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

2 Medical Imaging, SS-2010 Mohammad Dawood 2 Medical Imaging, SS-2010 Mohammad Dawood Edge detection

3 Medical Imaging, SS-2010 Mohammad Dawood 3 Medical Imaging, SS-2010 Mohammad Dawood *=*= Recognizing the edge

4 Medical Imaging, SS-2010 Mohammad Dawood 4 Medical Imaging, SS-2010 Mohammad Dawood *=*= Increasing edge thickness - easier to detect and better connected edges

5 Medical Imaging, SS-2010 Mohammad Dawood 5 Medical Imaging, SS-2010 Mohammad Dawood *=*= Strengthening the edges

6 Medical Imaging, SS-2010 Mohammad Dawood 6 Medical Imaging, SS-2010 Mohammad Dawood Edge detection with spatial operators Prewitt operators

7 Medical Imaging, SS-2010 Mohammad Dawood 7 Medical Imaging, SS-2010 Mohammad Dawood Adding operators =+=

8 Medical Imaging, SS-2010 Mohammad Dawood 8 Medical Imaging, SS-2010 Mohammad Dawood Derivatives of an image

9 Medical Imaging, SS-2010 Mohammad Dawood 9 Medical Imaging, SS-2010 Mohammad Dawood Laplace operator H+V Laplace

10 Medical Imaging, SS-2010 Mohammad Dawood 10 Medical Imaging, SS-2010 Mohammad Dawood Cardiac PET

11 Medical Imaging, SS-2010 Mohammad Dawood 11 Medical Imaging, SS-2010 Mohammad Dawood Gaussian+Gradient *=*=

12 Medical Imaging, SS-2010 Mohammad Dawood 12 Medical Imaging, SS-2010 Mohammad Dawood Sobel operators Edge detection with spatial operators

13 Medical Imaging, SS-2010 Mohammad Dawood 13 Medical Imaging, SS-2010 Mohammad Dawood =+=

14 Medical Imaging, SS-2010 Mohammad Dawood 14 Medical Imaging, SS-2010 Mohammad Dawood Scharr operators Edge detection with spatial operators

15 Medical Imaging, SS-2010 Mohammad Dawood 15 Medical Imaging, SS-2010 Mohammad Dawood Roberts operators Edge detection with spatial operators +

16 Medical Imaging, SS-2010 Mohammad Dawood 16 Medical Imaging, SS-2010 Mohammad Dawood Canny operator Gaussian for noise reduction Calculation of edges in four direction 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

17 Medical Imaging, SS-2010 Mohammad Dawood 17 Medical Imaging, SS-2010 Mohammad Dawood Canny operator

18 Medical Imaging, SS-2010 Mohammad Dawood 18 Medical Imaging, SS-2010 Mohammad Dawood Marr-Hildreth operator Laplace of the Gaussian (LoG)

19 Medical Imaging, SS-2010 Mohammad Dawood 19 Medical Imaging, SS-2010 Mohammad Dawood Marr Hildreth operator

20 Medical Imaging, SS-2010 Mohammad Dawood 20 Medical Imaging, SS-2010 Mohammad Dawood Hough Transform

21 Medical Imaging, SS-2010 Mohammad Dawood 21 Medical Imaging, SS-2010 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

22 Medical Imaging, SS-2010 Mohammad Dawood 22 Medical Imaging, SS-2010 Mohammad Dawood Hough transform for detecting lines Alternative definition of lines

23 Medical Imaging, SS-2010 Mohammad Dawood 23 Medical Imaging, SS-2010 Mohammad Dawood Hough transform Similar transforms can be defined for circles, ellipses or other parametric curves

24 Medical Imaging, SS-2010 Mohammad Dawood 24 Medical Imaging, SS-2010 Mohammad Dawood Morphological operations

25 Medical Imaging, SS-2010 Mohammad Dawood 25 Medical Imaging, SS-2010 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

26 Medical Imaging, SS-2010 Mohammad Dawood 26 Medical Imaging, SS-2010 Mohammad Dawood Erosion If A is an image and B is a structure element then X

27 Medical Imaging, SS-2010 Mohammad Dawood 27 Medical Imaging, SS-2010 Mohammad Dawood Dilation X

28 Medical Imaging, SS-2010 Mohammad Dawood 28 Medical Imaging, SS-2010 Mohammad Dawood Closing Dilation + Erosion

29 Medical Imaging, SS-2010 Mohammad Dawood 29 Medical Imaging, SS-2010 Mohammad Dawood Opening Erosion + Dilation