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Medical Image Registration A Quick Win

Medical Image Registration A Quick Win. Richard Ansorge. The problem. CT, MRI, PET and Ultrasound produce 3D volume images Typically 256 x 256 x 256 = 16,777,216 image voxels . Combining modalities ( inter modality ) gives extra information.

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Medical Image Registration A Quick Win

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  1. Medical Image RegistrationA Quick Win Richard Ansorge Richard Ansorge

  2. The problem • CT, MRI, PET and Ultrasound produce 3D volume images • Typically 256 x 256 x 256 = 16,777,216 image voxels. • Combining modalities (intermodality) gives extra information. • Repeated imaging over time same modality, e.g. MRI, (intramodality) equally important. • Have to spatially register the images. Richard Ansorge

  3. Example – brain lesion CT MRI PET Richard Ansorge

  4. PET-MR Fusion The PET image shows metabolic activity. This complements the MR structural information Richard Ansorge

  5. Registration Algorithm Im A Im A Transform Im B to match Im A Compute Cost Function Im B′ Im B Update transform parameters good fit? No Yes NB Cost function calculation dominates for 3D images and is inherently parallel Done Richard Ansorge

  6. Transformations General affine transform has 12 parameters: Polynomial transformations can be useful for e.g. pin-cushion type distortions: Local, non-linear transformations, e.g using cubic BSplines, increasingly popular, very computationally demanding. Richard Ansorge

  7. We tried this before Richard Ansorge

  8. Now - Desktop PC - Windows XP Needs 400 W power supply Richard Ansorge

  9. Free Software: CUDA & Visual C++ Express Richard Ansorge

  10. Visual C++ SDK in action Richard Ansorge

  11. Visual C++ SDK in action Richard Ansorge

  12. Architecture Richard Ansorge

  13. Current GTX 280 has 240 cores! 9600 GT Device Query Richard Ansorge

  14. Matrix Multiply from SDK NB using 4-byte floats Richard Ansorge

  15. Matrix Multiply (from SDK) Richard Ansorge

  16. Matrix Multiply (from SDK) Richard Ansorge

  17. Matrix Multiply (from SDK) Richard Ansorge

  18. Image Registration CUDA Code Richard Ansorge

  19. #include <cutil_math.h> texture<float, 3, cudaReadModeElementType> tex1; // Target Image in texture __constant__ float c_aff[16]; // 4x4 Affine transform // Function arguments are image dimensions and pointers to output buffer b // and Source Image s. These buffers are in device memory __global__ void d_costfun(int nx,int ny,int nz,float *b,float *s) { int ix = blockIdx.x*blockDim.x + threadIdx.x; // Thread ID matches int iy = blockIdx.y*blockDim.y + threadIdx.y; // Source Image x-y float x = (float)ix; float y = (float)iy; float z = 0.0f; // start with slice zero float4 v = make_float4(x,y,z,1.0f); float4 r0 = make_float4(c_aff[ 0],c_aff[ 1],c_aff[ 2],c_aff[ 3]); float4 r1 = make_float4(c_aff[ 4],c_aff[ 5],c_aff[ 6],c_aff[ 7]); float4 r2 = make_float4(c_aff[ 8],c_aff[ 9],c_aff[10],c_aff[11]); float4 r3 = make_float4(c_aff[12],c_aff[13],c_aff[14],c_aff[15]); // 0,0,0,1? float tx = dot(r0,v); // Matrix Multiply using dot products float ty = dot(r1,v); float tz = dot(r2,v); float source = 0.0f; float target = 0.0f; float cost = 0.0f; uint is = iy*nx+ix; uint istep = nx*ny; for(int iz=0;iz<nz;iz++) { // process all z's in same thread here source = s[is]; target = tex3D(tex1, tx, ty, tz); is += istep; v.z += 1.0f; tx = dot(r0,v); ty = dot(r1,v); tz = dot(r2,v); cost += fabs(source-target); // other costfuns here as required } b[iy*nx+ix]=cost; // store thread sum for host } Richard Ansorge

