Medical Image Analysis

Dr. Mohammad Dawood

Department of Computer Science

University of Münster Germany

Dr. Mohammad Dawood Medical Imaging, SS-2014

Recap

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 Dr. Mohammad Dawood Medical Imaging, SS-2014 3 3 3 0 0 3 5 3 0 0 3 3 3 0 0 3 3 3 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 3

Dr. Mohammad Dawood Medical Imaging, SS-2014

Edge detection

Medical Imaging, SS-2014 What is an “edge”?

Discontinuity in Image brightness Dr. Mohammad Dawood 5

Medical Imaging, SS-2014 Recognizing the edge 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 0 0 0 0 0 0 0 0 0 0 * 1 -1 = Dr. Mohammad Dawood 0 0 15 15 15 15 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6

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

Strengthening the edges Medical Imaging, SS-2014 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 0 0 0 0 0 0 0 0 0 0 * 1 1 1 0 0 0 -1 -1 -1 = Dr. Mohammad Dawood 0 0 45 45 45 45 45 45 45 45 45 45 0 0 0 0 0 0 0 0 0 0 0 0 0 8

Medical Imaging, SS-2014 Edge detection with spatial operators Prewitt operators Dr. Mohammad Dawood 1 0 1 0 1 0 -1 -1 -1 1 1 1 0 0 0 -1 -1 -1 9

Adding operators Medical Imaging, SS-2014 Dr. Mohammad Dawood 1 0 1 0 1 0 -1 -1 -1 + 1 1 1 0 0 0 -1 -1 -1 = 2 1 0 1 0 0 -1 -1 -2 10

Derivatives of an image Medical Imaging, SS-2014

-1 1 1 -2 1

Magnitude of gradient: Angle: Dr. Mohammad Dawood 11

Medical Imaging, SS-2014 First derivative Forward difference Backward difference Central difference

1 -1 1 -1 -0.5

0 0.5

MRI Spine Dr. Mohammad Dawood fw bw cd bw_i bw+bw_i 12

Laplace operator Dr. Mohammad Dawood 0 1 0 1 -4 1 0 1 0 Medical Imaging, SS-2014 H+V Laplace 13

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

Medical Imaging, SS-2014 Gaussian+Gradient 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 0 0 0 0 0 0 0 0 0 0 * 1 0 2 0 1 0 -1 -2 -1 = Dr. Mohammad Dawood 0 0 60 60 60 60 60 60 60 60 60 60 0 0 0 0 0 0 0 0 0 0 0 0 0 15

Medical Imaging, SS-2014 Edge detection with spatial operators Sobel operators Dr. Mohammad Dawood 1 0 2 0 1 0 -1 -2 -1 1 2 1 0 0 0 -1 -2 -1 16

Medical Imaging, SS-2014 Dr. Mohammad Dawood 1 0 2 0 1 0 -1 -2 -1 + 1 2 1 0 0 0 -1 -2 -1 = 2 2 0 2 0 0 -2 -2 -2 17

Medical Imaging, SS-2014 Edge detection with spatial operators Scharr operators Dr. Mohammad Dawood 3 10 3 0 0 0 -3 -10 -3 3 10 3 0 0 0 -3 -10 -3 18

Medical Imaging, SS-2014 Edge detection with spatial operators Roberts operators 1 0 0 -1 + 0 -1 1 0 Dr. Mohammad Dawood 19

Medical Imaging, SS-2014 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 Dr. Mohammad Dawood 20

Medical Imaging, SS-2014 Canny operator Dr. Mohammad Dawood th=0.5

th=0.1

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

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

Dr. Mohammad Dawood Medical Imaging, SS-2014

Hough Transform

Medical Imaging, SS-2014 Hough transform for detecting lines A line can be defined as: Take the edge map of the image

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 Dr. Mohammad Dawood 25

Medical Imaging, SS-2014 Hough transform for detecting lines Alternative definition of lines Dr. Mohammad Dawood 26

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

Dr. Mohammad Dawood Medical Imaging, SS-2014

Morphological operations

Medical Imaging, SS-2014 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 Dr. Mohammad Dawood 29

Medical Imaging, SS-2014 Erosion If A is an image and B is a

structure element then

0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 Dr. Mohammad Dawood 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 30

Medical Imaging, SS-2014 Dilation 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 Dr. Mohammad Dawood 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 31

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

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