT

• real input is transformed into real output
• ? ½ memory requirements
• scrambling the same as in FFT
• double-butterfly operation
• three source values, cos and sin
• HT not separable
• ? additional correction pass required
• ? GPU implementation not faster than FFT

12
Fast Hartley Transform on the GPU

• similar to FFT ping-pong rendering
• only one channel rendering buffers required
• scrambling the same
• double-butterfly
• two lookup textures
• addresses of source values (3 channels)
• cos and sin terms (2 channels)

13
Results

• Framerates for ATI Radeon 9800 XT

14
Demo
15
Conclusions

• rendering stage of FVR very fast on GPU
• slicing high performance gain
• wrap around is for free
• speed-up also for inverse FFT
• nearest neighbour very poor quality
• tri-linear interpolation high performace
• tri-cubic interpolation high quality

16
Thank You!

• viola_at_cg.tuwien.ac.at