  20. #include <cutil_math.h> texture<float, 3, cudaReadModeElementType> tex1; // Target Image in texture __constant__ float c_aff[16]; // 4x4 Affine transform // Function arguments are image dimensions and pointers to output buffer b // and Source Image s. These buffers are in device memory __global__ void d_costfun(int nx,int ny,int nz,float *b,float *s) { int ix = blockIdx.x*blockDim.x + threadIdx.x; // Thread ID matches int iy = blockIdx.y*blockDim.y + threadIdx.y; // Source Image x-y float x = (float)ix; float y = (float)iy; float z = 0.0f; // start with slice zero float4 v = make_float4(x,y,z,1.0f); float4 r0 = make_float4(c_aff[ 0],c_aff[ 1],c_aff[ 2],c_aff[ 3]); float4 r1 = make_float4(c_aff[ 4],c_aff[ 5],c_aff[ 6],c_aff[ 7]); float4 r2 = make_float4(c_aff[ 8],c_aff[ 9],c_aff[10],c_aff[11]); float4 r3 = make_float4(c_aff[12],c_aff[13],c_aff[14],c_aff[15]); // 0,0,0,1? float tx = dot(r0,v); // Matrix Multiply using dot products float ty = dot(r1,v); float tz = dot(r2,v); float source = 0.0f; float target = 0.0f; float cost = 0.0f; uint is = iy*nx+ix; uint istep = nx*ny; for(int iz=0;iz<nz;iz++) { // process all z's in same thread here source = s[is]; target = tex3D(tex1, tx, ty, tz); is += istep; v.z += 1.0f; tx = dot(r0,v); ty = dot(r1,v); tz = dot(r2,v); cost += fabs(source-target); // other costfuns here as required } b[iy*nx+ix]=cost; // store thread sum for host } texture<float, 3, cudaReadModeElementType> tex1; __constant__ float c_aff[16]; tex1: moving image, stored as 3D texture c_aff: affine transformation matrix, stored as constants Richard Ansorge

  21. #include <cutil_math.h> texture<float, 3, cudaReadModeElementType> tex1; // Target Image in texture __constant__ float c_aff[16]; // 4x4 Affine transform // Function arguments are image dimensions and pointers to output buffer b // and Source Image s. These buffers are in device memory __global__ void d_costfun(int nx,int ny,int nz,float *b,float *s) { int ix = blockIdx.x*blockDim.x + threadIdx.x; // Thread ID matches int iy = blockIdx.y*blockDim.y + threadIdx.y; // Source Image x-y float x = (float)ix; float y = (float)iy; float z = 0.0f; // start with slice zero float4 v = make_float4(x,y,z,1.0f); float4 r0 = make_float4(c_aff[ 0],c_aff[ 1],c_aff[ 2],c_aff[ 3]); float4 r1 = make_float4(c_aff[ 4],c_aff[ 5],c_aff[ 6],c_aff[ 7]); float4 r2 = make_float4(c_aff[ 8],c_aff[ 9],c_aff[10],c_aff[11]); float4 r3 = make_float4(c_aff[12],c_aff[13],c_aff[14],c_aff[15]); // 0,0,0,1? float tx = dot(r0,v); // Matrix Multiply using dot products float ty = dot(r1,v); float tz = dot(r2,v); float source = 0.0f; float target = 0.0f; float cost = 0.0f; uint is = iy*nx+ix; uint istep = nx*ny; for(int iz=0;iz<nz;iz++) { // process all z's in same thread here source = s[is]; target = tex3D(tex1, tx, ty, tz); is += istep; v.z += 1.0f; tx = dot(r0,v); ty = dot(r1,v); tz = dot(r2,v); cost += fabs(source-target); // other costfuns here as required } b[iy*nx+ix]=cost; // store thread sum for host } // device function declaration __global__ void d_costfun(int nx,int ny,int nz,float *b,float *s) nx, ny & nz: image dimensions (assumed same of both) b: output array for partial sums s: reference image (mislabelled in code) Richard Ansorge

  22. #include <cutil_math.h> texture<float, 3, cudaReadModeElementType> tex1; // Target Image in texture __constant__ float c_aff[16]; // 4x4 Affine transform // Function arguments are image dimensions and pointers to output buffer b // and Source Image s. These buffers are in device memory __global__ void d_costfun(int nx,int ny,int nz,float *b,float *s) { int ix = blockIdx.x*blockDim.x + threadIdx.x; // Thread ID matches int iy = blockIdx.y*blockDim.y + threadIdx.y; // Source Image x-y float x = (float)ix; float y = (float)iy; float z = 0.0f; // start with slice zero float4 v = make_float4(x,y,z,1.0f); float4 r0 = make_float4(c_aff[ 0],c_aff[ 1],c_aff[ 2],c_aff[ 3]); float4 r1 = make_float4(c_aff[ 4],c_aff[ 5],c_aff[ 6],c_aff[ 7]); float4 r2 = make_float4(c_aff[ 8],c_aff[ 9],c_aff[10],c_aff[11]); float4 r3 = make_float4(c_aff[12],c_aff[13],c_aff[14],c_aff[15]); // 0,0,0,1? float tx = dot(r0,v); // Matrix Multiply using dot products float ty = dot(r1,v); float tz = dot(r2,v); float source = 0.0f; float target = 0.0f; float cost = 0.0f; uint is = iy*nx+ix; uint istep = nx*ny; for(int iz=0;iz<nz;iz++) { // process all z's in same thread here source = s[is]; target = tex3D(tex1, tx, ty, tz); is += istep; v.z += 1.0f; tx = dot(r0,v); ty = dot(r1,v); tz = dot(r2,v); cost += fabs(source-target); // other costfuns here as required } b[iy*nx+ix]=cost; // store thread sum for host } int ix = blockIdx.x*blockDim.x + threadIdx.x; // Thread ID matches int iy = blockIdx.y*blockDim.y + threadIdx.y; // Source Image x-y float x = (float)ix; float y = (float)iy; float z = 0.0f; // start with slice zero Which thread am I? (similar to MPI) however one thread for each x-y pixel, 240x256=61440 threads (CF ~128 nodes for MPI) Richard Ansorge

  23. #include <cutil_math.h> texture<float, 3, cudaReadModeElementType> tex1; // Target Image in texture __constant__ float c_aff[16]; // 4x4 Affine transform // Function arguments are image dimensions and pointers to output buffer b // and Source Image s. These buffers are in device memory __global__ void d_costfun(int nx,int ny,int nz,float *b,float *s) { int ix = blockIdx.x*blockDim.x + threadIdx.x; // Thread ID matches int iy = blockIdx.y*blockDim.y + threadIdx.y; // Source Image x-y float x = (float)ix; float y = (float)iy; float z = 0.0f; // start with slice zero float4 v = make_float4(x,y,z,1.0f); float4 r0 = make_float4(c_aff[ 0],c_aff[ 1],c_aff[ 2],c_aff[ 3]); float4 r1 = make_float4(c_aff[ 4],c_aff[ 5],c_aff[ 6],c_aff[ 7]); float4 r2 = make_float4(c_aff[ 8],c_aff[ 9],c_aff[10],c_aff[11]); float4 r3 = make_float4(c_aff[12],c_aff[13],c_aff[14],c_aff[15]); // 0,0,0,1? float tx = dot(r0,v); // Matrix Multiply using dot products float ty = dot(r1,v); float tz = dot(r2,v); float source = 0.0f; float target = 0.0f; float cost = 0.0f; uint is = iy*nx+ix; uint istep = nx*ny; for(int iz=0;iz<nz;iz++) { // process all z's in same thread here source = s[is]; target = tex3D(tex1, tx, ty, tz); is += istep; v.z += 1.0f; tx = dot(r0,v); ty = dot(r1,v); tz = dot(r2,v); cost += fabs(source-target); // other costfuns here as required } b[iy*nx+ix]=cost; // store thread sum for host } float4 v = make_float4(x,y,z,1.0f); float4 r0 = make_float4(c_aff[ 0],c_aff[ 1],c_aff[ 2],c_aff[ 3]); float4 r1 = make_float4(c_aff[ 4],c_aff[ 5],c_aff[ 6],c_aff[ 7]); float4 r2 = make_float4(c_aff[ 8],c_aff[ 9],c_aff[10],c_aff[11]); float4 r3 = make_float4(c_aff[12],c_aff[13],c_aff[14],c_aff[15]); // 0,0,0,1? float tx = dot(r0,v); //Matrix Multiply using dot products float ty = dot(r1,v); float tz = dot(r2,v); float source = 0.0f; float target = 0.0f; float cost = 0.0f; // accumulates cost function contributions v.z=0.0f; // z of first slice is zero (redundant as done above) uint is = iy*nx+ix; // this is index of my voxel in first z-slice uint istep = nx*ny; // stride to index same voxel in subsequent slices Initialisations and first matrix multiply. “v” is 4-vector current voxel x,y,z address “tx,ty,tz” hold corresponding transformed position Richard Ansorge

