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Medical Image Analysis

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

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Medical Image Analysis

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

  2. Recap

  3. Grayscale transformations Linear Logarithmic Power law Point operations Local operators Histogram Equalization Adpative/Local HistEq Color space Fourier transform Spatial filtering

  4. Edge detection

  5. What is an “edge”? Discontinuity in Image brightness

  6. Recognizing the edge * =

  7. Increasing edge thickness - easier to detect and better connected edges * =

  8. Strengthening the edges * =

  9. Edge detection with spatial operators Prewitt operators

  10. Adding operators + =

  11. Derivatives of an image Magnitude of gradient: Angle:

  12. First derivative Forward difference Backward difference Central difference MRI Spine fwbwcdbw_ibw+bw_i

  13. Laplace operator H+V Laplace

  14. Cardiac PET

  15. Gaussian+Gradient * =

  16. Edge detection with spatial operators Sobel operators

  17. + =

  18. Edge detection with spatial operators Scharr operators

  19. Edge detection with spatial operators Roberts operators +

  20. 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

  21. Canny operator th=0.5 th=0.1

  22. Marr-Hildreth operator Laplacian of the Gaussian (LoG)

  23. Marr Hildreth operatorsigma=1 sigma=2

  24. Hough Transform

  25. 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

  26. Hough transform for detecting lines Alternative definition of lines

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

  28. Morphological operations

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

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

  31. Dilation X

  32. Closing Dilation + Erosion

  33. Opening Erosion + Dilation

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