1. Medical Imaging Mohammad Dawood Department of Computer Science University of Münster Germany

2. 2 Medical Imaging, SS-2011 Mohammad Dawood Recap

3. 3 Medical Imaging, SS-2011 Mohammad Dawood Grayscale transformations 1.Linear 2.Logarithmic 3.Power law Point operations Local operators 1.Histogram Equalization 2.Adpative/Local Hist Eq 3.Color space 4.Fourier transform 5.Spatial filtering 33330 35330 33330 00000 00000 111 111 111

4. 4 Medical Imaging, SS-2011 Mohammad Dawood Edge detection

5. 5 Medical Imaging, SS-2011 Mohammad Dawood 15 00000 00000 1 00000 00000 15 00000 00000 *=*= Recognizing the edge

6. 6 Medical Imaging, SS-2011 Mohammad Dawood 15 00000 00000 1 0 00000 00000 15 00000 *=*= Increasing edge thickness - easier to detect and better connected edges

7. 7 Medical Imaging, SS-2011 Mohammad Dawood 111 000 *=*= 15 00000 00000 00000 00000 45 00000 Strengthening the edges

8. 8 Medical Imaging, SS-2011 Mohammad Dawood 10 10 10 111 000 Edge detection with spatial operators Prewitt operators

9. 9 Medical Imaging, SS-2011 Mohammad Dawood 210 10 0 -2 Adding operators 10 10 10 111 000 +=+=

10. 10 Medical Imaging, SS-2011 Mohammad Dawood Derivatives of an image 1 1-21 Magnitude of gradient: Angle:

11. 11 Medical Imaging, SS-2011 Mohammad Dawood 1 First derivative Forward difference Backward difference Central difference 1 -0.500.5 MRI Spinefw bw cdbw_i bw+bw_i

12. 12 Medical Imaging, SS-2011 Mohammad Dawood 010 1-41 010 Laplace operator H+V Laplace

13. 13 Medical Imaging, SS-2011 Mohammad Dawood Cardiac PET

14. 14 Medical Imaging, SS-2011 Mohammad Dawood 121 000 -2 15 00000 00000 00000 00000 60 00000 Gaussian+Gradient *=*=

15. 15 Medical Imaging, SS-2011 Mohammad Dawood Sobel operators 10 20-2 10 121 000 -2 Edge detection with spatial operators

16. 16 Medical Imaging, SS-2011 Mohammad Dawood 220 20-2 0 10 20-2 10 121 000 -2 +=+=

17. 17 Medical Imaging, SS-2011 Mohammad Dawood Scharr operators 30-3 100-10 30-3 3103 000 -3-10-3 Edge detection with spatial operators

18. 18 Medical Imaging, SS-2011 Mohammad Dawood Roberts operators 01 0 10 0 Edge detection with spatial operators +

19. 19 Medical Imaging, SS-2011 Mohammad Dawood Canny operator Gaussian for noise reduction Calculation of edges in four directions (sobel operator) non-maximum suppression angle zero: if intensity >the intensities in the N and S directions angle is 90: if intensity >the intensities in the W and E directions angle is 135: if intensity >the intensities in the NE and SW directions angle is 45 degrees: if intensity >the intensities in the NW and SE directions

20. 20 Medical Imaging, SS-2011 Mohammad Dawood Canny operatorth=0.5 th=0.1

21. 21 Medical Imaging, SS-2011 Mohammad Dawood Marr-Hildreth operator Laplace of the Gaussian (LoG)

22. 22 Medical Imaging, SS-2011 Mohammad Dawood Marr Hildreth operator sigma=1 sigma=2

23. 23 Medical Imaging, SS-2011 Mohammad Dawood Marr Hildreth operator

24. 24 Medical Imaging, SS-2011 Mohammad Dawood Hough Transform

25. 25 Medical Imaging, SS-2011 Mohammad Dawood Hough transform for detecting lines A line can be defined as: Take the edge map of the image I Look for the neighbors of a pixel and determine m and b Accumulate the m and b in an accumulator array Find the maxima of the accumulator array Transform them back to image space

26. 26 Medical Imaging, SS-2011 Mohammad Dawood Hough transform for detecting lines Alternative definition of lines

27. 27 Medical Imaging, SS-2011 Mohammad Dawood Hough transform Similar transforms can be defined for circles, ellipses or other parametric curves

28. 28 Medical Imaging, SS-2011 Mohammad Dawood Morphological operations

29. 29 Medical Imaging, SS-2011 Mohammad Dawood Morphological operators Operations are based on Set Theory and require a structure element Basic morphological operations are: 1.Erosion 2.Dilation 3.Opening 4.Closing

30. 30 Medical Imaging, SS-2011 Mohammad Dawood Erosion If A is an image and B is a structure element then 00000 01110 00110 00110 00010 000 011 010 00000 00100 00100 00000 00000 X

31. 31 Medical Imaging, SS-2011 Mohammad Dawood Dilation 00000 01110 00110 00110 00010 000 011 010 01110 11110 01110 01110 00110 X

32. 32 Medical Imaging, SS-2011 Mohammad Dawood Closing Dilation + Erosion

33. 33 Medical Imaging, SS-2011 Mohammad Dawood Opening Erosion + Dilation