Computer Architectures for Medical Applications 3 rd Exercise, May 2, 2016

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1 Computer Architectures for Medical Applications 3 rd Exercise, May 2, 2016 University Erlangen-Nuremberg Computer Science 3 & Professorship for High Performance Computing CAMA Exercise 03 May 2,

2 Overview Solution of Previous Assignment Visualization of the Reconstruction Bilinear Interpolation Optimization o Exercise 1. Avoid Unnecessary Computations CAMA Exercise 03 May 2,

3 Sample Solution int RCTLoadAlgorithm(RabbitCtGlobalData* rcgd) { int L = rcgd->l; float *VOL = rcgd->f_l; /* allocate memory for the volume */ VOL = (float *)malloc(l*l*l * sizeof(float)); if (VOL == NULL) { perror("malloc"); exit(exit_failure); } /* initialize all voxels with 0.0f */ for (int i = 0; i < L*L*L; ++i) VOL[i] = 0.0f; return 1; } CAMA Exercise 03 May 2,

4 Sample Solution struct RabbitCtGlobalData { ///< problem size \in {128, 256, 512, 1024} unsigned int L; ///< projection image width unsigned int S_x; ///< projection image height (detector rows) unsigned int S_y; ///< 3x4 projetion matrix double * A_n; ///< projection image buffer float * I_n; ///< position of the 0-index in the world coordinate system float O_L;... CAMA Exercise 03 May 2,

5 Sample Solution int RCTAlgorithmBackprojection(RabbitCtGlobalData* rcgd) { int L = rcgd->l; float *I = rcgd->i_n; float *VOL = rcgd->f_l; double *A = rcgd->a_n; float O = rcgd->o_l; float V = rcgd->r_l; int width = rcgd->s_x; int height = rcgd->s_y; for (int z = 0; z < L; ++z) { for (int y = 0; y < L; ++y) { for (int x = 0; x < L; ++x) { // voxel update... CAMA Exercise 03 May 2,

6 Sample Solution /* convert voxel coordinates to world coordinates */ float wx = O+x*V; float wy = O+y*V; float wz = O+z*V; /* convert world coordinates to image coordinates */ float u = wx*a[0] + wy*a[3] + wz*a[6] + A[9]; float v = wx*a[1] + wy*a[4] + wz*a[7] + A[10]; float w = wx*a[2] + wy*a[5] + wz*a[8] + A[11]; /* normalize image coordinates */ int ix = u/w; int iy = v/w; CAMA Exercise 03 May 2,

7 Sample Solution... /* normalize image coordinates */ int ix = u/w; int iy = v/w; /* load intensity value from projection image; */ /* if the ray doesn t hit the detector, set value to 0.0f */ float val = 0.0f; if (ix >= 0 && ix < width && iy >= 0 && iy < height) val = I[iy*width+ix]; /* add weighted value to voxel in volume */ VOL[z*L*L + y*l + x] += val / (w*w); CAMA Exercise 03 May 2,

8 Sample Solution $./rabbitctrunner reference.so Running... this may take some time. (\_/) (=. =) (")_(") Quality of reconstructed volume: Root Mean Squared Error: HU Mean Squared Error: HU^2 Max. Absolute Error: 674 HU PSNR: db CAMA Exercise 03 May 2,

9 Overview Solution of Previous Assignment Visualization of the Reconstruction Bilinear Interpolation Optimization o Exercise 1. Avoid Unnecessary Computations CAMA Exercise 03 May 2,

10 Visualization of the Reconstruction Save volume to disk after reconstruction emmyxx$./rabbitctrunner reference.so o output_file Copy volume from Emmy to your CIP home faui04d$ scp camaxx@lima:path/to/rabbit/output_file.vol. Start Paraview faui04d$ paraview Open Volume in Paraview CAMA Exercise 03 May 2,

11 Visualization of the Reconstruction Paraview o File - Open output_file.vol (might not be shown in file dialog) o Open Data with RAW (binary) Files o Data Scalar Type: float o Data Byte Order: LittleEndian (x86) o Data Extent: 0, 127, 0, 127, 0, 127 o Representation: Volume CAMA Exercise 03 May 2,

12 Visualization of the Reconstruction CAMA Exercise 03 May 2,

13 Overview Visualization of the Reconstruction Bilinear Interpolation Optimization o Exercise 1. Avoid Unnecessary Computations CAMA Exercise 03 May 2,

14 Bilinear Interpolation Flat Panel Detector X-Ray Source CAMA Exercise 03 May 2,

15 Bilinear Interpolation Flat Panel Detector X-Ray Source CAMA Exercise 03 May 2,

16 Bilinear Interpolation iy 3 Integral values of the DCS are located in the pixel centers ix CAMA Exercise 03 May 2,

17 Bilinear Interpolation iy 3 Integral values of the DCS are located in the pixel centers ix CAMA Exercise 03 May 2,

18 Bilinear Interpolation iy 3 Integral values of the DCS are located in the pixel centers ix CAMA Exercise 03 May 2,

19 Bilinear Interpolation iy Integral values of the DCS are located in the pixel centers ix CAMA Exercise 03 May 2,

20 Bilinear Interpolation iy Integral values of the DCS are located in the pixel centers Up until now Round down (cast to int) ix CAMA Exercise 03 May 2,

