GPUBased Frequency Domain Volume Rendering Ivan Viola Armin

GPU-Based Frequency Domain Volume Rendering Ivan Viola, Armin Kanitsar, and Meister Eduard Gröller Institute of Computer Graphics and Algorithms Vienna University of Technology

Motivation nvolume rendering is time consuming ncomputational complexity is O(N 3) nour goal: fastest volume rendering n. GPUs u very fast fragment processor u very fast memory access n. Fourier Volume Rendering (FVR) u theoretically fastest volume rendering Ivan Viola 2 Vienna University of Technology

Frequency Domain Volume Rendering CPU GPU Ivan Viola 3 Vienna University of Technology

FVR Characteristics Pros n computational complexity O(N 2 log(N)) n renders the whole volume not iso-surfaces n very fast rendering stage: u slicing in frequency domain u inverse 2 D Fourier transform Cons n rendering results into X-ray images n time-consuming preprocessing Ivan Viola 4 Vienna University of Technology

Rendering Stage 1: Slicing n stage with the highest speed-up n nearest neighbor interpolation u supported by GPU n tri-linear interpolation n tri-cubic interpolation n windowed sinc of width four Ivan Viola 5 Vienna University of Technology

Tri-Linear Interpolation nnot natively supported by graphics hardware ncan be computed using the LRP instruction [1, 1] frac(8 X) [X, Y] [0, 0] Ivan Viola 6 Vienna University of Technology

Cubic Interpolation & Windowed sinc nnot natively supported by graphics hardware nno equivalent to LRP instruction nfilter kernel stored in textures [Hadwiger et al. VMV’ 01] u separability of 3 D kernel u filters of width four stored in RGBA 1 D texture Ivan Viola 7 Vienna University of Technology

Rendering Stage 2: Inverse 2 D FFT n 1 D FFT consists of two parts u scrambling u butterfly operation Ivan Viola 8 Vienna University of Technology

Fast Fourier Transform in 1 D a 0 a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 0 a 4 a 2 a 6 a 1 a 5 a 3 a 7 1 -1 W 08 W 28 W 48 W 68 W 08 W 18 W 28 W 38 W 48 W 58 W 68 W 78 A 0 A 1 A 2 A 3 A 4 A 5 A 6 A 7 scramble butterfly Ivan Viola 9 Vienna University of Technology Wk. N

Fast Fourier Transform on the GPU n two buffers – ping-pong rendering n two channels rendering buffers required n scramble pass u 1 D lookup n butterfly passes u log 2(N) passes u texture encodes n n n Ivan Viola Wk. N p and q coordinate butterfly sign 10 Vienna University of Technology

Hartley Transform - Alternative to FFT nreal input is transformed into real output ½ memory requirements nscrambling the same as in FFT ndouble-butterfly operation u three source values, cos and sin n. HT not separable additional correction pass required GPU implementation not faster than FFT Ivan Viola 11 Vienna University of Technology

Fast Hartley Transform on the GPU n n similar to FFT – ping-pong rendering only one channel rendering buffers required scrambling the same double-butterfly u two lookup textures n n Ivan Viola addresses of source values (3 channels) cos and sin terms (2 channels) 12 Vienna University of Technology

Results Framerates for ATI Radeon 9800 XT Resolution NN TL TC IFFT 2 D 256 x 256 1450 1050 180 153 512 x 512 500 350 45 35 Ivan Viola 13 Vienna University of Technology

Demo Ivan Viola 14 Vienna University of Technology

Conclusions n rendering stage of FVR very fast on GPU u slicing – high performance gain u wrap around is “for free” u speed-up also for inverse FFT n nearest neighbour – very poor quality n tri-linear interpolation – high performace n tri-cubic interpolation – high quality Ivan Viola 15 Vienna University of Technology

Thank You! viola@cg. tuwien. ac. at Ivan Viola 16 Vienna University of Technology