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

2. Recap

3. Grayscale transformations Linear Logarithmic Power law
Point operations
Local operators
Histogram Equalization
Adpative/Local Hist Eq
Color space
Fourier transform
Spatial filtering 3 5 1

4. Edge detection

5. What is an “edge”?
Discontinuity in Image brightness

6. Recognizing the edge 15 15 1 -1
* =

7. Increasing edge thickness
- easier to detect and better connected edges 15 15 1 -1
* =

8. Strengthening the edges15 45 1 -1
* =

9. Edge detection with spatial operators1 -1 1 -1
Prewitt operators

10. Adding operators 1 -1 1 -1 2 1 -1 -2
+ =

11. Derivatives of an image-1 1 1 -2
Magnitude of gradient:
Angle:

12. First derivative
Forward difference
Backward difference
Central difference -1 1 1 -1
-0.5
0.5
MRI Spine fw bw cd bw_i bw+bw_i

13. Laplace operator 1 -4
H+V Laplace

14. Cardiac PET

15. Gaussian+Gradient 15 60 1 2 -1 -2
* =

16. Edge detection with spatial operators1 2 -1 -2 1 -1 2 -2
Sobel operators

17. 1 2 -1 -2 1 -1 2 -2 2 -2
+ =

18. Edge detection with spatial operators3 10 -3
-10 3 -3 10
-10
Scharr operators

19. Edge detection with spatial operators1 -1 1 -1
Roberts operators +

20. Canny operator
Gaussian for noise reduction
Calculation of edges (sobel operator)
Non-maximum suppression, no neighbor should have a higher gradient except in the same direction
0 : if intensity > the intensities in the N and S directions
45 : if intensity > the intensities in the NW and SE directions
90 : if intensity > the intensities in the W and E directions
135 : if intensity > the intensities in the NE and SW directions
Hysteresis
delete edges below threshold 1
keep edges above threshold 2
keep edges between thresholds, if one neighbor is above threshold 2

21. Canny operator th= th=0.1

22. Marr-Hildreth operator
Laplacian of the Gaussian (LoG)

23. Marr Hildreth operator sigma=1 sigma=2

24. Hough Transform

25. 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. Hough transform for detecting lines
Alternative definition of lines

27. Hough transform
Similar transforms can be defined for circles, ellipses or other parametric curves

28. Morphological operations

29. Morphological operators
Operations are based on Set Theory and require a structure element
Basic morphological operations are:
Erosion
Dilation
Opening
Closing

30. Erosion
If A is an image and B is a structure element then 1 1 1 X

31. Dilation 1 1 1 X

32. Closing
Dilation + Erosion

33. Opening
Erosion + Dilation