1. 3D Vision
Interest Points

2. correspondence and alignment
Correspondence: matching points, patches, edges, or regions across images ≈

3. correspondence and alignment
Alignment: solving the transformation that makes two things match better T

4. Example: estimating “fundamental matrix” that corresponds two views

5. Example: tracking points
frame 0
frame 22
frame 49
Your problem 1 for HW 2!

6. Human eye movements
Your eyes don’t see everything at once, but they jump around. You see only about 2 degrees with high resolution

7. Human eye movements

8. Interest points
original
Suppose you have to click on some point, go away and come back after I deform the image, and click on the same points again.
Which points would you choose?
deformed

9. Overview of Keypoint Matching
1. Find a set of distinctive key- points
2. Define a region around each keypoint A1 A2 A3 B1 B2 B3
3. Extract and normalize the region content
4. Compute a local descriptor from the normalized region
5. Match local descriptors

10. Goals for Keypoints
Detect points that are repeatable and distinctive

11. Choosing interest points
Where would you tell your friend to meet you?
Corners!

12. Moravec corner detector (1980)
We should easily recognize the point by looking through a small window
Shifting a window in any direction should give a large change in intensity

13. Moravec corner detector
flat

14. Moravec corner detector
flat

15. Moravec corner detector
flat
edge

16. Moravec corner detector
isolated point
flat
edge

17. Moravec corner detector
Change of intensity for the shift [u,v]:
Intensity
Window function
Shifted intensity
Four shifts: (u,v) = (1,0), (1,1), (0,1), (-1, 1)
Look for local maxima in min{E}

18. Problems of Moravec detector
Noisy response due to a binary window function
Only a set of shifts at every 45 degree is considered
Responds too strong for edges because only minimum of E is taken into account
Harris corner detector (1988) solves these problems.

19. Harris corner detector
Noisy response due to a binary window function
Use a Gaussian function

20. Harris corner detector
Only a set of shifts at every 45 degree is considered
Consider all small shifts by Taylor’s expansion

21. 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:

22. Harris corner detector
Responds too strong for edges because only minimum of E is taken into account
A new corner measurement

23. Harris corner detector
Intensity change in shifting window: eigenvalue analysis
1, 2 – eigenvalues of M
direction of the fastest change
Ellipse E(u,v) = const
direction of the slowest change
(max)-1/2
(min)-1/2

24. Harris corner detector2
edge 2 >> 1
Classification of image points using eigenvalues of M:
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
flat 1

25. Harris corner detector
Measure of corner response:
(k – empirical constant, k = )

26. Another view

27. Another view

28. Another view

29. Harris corner detector (input)

30. Corner response R

31. Threshold on R

32. Local maximum of R

33. Harris corner detector

34. Harris Detector: Summary
Average intensity change in direction [u,v] can be expressed as a bilinear form:
Describe a point in terms of eigenvalues of M: measure of corner response
A good (corner) point should have a large intensity change in all directions, i.e. R should be large positive

35. Harris Detector: Some Properties
Partial invariance to affine intensity change
Only derivatives are used => invariance to intensity shift I  I + b
Intensity scale: I  a I R
x (image coordinate)
threshold

36. Harris Detector: Some Properties
Rotation invariance
Ellipse rotates but its shape (i.e. eigenvalues) remains the same
Corner response R is invariant to image rotation

37. Harris Detector is rotation invariant
Repeatability rate:
# correspondences # possible correspondences

38. Harris Detector: Some Properties
But: non-invariant to image scale!
All points will be classified as edges
Corner !

39. Harris Detector: Some Properties
Quality of Harris detector for different scale changes
Repeatability rate:
# correspondences # possible correspondences