1 Medical Imaging, SS-2014 Dr. Mohammad Dawood Medical Image Analysis Dr. Mohammad Dawood Department of Computer Science University of Münster Germany
Medical Image Analysis Dr. Mohammad Dawood Department of Computer Science University of Münster Germany.
Apr 01, 2015
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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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Recognizing the edge
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
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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
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-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
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-1 -1 -1
Edge detection with spatial operators
Prewitt operators
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
2 1 0
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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-1 -2 -1
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Gaussian+Gradient
* =
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Sobel operators
1 0 -1
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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X
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Dilation
0 0 0 0 0
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0 1 1
0 1 0
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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
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