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Medical Image Analysis
Dr. Mohammad Dawood
Department of Computer Science
University of MünsterGermany
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Recap
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Grayscale transformations1. Linear2. Logarithmic3. Power law
Point operations
Local operators
4. Histogram Equalization5. Adpative/Local Hist Eq6. Color space7. Fourier transform8. Spatial filtering
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Edge detection
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
What is an “edge”?Discontinuity in Image brightness
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
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-1
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* =
Recognizing the edge
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
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-1
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Increasing edge thickness- easier to detect and better connected edges
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
1 1 1
0 0 0
-1 -1 -1* =
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Strengthening the edges
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
1 0 -1
1 0 -1
1 0 -1
1 1 1
0 0 0
-1 -1 -1
Edge detection with spatial operators
Prewitt operators
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
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1 0 -1
0 -1 -2
Adding operators
1 0 -1
1 0 -1
1 0 -1
1 1 1
0 0 0
-1 -1 -1+ =
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Derivatives of an image
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1 -2 1
Magnitude of gradient:
Angle:
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
-1 1
First derivative
Forward difference
Backward difference
Central difference
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-0.5 0 0.5
MRI Spine fw bw cd bw_i bw+bw_i
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
0 1 0
1 -4 1
0 1 0
Laplace operator
H+V Laplace
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Cardiac PET
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
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0 0 0
-1 -2 -1
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0 0 0 0 0
Gaussian+Gradient
* =
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Sobel operators
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2 0 -2
1 0 -1
1 2 1
0 0 0
-1 -2 -1
Edge detection with spatial operators
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
2 2 0
2 0 -2
0 -2 -2
1 0 -1
2 0 -2
1 0 -1
1 2 1
0 0 0
-1 -2 -1+ =
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Scharr operators
3 0 -3
10 0 -10
3 0 -3
3 10 3
0 0 0
-3 -10 -3
Edge detection with spatial operators
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Roberts operators0 1
-1 0
1 0
0 -1
Edge detection with spatial operators
+
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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 directions45 : if intensity > the intensities in the NW and SE directions90 : if intensity > the intensities in the W and E directions135 : if intensity > the intensities in the NE and SW directions
4. Hysteresisdelete edges below threshold 1keep edges above threshold 2keep edges between thresholds, if one neighbor is above threshold 2
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Canny operator th=0.5 th=0.1
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Marr-Hildreth operator
Laplacian of the Gaussian (LoG)
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Marr Hildreth operator sigma=1 sigma=2
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Hough Transform
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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
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Hough transform for detecting lines
Alternative definition of lines
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Hough transform
Similar transforms can be defined for circles, ellipses or other parametric curves
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Morphological operations
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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. Erosion2. Dilation3. Opening4. Closing
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Erosion
If A is an image and B is a structure element then
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0 0 0 0 0
X
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Dilation
0 0 0 0 0
0 1 1 1 0
0 0 1 1 0
0 0 1 1 0
0 0 0 1 0
0 0 0
0 1 1
0 1 0
0 1 1 1 0
1 1 1 1 0
0 1 1 1 0
0 1 1 1 0
0 0 1 1 0
X
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Closing
Dilation + Erosion
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Opening
Erosion + Dilation
