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

2 Medical Imaging, SS-2011 Mohammad Dawood Recap

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

4 Medical Imaging, SS-2011 Mohammad Dawood Edge detection

5 Medical Imaging, SS-2011 Mohammad Dawood *=*= Recognizing the edge

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

7 Medical Imaging, SS-2011 Mohammad Dawood *=*= Strengthening the edges

8 Medical Imaging, SS-2011 Mohammad Dawood Edge detection with spatial operators Prewitt operators

9 Medical Imaging, SS-2011 Mohammad Dawood Adding operators =+=

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

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

12 Medical Imaging, SS-2011 Mohammad Dawood Laplace operator H+V Laplace

13 Medical Imaging, SS-2011 Mohammad Dawood Cardiac PET

14 Medical Imaging, SS-2011 Mohammad Dawood Gaussian+Gradient *=*=

15 Medical Imaging, SS-2011 Mohammad Dawood Sobel operators Edge detection with spatial operators

16 Medical Imaging, SS-2011 Mohammad Dawood =+=

17 Medical Imaging, SS-2011 Mohammad Dawood Scharr operators Edge detection with spatial operators

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

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

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

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

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

24 Medical Imaging, SS-2011 Mohammad Dawood Hough Transform

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

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

28 Medical Imaging, SS-2011 Mohammad Dawood Morphological operations

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 Medical Imaging, SS-2011 Mohammad Dawood Erosion If A is an image and B is a structure element then X

31 Medical Imaging, SS-2011 Mohammad Dawood Dilation X

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

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