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# Harris Method

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### Harris Method

1. 1. Harris corner detector
2. 2. Moravec corner detector (1980) <ul><li>We should easily recognize the point by looking through a small window </li></ul><ul><li>Shifting a window in any direction should give a large change in intensity </li></ul>
3. 3. Moravec corner detector flat
4. 4. Moravec corner detector flat
5. 5. Moravec corner detector flat edge
6. 6. Moravec corner detector flat edge corner isolated point
7. 7. Moravec corner detector <ul><li>Change of intensity for the shift [ u,v ]: </li></ul>Four shifts: (u,v) = (1,0), (1,1), (0,1), (-1, 1) Look for local maxima in min{E} Intensity Shifted intensity Window function
8. 8. Problems of Moravec detector <ul><li>Noisy response due to a binary window function </li></ul><ul><li>Only a set of shifts at every 45 degree is considered </li></ul><ul><li>Responds too strong for edges because only minimum of E is taken into account </li></ul><ul><li>Harris corner detector (1988) solves these problems. </li></ul>
9. 9. Harris corner detector <ul><li>Noisy response due to a binary window function </li></ul><ul><li>Use a Gaussian function </li></ul>
10. 10. Harris corner detector <ul><li>Only a set of shifts at every 45 degree is considered </li></ul><ul><li>Consider all small shifts by Taylor’s expansion </li></ul>
11. 11. Harris corner detector Equivalently, for small shifts [ u,v ] we have a bilinear approximation: , where M is a 2  2 matrix computed from image derivatives :
12. 12. Harris corner detector <ul><li>Responds too strong for edges because only minimum of E is taken into account </li></ul><ul><li>A new corner measurement </li></ul>
13. 13. Harris corner detector Intensity change in shifting window: eigenvalue analysis  1 ,  2 – eigenvalues of M direction of the slowest change direction of the fastest change (  max ) -1/2 (  min ) -1/2 Ellipse E(u,v) = const
14. 14. Harris corner detector  1  2 Corner  1 and  2 are large,  1 ~  2 ; E increases in all directions  1 and  2 are small; E is almost constant in all directions edge  1 >>  2 edge  2 >>  1 flat Classification of image points using eigenvalues of M :
15. 15. Harris corner detector Measure of corner response: ( k – empirical constant, k = 0.04-0.06)
16. 16. Another view
17. 17. Another view
18. 18. Another view
19. 19. Summary of Harris detector
20. 20. Harris corner detector (input)
21. 21. Corner response R
22. 22. Threshold on R
23. 23. Local maximum of R
24. 24. Harris corner detector
25. 25. Harris Detector: Summary <ul><li>Average intensity change in direction [ u,v ] can be expressed as a bilinear form: </li></ul><ul><li>Describe a point in terms of eigenvalues of M : measure of corner response </li></ul><ul><li>A good (corner) point should have a large intensity change in all directions , i.e. R should be large positive </li></ul>