  24. Z Y X #include <cutil_math.h> texture<float, 3, cudaReadModeElementType> tex1; // Target Image in texture __constant__ float c_aff[16]; // 4x4 Affine transform // Function arguments are image dimensions and pointers to output buffer b // and Source Image s. These buffers are in device memory __global__ void d_costfun(int nx,int ny,int nz,float *b,float *s) { int ix = blockIdx.x*blockDim.x + threadIdx.x; // Thread ID matches int iy = blockIdx.y*blockDim.y + threadIdx.y; // Source Image x-y float x = (float)ix; float y = (float)iy; float z = 0.0f; // start with slice zero float4 v = make_float4(x,y,z,1.0f); float4 r0 = make_float4(c_aff[ 0],c_aff[ 1],c_aff[ 2],c_aff[ 3]); float4 r1 = make_float4(c_aff[ 4],c_aff[ 5],c_aff[ 6],c_aff[ 7]); float4 r2 = make_float4(c_aff[ 8],c_aff[ 9],c_aff[10],c_aff[11]); float4 r3 = make_float4(c_aff[12],c_aff[13],c_aff[14],c_aff[15]); // 0,0,0,1? float tx = dot(r0,v); // Matrix Multiply using dot products float ty = dot(r1,v); float tz = dot(r2,v); float source = 0.0f; float target = 0.0f; float cost = 0.0f; uint is = iy*nx+ix; uint istep = nx*ny; for(int iz=0;iz<nz;iz++) { // process all z's in same thread here source = s[is]; target = tex3D(tex1, tx, ty, tz); is += istep; v.z += 1.0f; tx = dot(r0,v); ty = dot(r1,v); tz = dot(r2,v); cost += fabs(source-target); // other costfuns here as required } b[iy*nx+ix]=cost; // store thread sum for host } for(int iz=0;iz<nz;iz++) { // process all z's in same thread here source = s[is]; target = tex3D(tex1, tx, ty, tz); // NB very FAST trilinear interpolation!! is += istep; v.z += 1.0f; // step to next z slice tx = dot(r0,v); ty = dot(r1,v); tz = dot(r2,v); cost += fabs(source-target); // other costfuns here as required } b[iy*nx+ix]=cost; // store thread sum for host Loop sums contributions for all z values at fixed x,y position. Each tread updates a different element of 2D results array b. Richard Ansorge

