Medical Image Analysis Dr. Mohammad Dawood Department of Computer Science University of Münster Germany

2 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Recap

3 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood α decay β - decay β + decay Gamma scintigraphyPETSinogram

4 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Ultrasound / Sonography

5 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood The frequency range of sound above 20kHz is known as ultrasound Sound spectrum

6 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Sound wave propagation

7 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Ultrasound

8 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Ultrasound

9 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Ultrasound - is produced through the conversion of electrical energy into mechanical energy - is detected by the reverse process, by converting mechanical energy into electrical energy. - The transducer is a device that is both a transmitter and receiver of the ultrasound signal and it serves a dual role in pulse echo imaging.

10 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Inge Edler und Helmut Hertz (1954)

11 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Ultrasound

12 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood ReflexionScatterTransmission Ultrasound

13 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Frequency Depth Resolution Ultrasound

14 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Ultrasound

15 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Ultrasound

16 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Medium Speed of sound  m/s  Air331 Water1483 Tissue Liver1549 Blood1570 Glycerin1923 Bones (Compact)3600

17 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood

18 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Ultrasound - A mode (amplitude) - B mode (brightness) - M mode (moving)

19 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Ultrasound - no functional information - fast - cheap - no radiation - portable - no injection -Bone / gas -Obesity -Operator dependence

20 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Image Reconstruction

21 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Tomography

22 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Law of Attenuation

23 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Problem What is inside the object? ?

24 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood What can we do? Use the principle of radiation absorption in an object

25 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood What can we do? Use the principle of radiation absorption in an object SourceDetector S

26 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood What can we do? Use the principle of radiation absorption in an object SourceDetector S

27 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Law of Attenuation (Line integral)

28 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood SourcesDetectors Reconstruction Line integrals

29 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Parallel projections

30 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood ObjectSinogram Reconstruction Sinograms

31 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Sinogram Reconstruction What now? Object ?

32 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Radon Transformation

33 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Radon Transformation

34 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Radon Transformations

35 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Inverse Radon Transformation

36 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Inverse Radon Transformation Problems with Missing data and Noise!

37 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Filtered Back Projection

38 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood AB DC A+B C+D 1 A+D B+C 3 2 B A+C D Reconstruction Projections A B+D C 4

39 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood ?? ?? Reconstruction Back projections A+B C+D 1 A+B C+D 2 B A+C D 2A+B +C A+2B C+2D A+2C +D A+D B+C 3 3A+B +C+D A+3B +C A+C+ 3D A+B+ 3C+D A B+D C 4 4A+B +C+D A+4B +C+D A+B+ C+4D A+B+ 4C+D

40 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood 4A+B +C+D A+4B +C+D A+B+ C+4D A+B+ 4C+D Reconstruction Back projections 3A3B 3D3C - (A+B+C+D) =/ (n-1) = AB DC

41 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Filtered back projection 18 Projections36 Projections90 Projections180 Projections

42 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood 1=Ram-Lak (ramp), 2=Shepp-Logan, 3=Cosine, and 4=Hamming Reconstruction FBP: Commonly used filters

43 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Filter application to sinogram in FFT space

44 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Filter application to sinogram in FFT space

45 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood

46 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood

47 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Projections Backproject Filter 1D Filter 2D Backproject Image Reconstruction Filtered back projection 2D/3D filtering is costly

48 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Fourier slice theorem Take a two-dimensional function f(r), project it onto a line, and do a Fourier transform of that projection Take that same function, but do a two-dimensional Fourier transform first, and then slice it through its origin parallel to the projection line

49 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Reconstruction Iterative Reconstruction Kaczmarz Method (=ART: Algebraic Reconstruction Technique) 1. Start by setting x(0) = 0 2. Compute the forward projection 3. Update the current estimate 4. Iterate steps 2,3 until the difference between new forward projection, computed in 2, and the old one is below tolerance

50 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood