GPU Acceleration in Registration

GPU Acceleration in Registration

Danny Ruijters26 April 2007

GPU Acceleration in Registration, Danny Ruijters 2

Outline

• The GPU• Rigid 3D-3D Registration• Elastic Registration• Conclusions


The GPU


The graphics card

• Raserization of primitives• Texture mapping• Colour interpolation


The GPU

• Graphics Processing Unit• Programmable processor in the

graphics rendering pipeline• Parallel execution (SIMD like)


on-chip cache memoryvideo memory

system memory

rasterization

CPU

vertex shading

(T&L)

triangle setup

fragment shading

andraster

operations

textures

frame buffer

geometry

commands

pre-TnL cache

post-TnL cache

texture cache

Graphics rendering pipeline


Bottleneckson-chip cache memoryvideo memory

system memory

rasterization

CPU

vertex shading

(T&L)

triangle setup

fragment shading

andraster

operations

textures

frame buffer

geometry

commands

pre-TnL cache

post-TnL cache

texture cache

transform limited

fragment shader limited

CPU limited

texture limited

frame buffer limited

setup limited

raster limited

transfer limited


128 processing units

Local cache

Shared memory


Performance


Performance• Parallelism & pipelining (up to 16 parallel pipelines)• Vector processor• Moore’s Law: CPU: 2* performance per 18 months• GPU: 2* performance per 6 months

GeForce 7900 GTX GeForce 8800 GTX

Code name G71 G80

Release date 3 / 2006 11 / 2006

Transistors 278 M (90 nm) 681 M (90 nm)

Clock speed 650 MHz 1350 MHz

Processing units 24+8 (pixel + vertex) 128 (unified)

Peak pixel fill rate 10.4 Gigapixels/s 36.8 Gigapixels/s

Peak memory bandwidth

51.2 GB/s (256 bit) 86.4 GB/s (384 bit)

Memory 512 MB 768 MB

Peak performance 250 Gigaflops 520 Gigaflops


Textures & buffers

• 1D, 2D, 3D textures

• 2D output buffers (frame buffer, accumulation buffer, stencil buffer, p-buffer)

• 8, 10, 12, 16 bit integers, 16, 32 bit floating point

• 1 (intensity), 2 (luminance-alpha), 3 (RGB), 4 (RGBA) components per pixel


Historic overview GPU• RenderMan (1988, pre-history)• Intel MMX (SIMD, 1997, pre-history)• Register combiners (nVidia, 1999, bronze age)• Vender specific APIs (2001, iron age)• Generic assembly-like language (2002, middle-

ages) • Different high-level languages (2003, industrial

age)• CUDA: general purpose C-like language (2007,

modern age)


Register combiners (1999, bronse age)// Stage 0// spare0.rgb = gradient dot ViewDir, spare1.rgb = -(gradient dot ViewDir)glCombinerInputNV(GL_COMBINER0_NV,GL_RGB,GL_VARIABLE_A_NV,GL_TEXT

URE0_ARB,GL_EXPAND_NORMAL_NV,GL_RGB);glCombinerInputNV(GL_COMBINER0_NV,GL_RGB,GL_VARIABLE_B_NV,GL_CONS

TANT_COLOR1_NV,GL_EXPAND_NORMAL_NV,GL_RGB);glCombinerInputNV(GL_COMBINER0_NV,GL_RGB,GL_VARIABLE_C_NV,GL_TEXT

URE0_ARB,GL_EXPAND_NEGATE_NV,GL_RGB);glCombinerInputNV(GL_COMBINER0_NV,GL_RGB,GL_VARIABLE_D_NV,GL_CONS

TANT_COLOR1_NV,GL_EXPAND_NORMAL_NV,GL_RGB);glCombinerOutputNV(GL_COMBINER0_NV,GL_RGB,GL_SPARE0_NV,GL_SPARE1_

NV,GL_DISCARD_NV,GL_NONE,GL_NONE,GL_TRUE,GL_TRUE,GL_FALSE);


GL_ARB_fragment_program (2002)

!!ARBfp1.0

ATTRIB coord = fragment.texcoord[0];ATTRIB color = fragment.color;OUTPUT out = result.color;TEMP texel;TEMP lookup;

TEX texel, coord, texture[0], 3D;TEX lookup, texel, texture[1], 1D;

MUL out, lookup, color;END


GLSlang (2003)

uniform vec3 ViewDir;

void main (void){

float value;vec3 gradient;gradient = texture3(0, gl_TexCoord0) * 2.0 - 1.0;value = 1.0 - abs(dot(gradient, ViewDir));value *= 1.3 * dot(gradient, gradient);value = clamp(value, 0.0, 1.0);gl_FragColor = vec4(value);

