Computer Architectures for! Medical Applications

Transcription

1 Computer Architectures for! Medical Applications 1. Exercise, University Erlangen-Nuremberg Chair for Computer Architecture & Professorship for High Performance Computing

2 Organizational Matters! Did you activate your CIP accounts for the Casa Huber? Programming exercises can be solved in teams of two Hand in (per ) your solution before the next exercise Exercise Activity (Presentation of the solution of the last exercise) New exercise is presented Supervised working on the new exercise Questions Office: Room (blue tower) 2

3 Computer Tomograph Setup! Flat Panel Detector X-Ray Source 3

4 Computer Tomograph Setup! Flat Panel Detector X-Ray Source 4

5 Computer Tomograph Setup! Flat Panel Detector X-Ray Source 5

6 Computer Tomograph Setup! Flat Panel Detector X-Ray Source 6

7 Computer Tomograph Setup! Acquisition of 2D projection images The recorded values in the projection images correspond to the x-ray intensity measured at the flat panel detector E.g. Bones absorb more radiation than soft tissue Ray that passes through bone will have lower intensity when arriving at the flat panel detector In a circular CT all projection images are recorded along a circular trajectory 7

8 Data Acquisition in Circular CT! 8

9 Data Acquisition in Circular CT! 9

10 Data Acquisition in Circular CT! 10

11 Data Acquisition in Circular CT! 11

12 Data Acquisition in Circular CT! 12

13 Reconstruction in Computed Tomography! The goal of reconstruction in CT is to compute the 3D volume from the set of recorded 2D projection images In general, two approaches for reconstruction Algebraic Reconstruction Techniques (ART) Filtered Backprojection (FBP) Algebraic Methods function after the principle of iteratively solving a set of linear equations and produce an exact result; however, they a are relatively slow Algorithms based on the filtered backprojection are much faster; however, they are not exact 13

14 Algebraic Reconstruction! Acquisition of data 14

15 Algebraic Reconstruction! Acquisition of data

16 Algebraic Reconstruction! Acquisition of data

17 Algebraic Reconstruction! x 1 x 2 x 3 x Acquisition of data Algebraic Reconstruction Techniques (ART) provide an exact solution Solve the linear equations x 1 + x 2 = 15 x 3 + x 4 = 11 x 1 + x 3 = 19 x 2 + x 4 =7 17

18 Algebraic Reconstruction! Acquisition of data Algebraic Reconstruction Techniques (ART) provide an exact solution Solve the linear equations x 1 + x 2 = 15 x 3 + x 4 = 11 x 1 + x 3 = 19 x 2 + x 4 =7 18

19 Gefilterte Rückprojektion! x 1 x 2 x 3 x Same set of recorded projection images as in the case for ART In this example, we ll be using the Feldkamp-Davis-Kress (FDK) algorithm as a representative from the set of FBP algorithms

20 Gefilterte Rückprojektion! Same set of recorded projection images as in the case for ART In this example, we ll be using the Feldkamp-Davis-Kress (FDK) algorithm as a representative from the set of FBP algorithms Backprojection: Smearing back the recorded intensity values along the x-ray 20

21 Gefilterte Rückprojektion! Same set of recorded projection images as in the case for ART In this example, we ll be using the Feldkamp-Davis-Kress (FDK) algorithm as a representative from the set of FBP algorithms Backprojection: Smearing back the recorded intensity values along the x-ray 21

22 Gefilterte Rückprojektion! Same set of recorded projection images as in the case for ART In this example, we ll be using the Feldkamp-Davis-Kress (FDK) algorithm as a representative from the set of FBP algorithms Backprojection: Smearing back the recorded intensity values along the x-ray Add up values in volume elements (voxels) 22

23 Gefilterte Rückprojektion! Same set of recorded projection images as in the case for ART In this example, we ll be using the Feldkamp-Davis-Kress (FDK) algorithm as a representative from the set of FBP algorithms Backprojection: Smearing back the recorded intensity values along the x-ray Add up values in volume elements (voxels) 23

24 Gefilterte Rückprojektion! 34 (9) 30 (10) 22 (6) 18 (1) Same set of recorded projection images as in the case for ART In this example, we ll be using the Feldkamp-Davis-Kress (FDK) algorithm as a representative from the set of FBP algorithms Backprojection: Smearing back the recorded intensity values along the x-ray Add up values in volume elements (voxels) Comparison with ART: values not correct Filtering with Ramp Filter improves result 24

25 Simplified FDK Implementation in C! Iterate over all voxels X-Ray Source for (z=0; z<l; ++z) { } for (y=0; y<l; ++y) { } for (x=0; x<l; ++x) { // voxel update... } 25

