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

## Presentation on theme: "Medical Image Analysis Dr. Mohammad Dawood Department of Computer Science University of Münster Germany."— Presentation transcript:

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

2 Medical Imaging, SS-2014 Dr. Mohammad Dawood Recap

3 Medical Imaging, SS-2014 Dr. 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 Medical Imaging, SS-2014 Dr. Mohammad Dawood Edge detection

5 Medical Imaging, SS-2014 Dr. Mohammad Dawood What is an “edge”? Discontinuity in Image brightness

6 Medical Imaging, SS-2014 Dr. Mohammad Dawood 15 00000 00000 1 00000 00000 15 00000 00000 *=*= Recognizing the edge

7 Medical Imaging, SS-2014 Dr. Mohammad Dawood 15 00000 00000 1 0 00000 00000 15 00000 *=*= Increasing edge thickness - easier to detect and better connected edges

8 Medical Imaging, SS-2014 Dr. Mohammad Dawood 111 000 *=*= 15 00000 00000 00000 00000 45 00000 Strengthening the edges

9 Medical Imaging, SS-2014 Dr. Mohammad Dawood 10 10 10 111 000 Edge detection with spatial operators Prewitt operators

10 Medical Imaging, SS-2014 Dr. Mohammad Dawood 210 10 0 -2 Adding operators 10 10 10 111 000 +=+=

11 Medical Imaging, SS-2014 Dr. Mohammad Dawood Derivatives of an image 1 1-21 Magnitude of gradient: Angle:

12 Medical Imaging, SS-2014 Dr. Mohammad Dawood 1 First derivative Forward difference Backward difference Central difference 1 -0.500.5 MRI Spinefw bw cdbw_i bw+bw_i

13 Medical Imaging, SS-2014 Dr. Mohammad Dawood 010 1-41 010 Laplace operator H+V Laplace

14 Medical Imaging, SS-2014 Dr. Mohammad Dawood Cardiac PET

15 Medical Imaging, SS-2014 Dr. Mohammad Dawood 121 000 -2 15 00000 00000 00000 00000 60 00000 Gaussian+Gradient *=*=

16 Medical Imaging, SS-2014 Dr. Mohammad Dawood Sobel operators 10 20-2 10 121 000 -2 Edge detection with spatial operators

17 Medical Imaging, SS-2014 Dr. Mohammad Dawood 220 20-2 0 10 20-2 10 121 000 -2 +=+=

18 Medical Imaging, SS-2014 Dr. Mohammad Dawood Scharr operators 30-3 100-10 30-3 3103 000 -3-10-3 Edge detection with spatial operators

19 Medical Imaging, SS-2014 Dr. Mohammad Dawood Roberts operators 01 0 10 0 Edge detection with spatial operators +

20 Medical Imaging, SS-2014 Dr. Mohammad Dawood Canny operator 1.Gaussian for noise reduction 2.Calculation of edges (sobel operator) 3.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 4.Hysteresis delete edges below threshold 1 keep edges above threshold 2 keep edges between thresholds, if one neighbor is above threshold 2

21 Medical Imaging, SS-2014 Dr. Mohammad Dawood Canny operatorth=0.5 th=0.1

22 Medical Imaging, SS-2014 Dr. Mohammad Dawood Marr-Hildreth operator Laplacian of the Gaussian (LoG)

23 Medical Imaging, SS-2014 Dr. Mohammad Dawood Marr Hildreth operator sigma=1 sigma=2

24 Medical Imaging, SS-2014 Dr. Mohammad Dawood Hough Transform

25 Medical Imaging, SS-2014 Dr. 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-2014 Dr. Mohammad Dawood Hough transform for detecting lines Alternative definition of lines

27 Medical Imaging, SS-2014 Dr. Mohammad Dawood Hough transform Similar transforms can be defined for circles, ellipses or other parametric curves

28 Medical Imaging, SS-2014 Dr. Mohammad Dawood Morphological operations

29 Medical Imaging, SS-2014 Dr. 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-2014 Dr. 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 Medical Imaging, SS-2014 Dr. Mohammad Dawood Dilation 00000 01110 00110 00110 00010 000 011 010 01110 11110 01110 01110 00110 X

32 Medical Imaging, SS-2014 Dr. Mohammad Dawood Closing Dilation + Erosion

33 Medical Imaging, SS-2014 Dr. Mohammad Dawood Opening Erosion + Dilation