  25. Host Code Initialization Fragment ... blockSize.x = blockSize.y = 16; // multiples of 16 a VERY good idea gridSize.x = (w2+15) / blockSize.x; gridSize.y = (h2+15) / blockSize.y; // allocate working buffers, image is W2 x H2 x D2 cudaMalloc((void**)&dbuff,w2*h2*sizeof(float)); // passed as “b” to kernel bufflen = w2*h2; Array1D<float> shbuff = Array1D<float>(bufflen); shbuff.Zero(); hbuff = shbuff.v; cudaMalloc((void**)&dnewbuff,w2*h2*d2*sizeof(float)); //passed as “s” to kernel cudaMemcpy(dnewbuff,vol2,w2*h2*d2*sizeof(float),cudaMemcpyHostToDevice); e = make_float3((float)w2/2.0f,(float)h2/2.0f,(float)d2/2.0f); // fixed rotation origin o = make_float3(0.0f); // translations r = make_float3(0.0f); // rotations s = make_float3(1.0f,1.0f,1.0f); // scale factors t = make_float3(0.0f); // tans of shears ... Richard Ansorge

  26. Calling the Kernel double nr_costfun(Array1D<double> &a) { static Array2D<float> affine = Array2D<float>(4,4); // a holds current transformation double sum = 0.0; make_affine_from_a(nr_fit,affine,a); // convert to 4x4 matrix of floats cudaMemcpyToSymbol(c_aff,affine.v[0],4*4*sizeof(float)); // load constant mem d_costfun<<<gridSize, blockSize>>>(w2,h2,d2,dbuff,dnewbuff); // run kernel CUT_CHECK_ERROR("kernel failed"); // OK? cudaThreadSynchronize(); // make sure all done // copy partial sums from device to host cudaMemcpy(hbuff,dbuff,bufflen*sizeof(float),cudaMemcpyDeviceToHost); for(int iy=0;iy<h2;iy++) for(int ix=0;ix<w2;ix++) sum += hbuff[iy*w2+ix]; // final sum calls++; if(verbose>1){ printf("call %d costfun %12.0f, a:",calls,sum); for(int i=0;i<a.sizex();i++)printf(" %f",a.v[i]); printf("\n"); } return sum; } Richard Ansorge

  27. Example Run (240x256x176 images) C: >airwc airwc v2.5 Usage: AirWc <target> <source> <result> opts(12rtdgsf) C:>airwc sb1 sb2 junk 1f NIFTI Header on File sb1.nii converting short to float 0 0.000000 NIFTI Header on File sb2.nii converting short to float 0 0.000000 Using device 0: GeForce 9600 GT Initial correlation 0.734281 using cost function 1 (abs-difference) using cost function 1 (abs-difference) Amoeba time: 4297, calls 802, cost:127946102 Cuda Total time 4297, Total calls 802 File dofmat.mat written Nifti file junk.nii written, bswop=0 Full Time 6187 timer 0 1890 ms timer 1 0 ms timer 2 3849 ms timer 3 448 ms timer 4 0 ms Total 6.187 secs Final Transformation: 0.944702 -0.184565 0.017164 40.637428 0.301902 0.866726 -0.003767 -38.923237 -0.028792 -0.100618 0.990019 18.120852 0.000000 0.000000 0.000000 1.000000 Final rots and shifts 6.096217 -0.156668 -19.187197 -0.012378 0.072203 0.122495 scales and shears 0.952886 0.912211 0.995497 0.150428 -0.101673 0.009023 Richard Ansorge

  28. Registration with FLIRT 4.1 8.5 Minutes Registration with CUDA 6 Seconds Desktop 3D Registration Richard Ansorge

  29. Comments • This is actually already very useful. Almost interactive (add visualisation) • Further speedups possible • Faster card • Smarter optimiser • Overlap IO and Kernel execution • Tweek CUDA code • Extend to non-linear local registration Richard Ansorge

  30. Figure 1: Schematic of the Larabee many-core architecture: The number of CPU cores and the number and type of co-processors and I/O blocks are implementation-dependent, as are the positions of the CPU and non-CPU blocks on the chip. Intel Larabee? Porting from CUDA to Larabee should be easy Richard Ansorge

  31. Thank you Richard Ansorge

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