26 Simplified FDK Implementation in C! Iterate over all voxels X-Ray Source for (z=0; z<l; ++z) { } for (y=0; y<l; ++y) { } for (x=0; x<l; ++x) { // voxel update... } 26

27 Simplified FDK Implementation in C! Where does the ray hit the detector? int ix =... int iy =... Add intensity value in projection image to voxel offset = z*l*l+y*l+x; f=i[iy*width+ix]; VOL[offset]+=f*weight; X-Ray Source 27

28 Simplified FDK Implementation in C! X-Ray Source Where does the ray hit the detector? int ix =... int iy =... Add intensity value in projection image to voxel offset = z*l*l+y*l+z; f=i[iy*width+ix]; VOL[offset]+=f*weight; Next voxel 28

29 Simplified FDK Implementation in C! X-Ray Source Where does the ray hit the detector? int ix =... int iy =... Add intensity value in projection image to voxel offset = z*l*l+y*l+z; f=i[iy*width+ix]; VOL[offset]+=f*weight; Next voxel 29

30 Simplified FDK Implementation in C! X-Ray Source Where does the ray hit the detector? int ix =... int iy =... Add intensity value in projection image to voxel offset = z*l*l+y*l+z; f=i[iy*width+ix]; VOL[offset]+=f*weight; Next voxel 30

31 Simplified FDK Implementation in C! X-Ray Source Where does the ray hit the detector? int ix =... int iy =... Add intensity value in projection image to voxel offset = z*l*l+y*l+z; f=i[iy*width+ix]; VOL[offset]+=f*weight; Next voxel Next projection image 31

32 RabbitCT! Different implementations by different authors are difficult to compare, because they use different data sets (e.g. recorded projection images) and might measure different parts of the algorithm (e.g. ramp filter, other preprocessing) RabbitCT to the rescue! Developed by the Chair for Pattern Recognition at FAU Benchmarking-Framework Comes with a set of free reference recordings of the university clinic Erlangen (496 pre-filtered projection images, 1248x960px0 Only the runtime of the Feldkamp-Davis-Kress algorithm is measured A slow, but easily comprehendible reference implementation is included Users write modules (shared objects), which is run and evaluated (runtime, quality of reconstruction) y the framework For more information, see 32

33 RabbitCT Module interface! Functions that have to be implemented by a module Gets executed when the module is loaded int RCTLoadAlgorithm(RabbitCtGlobalData *r) Gets executed when the reconstruction has finished int RCTFinishAlgorithm(RabbitCtGlobalData *r) Handles potential pre-processing steps int RCTPrepareAlgorithm(RabbitCtGlobalData *r) Gets executed when the module is unloaded int RCTUnloadAlgorithm(RabbitCtGlobalData *r) Gets executed for each projection image; this function contains the actual FDK implementation int RCTAlgorithmBackprojection(RabbitCtGlobalData *r) 33

34 RabbitCT Modulinterface! Each of the functions is passed a pointer to a struct, which contains all the information necessary to perform the reconstruction typedef struct { uint32_t problemsize; uint32_t imagewidth; uint32_t imageheight; float voxelsize; float O_Index; float *volumedata; uint32_t numberofprojections; double *globalgeometry; Projection* projectionbuffer; } RabbitCtGlobalData; 34

35 First Exercise! Download and unpack code from www3.cs.fau.de/lehre/cama/ SS2014/ Implement the simplified version of the FDK-Algorithm Implement the function FDK in src/fdk.c You don t have to take the weighting factor into account for now Compile the module using make Workstations in the Huber CIP can be reached (from home) by SSH; ssh cip-username@faui04d.informatik.uni-erlangen.de On Windows, you can use PuTTY as SSH-client 35

36 First Exercise Hints! Log in to Headnode of the Emmy-Cluster ssh Copying files using scp scp <file> scp * username@emmy.rrze.uni-erlangen.de:<path> Copy directory using scp scp r <directory> username@emmy.rrze.uni-erlangen.de:<path> Downloading files wget [http ftp]://url.com/<path> Unpacking archives tar xvf <file>.tar tar xvzf <file>.tar.gz tar xvjf <file>.tar.bz2 36

37 First Exercise Filesystem Navigation! Change path cd <directory> Go to parent directory cd.. Go to home directory cd Print current working directory pwd Create directory mkdir <directory> 37

38 First Exercise Hints! Edit files with emacs or vim emacs <file> vi <file> Execute commands listed in Makefile make Load Intel Compiler module load intel64 (* For unexperienced users we recommend using emacs, because the learning curve for vim is pretty steep.) 38