}


CUDA (2007)

• Compute Unified Device Architecture• General purpose C-like language• nVidia only• Very recently released


Rigid 3D-3D Registration


3DRA – MR registration


3DRA – XperCT Registration 1

Pre-operative


3DRA – XperCT Registration 2

Post-operative:verification of the embolization


3DRA Slice


Mutual information

F. Maes et al., "Multimodality Image Registration by Maximization of Mutual Information,“IEEE Transactions on Medical Imaging 16(2), pp. 187-198, April 1997


Joint histogram


Resampling

Joint histogram: increment(g,g)


3DRA – MR, before, after


3DRA – MR: CPU interpolation


3DRA – MR: GPU interpolation


Elastic Registration


Elastic deformation

• Parameterized deformation:

• B-spline deformation:


Cubic B-spline


GPU linear interpolation

• Hardwired: linear interpolation is much faster than separate lookups


GPU Cubic Interpolation

• Compose cubic interpolation from weighted sum of linear interpolations:

=

C. Sigg, M. Hadwiger, “Fast Third-Order Texture Filtering”, GPU Gems 2


Outline of proof

=


GPU Cubic Interpolation

• 2D: 4 linear-interpolated lookups, instead of 16 direct lookups

• 3D: 8 linear-interpolated lookups, instead of 64 direct lookups


GPU Linear Interpolation AccuracynVidia QuadroFX 3500

-1

0

1

2

3

4

5

6

7

8

9

10

1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193 205 217 229 241 253

Err

or

* -1

0^-8


Linear deformation, linear interpolation


Linear deformation, cubic interpolation


Cubic deformation, linear interpolation


Cubic deformation, cubic interpolation


Optimization

• Many parameters: huge parameter space

• Solution: use derivatives like Jacobian, Hessian

• Examples: Gradient Descent, Quasi-Newton, Levenberg-Marquardt


GPU Elastic Registration Iteration

1. Generate deformed image on GPU & store to texture

2. Calculate Similarity Measure & First-Order Derivative on GPU

– Texture with reference image– Texture with deformed image


First-Order Derivative of Sim. Measure

J. Kybic, M. Unser, “Fast Parametric Elastic Image Registration”


Derivative of the Similarity Measure

SSD:


Derivative of the Deformed Image

• Sobel operator to calculate gradients:

-1 0 1

-4 0 4

-1 0 1

1 4 1

0 0 0

-1 -4 -1


Derivative of the Control Points

• Constant• B-spline: separatable kernel of fixed size


Original Fluoroscopy Sequence


2 * 2 Control Points


8 * 8 Control Points


Deformation Field


GPU Elastic Registration

• 40 images: Quasi Newton: 16 seconds

• Gradient Descent: 63 seconds• 8 * 8 Control Points: rest motion• Multi-resolution deformation field,

with reduced parameters (discussed with Dirk Loeckx)


CUDA Libraries


CUDA Software Stack


CUDA Libraries

• CUBLAS• CUFFT


CUBLAS

• Basic Linear Algebra Subprograms• Vector, Matrix, Numerical Math• Almost no initialization• Function calls


CUBLAS performanceexecution times scalar vector add dual-core Woodcrest and G80 core

0

50

100

150

200

250

300

350

400

450

500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

data s ize vector (kB)

exec

utio

n tim

e (m

s)

G80 (ms)

Woodcrest (ms)


CUBLAS performanceexecution times vector inproduct dual-core Woodcrest and G80 core

0.0000

50.0000

100.0000

150.0000

200.0000

250.0000

300.0000

350.0000

400.0000

450.0000

500.0000

0 500 1000 1500 2000 2500 3000 3500 4000 4500

data s ize vector (kB)

exec

utio

n tim

e (m

s)

G80 (ms)

Woodcrest (ms)


CUFFT performanceexecution times 2D FFT single-core Woodcrest and G80 core

(size 2^n)

0.001

0.01

0.1

1

10

100

1000

10000

1 10 100 1000 10000

N point 2D FFT

Ex

ec

uti

on

tim

e (

ms

)

G80 (CudaFFT)

Woodcrest (FFTW)


Conclusion & Future work


Conclusions

• GPU: powerful parallel processor, but has its limitations

• Rigid Registration: interpolation on the GPU

• Elastic Registration: calculation of the Similarity Measure & first order derivative on the GPU


Future work

• Multi-resolution deformation fields• 2D-3D registration of the Coronary

Arteries (not presented)


Questions?

GPU Acceleration in Registration

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