21 Bilinear Interpolation iy Integral values of the DCS are located in the pixel centers Up until now Round down (cast to int) To increase quality of the result Bilinear Interpolation ix CAMA Exercise 03 May 2,

22 Bilinear Interpolation iy ix Integral values of the DCS are located in the pixel centers Up until now Round down (cast to int) To increase quality of the result Bilinear Interpolation Example here: low=i[2*4+1]*0.8+i[2*4+2]*0.2 CAMA Exercise 03 May 2,

23 Bilinear Interpolation iy ix Integral values of the DCS are located in the pixel centers Up until now Round down (cast to int) To increase quality of the result Bilinear Interpolation Example here: low=i[2*4+1]*0.8+i[2*4+2]*0.2 high=i[3*4+1]*0.8+i[3*4+2]*0.2 CAMA Exercise 03 May 2,

24 Bilinear Interpolation iy ix Integral values of the DCS are located in the pixel centers Up until now Round down (cast to int) To increase quality of the result Bilinear Interpolation Example here: low=i[2*4+1]*0.8+i[2*4+2]*0.2 high=i[3*4+1]*0.8+i[3*4+2]*0.2 val=low*0.2+high*0.8 CAMA Exercise 03 May 2,

25 Overview Visualization of the Reconstruction Bilinear Interpolation Optimization o Exercise 1. Avoid Unnecessary Computations CAMA Exercise 03 May 2,

26 for (int z = 0; z < L; ++z) { for (int y = 0; y < L; ++y) { for (int x = 0; x < L; ++x) { /* convert voxel coordinates to world coordinates */ float wx = O+x*V; float wy = O+y*V; float wz = O+z*V; /* convert world coordinates to image coordinates */ float u = wx*a[0] + wy*a[3] + wz*a[6] + A[9]; float v = wx*a[1] + wy*a[4] + wz*a[7] + A[10]; float w = wx*a[2] + wy*a[5] + wz*a[8] + A[11]; /* normalize image coordinates */ int ix = u/w; int iy = v/w; /* load intensity value from projection image; */ /* if the ray doesn t hit the detector, set value to 0.0f */ float val = 0.0f; if (ix >= 0 && ix < width && iy >= 0 && iy < height) val = I[iy*width+ix]; /* add weighted value to voxel in volume */ VOL[z*L*L + y*l + x] += val / (w*w); }}} CAMA Exercise 03 May 2,

27 for (int z = 0; z < L; ++z) { for (int y = 0; y < L; ++y) { for (int x = 0; x < L; ++x) { /* convert voxel coordinates to world coordinates */ float wx = O+x*V; float wy = O+y*V; float wz = O+z*V; /* convert world coordinates to image coordinates */ float u = wx*a[0] + wy*a[3] + wz*a[6] + A[9]; float v = wx*a[1] + wy*a[4] + wz*a[7] + A[10]; float w = wx*a[2] + wy*a[5] + wz*a[8] + A[11]; /* normalize image coordinates */ int ix = u/w; int iy = v/w; /* load intensity value from projection image; */ /* if the ray doesn t hit the detector, set value to 0.0f */ float val = 0.0f; if (ix >= 0 && ix < width && iy >= 0 && iy < height) val = I[iy*width+ix]; /* add weighted value to voxel in volume */ VOL[z*L*L + y*l + x] += val / (w*w); }}} CAMA Exercise 03 May 2,

28 Overview Visualization of the Reconstruction Bilinear Interpolation Optimization o Exercise 1. Avoid Unnecessary Computations CAMA Exercise 03 May 2,

29 Exercise Implement the bilinear interpolation o Measure runtime without and with bilinear interpolation o Hint: PSNR should be 100+ db o Visualize the result and look for differences Avoid unnecessary computations o Runtime before/after Hint o Create a new shared object for each improvement $ cp modules/reference.c modules/bilinear.c $ cp modules/bilinear.c modules/bilinear_opt1.c o All new modules are automatically compiled using make o Run with e.g../rabbitctrunner bilinear.so CAMA Exercise 03 May 2,

Computer Architectures for Medical Applications 4 th Exercise, May 9, 2016

Computer Architectures for Medical Applications 4 th Exercise, May 9, 2016 Cmputer Architectures fr Medical Applicatins 4 th Exercise, May 9, 2016 Universität Erlangen-Nürnberg Lehrstuhl für Infrmatik 3 / Prfessur für Höchstleistungsrechnen CAMA Exercise 04 May 9, 2016 1 Overview