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

Recap

Grayscale transformations Linear Logarithmic Power law Point operations Local operators Histogram Equalization Adpative/Local Hist Eq Color space Fourier transform Spatial filtering 3 5 1

Edge detection

What is an “edge”? Discontinuity in Image brightness

Recognizing the edge 15 15 1 -1 * =

Increasing edge thickness - easier to detect and better connected edges 15 15 1 -1 * =

Strengthening the edges 15 45 1 -1 * =

Edge detection with spatial operators 1 -1 1 -1 Prewitt operators

Adding operators 1 -1 1 -1 2 1 -1 -2 + =

Derivatives of an image -1 1 1 -2 Magnitude of gradient: Angle:

First derivative Forward difference Backward difference Central difference -1 1 1 -1 -0.5 0.5 MRI Spine fw bw cd bw_i bw+bw_i

Laplace operator 1 -4 H+V Laplace

Cardiac PET

Gaussian+Gradient 15 60 1 2 -1 -2 * =

Edge detection with spatial operators 1 2 -1 -2 1 -1 2 -2 Sobel operators

1 2 -1 -2 1 -1 2 -2 2 -2 + =

Edge detection with spatial operators 3 10 -3 -10 3 -3 10 -10 Scharr operators

Edge detection with spatial operators 1 -1 1 -1 Roberts operators +

Canny operator Gaussian for noise reduction Calculation of edges (sobel operator) 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 Hysteresis delete edges below threshold 1 keep edges above threshold 2 keep edges between thresholds, if one neighbor is above threshold 2

Canny operator th=0.5 th=0.1

Marr-Hildreth operator Laplacian of the Gaussian (LoG)

Marr Hildreth operator sigma=1 sigma=2

Hough Transform

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

Hough transform for detecting lines Alternative definition of lines

Hough transform Similar transforms can be defined for circles, ellipses or other parametric curves

Morphological operations

Morphological operators Operations are based on Set Theory and require a structure element Basic morphological operations are: Erosion Dilation Opening Closing

Erosion If A is an image and B is a structure element then 1 1 1 X

Dilation 1 1 1 X

Closing Dilation + Erosion

Opening Erosion + Dilation