GPU-Based Frequency GPU-Based Frequency Domain Volume RenderingDomain Volume Rendering

Ivan Viola, Armin Kanitsar, and Ivan Viola, Armin Kanitsar, and MeisterMeister Eduard Gr Eduard Grölleröller

Institute of Computer Graphics and AlgorithmsInstitute of Computer Graphics and Algorithms

Vienna University of TechnologyVienna University of Technology

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MotivationMotivationvolume rendering is time consumingvolume rendering is time consumingcomputational complexity is computational complexity is O(NO(N33))our our goalgoal: fastest volume rendering: fastest volume rendering

GPUsGPUs very fast fragment processorvery fast fragment processor very fast memory accessvery fast memory access

Fourier Volume Rendering (FVR)Fourier Volume Rendering (FVR) theoretically fastest volume renderingtheoretically fastest volume rendering

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GPUGPU

Frequency Domain Volume RenderingFrequency Domain Volume Rendering

CPUCPU

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FVR CharacteristicsFVR CharacteristicsProsPros computational complexity computational complexity O(NO(N2 2 log(N))log(N)) renders the whole volume not iso-surfacesrenders the whole volume not iso-surfaces very fast rendering stage:very fast rendering stage:

slicing in frequency domainslicing in frequency domain inverse 2D Fourier transforminverse 2D Fourier transform

ConsCons rendering results into rendering results into X-rayX-ray images images time-consuming preprocessingtime-consuming preprocessing

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Rendering Stage 1: SlicingRendering Stage 1: Slicing stage with the highest speed-upstage with the highest speed-up nearest neighbor interpolationnearest neighbor interpolation

supported by GPUsupported by GPU tri-linear interpolationtri-linear interpolation tri-cubic interpolationtri-cubic interpolation windowed windowed sinc sinc of width fourof width four

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Tri-Linear InterpolationTri-Linear Interpolationnot not nativelynatively supported by graphics hardware supported by graphics hardwarecan be computed using the can be computed using the LRPLRP instruction instruction

[1,1][1,1]

[0,0][0,0]

[X,Y][X,Y]

frac(8X)frac(8X)

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Cubic Interpolation & Windowed Cubic Interpolation & Windowed sincsincnot natively supported by graphics hardwarenot natively supported by graphics hardwareno equivalent to no equivalent to LRPLRP instruction instructionfilterfilter kernel kernel stored in textures stored in textures [Hadwiger et al. VMV’01][Hadwiger et al. VMV’01]

separability of 3D kernelseparability of 3D kernel filters of width four filters of width four stored in RGBA stored in RGBA

1D texture1D texture

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Rendering Stage 2: Inverse 2D FFTRendering Stage 2: Inverse 2D FFT1D FFT consists of two parts1D FFT consists of two parts

scramblingscrambling butterfly operationbutterfly operation

SCRAMBLE

HORIZONTAL DIRECTION

BUTTERFLY

BUTTERFLY

VERTICAL DIRECTION

SCRAMBLE

INPUT IMAGE

INVERSETRANSFORMNORMALIZ.

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Fast Fourier Transform in 1DFast Fourier Transform in 1Daa00

aa11

aa22

aa33

aa44

aa55

aa66

aa77

aa00

aa44

aa22

aa66

aa11

aa55

aa33

aa77scramblescramble

11

-1-1

11

-1-1

11

-1-1

11

-1-1

WWkkNN

WW0088

WW2288

WW4488

WW6688

WW0088

WW2288

WW4488

WW6688butterflybutterfly

WW0088

WW1188

WW2288

WW3388

WW4488

WW5588

WW6688

WW7788

AA00

AA11

AA22

AA33

AA44

AA55

AA66

AA77

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Fast Fourier Transform on the GPUFast Fourier Transform on the GPU two buffers – ping-pong renderingtwo buffers – ping-pong rendering two channels rendering buffers requiredtwo channels rendering buffers required scramble passscramble pass

1D lookup1D lookup butterfly passesbutterfly passes

loglog22(N) passes(N) passes texture encodestexture encodes

WWkkNN

pp and and qq coordinate coordinate butterfly signbutterfly sign

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Hartley Transform - Alternative to FFTHartley Transform - Alternative to FFTreal input is transformed into real outputreal input is transformed into real output

½ memory requirements½ memory requirementsscrambling the same as in FFTscrambling the same as in FFTdouble-butterfly operationdouble-butterfly operation

three source values, cos and sinthree source values, cos and sinHT not separableHT not separable

additional additional correctioncorrection pass required pass required

GPU implementation not faster than FFTGPU implementation not faster than FFT

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Fast Hartley Transform on the GPUFast Hartley Transform on the GPU similar to FFT – ping-pong renderingsimilar to FFT – ping-pong rendering only one channel rendering buffers requiredonly one channel rendering buffers required scrambling the samescrambling the same double-butterflydouble-butterfly

two lookup texturestwo lookup textures addresses of source values (3 channels)addresses of source values (3 channels) cos and sin terms (2 channels)cos and sin terms (2 channels)

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ResultsResults

Framerates for ATI Radeon 9800 XTFramerates for ATI Radeon 9800 XT

ResolutionResolution NNNN TLTL TCTC IFFT 2DIFFT 2D

256x256256x256 14501450 10501050 180180 153153

512x512512x512 500500 350350 4545 3535

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DemoDemo

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ConclusionsConclusions rendering stage of FVR very fast on GPUrendering stage of FVR very fast on GPU

slicing – high performance gainslicing – high performance gain wrap around is “for free”wrap around is “for free” speed-up also for inverse FFTspeed-up also for inverse FFT

nearest neighbour – very poor qualitynearest neighbour – very poor quality tri-linear interpolation – high performacetri-linear interpolation – high performace tri-cubic interpolation – high qualitytri-cubic interpolation – high quality

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Thank You!Thank You!

viola@cg.tuwien.ac.atviola@cg.tuwien.ac.at