More on Features

1. More on Features Digital Visual Effects, Spring 2007 Yung-Yu Chuang 2007/3/27 with slides by Trevor DarrellCordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins, Brad Osgood, W W L Chen, and Jiwon Kim

2. Announcements • Project #1 is online, you have to write a program, not just using available software. • Send me the members of your team. • Sign up for scribe at the forum.

3. Blender http://www.blender3d.com/cms/Home.2.0.html Blender could be used for your project #3 matchmove.

4. In the forum • Barycentric coordinate • RBF

5. Outline • Block matching • Features • Harris corner detector • SIFT • SIFT extensions • Applications

6. Correspondence by block matching • Points are individually ambiguous • More unique matches are possible with small regions of images

7. Correspondence by block matching

8. Sum of squared distance

9. Image blocks as a vector

10. Image blocks as a vector

11. Matching metrics

12. Features • Properties of features • Detector: locates feature • Descriptor and matching metrics: describes and matches features • In the example for block matching: • Detector: none • Descriptor: block • Matching: distance

13. Desired properties for features • Invariant: invariant to scale, rotation, affine, illumination and noise for robust matching across a substantial range of affine distortion, viewpoint change and so on. • Distinctive: a single feature can be correctly matched with high probability

14. Harris corner detector

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

16. Moravec corner detector flat

17. Moravec corner detector flat

18. Moravec corner detector flat edge

19. Moravec corner detector corner isolated point flat edge

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

21. 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.

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

23. Announcements • Project #1 was due at noon today. You have a total of 10 delay days without penalty, but you are advised to use them wisely. • We reserve the rights for not including late homework for artifact voting. • Project #2 handout will be available on the web today. • We may not have class next week. I will send out mails if the class is canceled.

24. Outline • Harris corner detector • SIFT • SIFT extensions • MSOP

25. Three components for features • Feature detection • Feature description • Feature matching

26. Harris corner detector

27. Harris corner detector • Consider all small shifts by Taylor’s expansion

28. 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:

29. Harris corner detector (matrix form)

30. Quadratic forms • Quadratic form (homogeneous polynomial of degree two) of n variables xi • Examples =

31. Symmetric matrices • Quadratic forms can be represented by a real symmetric matrix A where

32. Eigenvalues of symmetric matrices Brad Osgood

33. Eigenvectors of symmetric matrices

34. Visualize quadratic functions

35. Visualize quadratic functions

36. Visualize quadratic functions

37. Visualize quadratic functions

38. 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

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

40. Harris corner detector Measure of corner response: (k – empirical constant, k = 0.04-0.06)

41. Harris corner detector

42. Summary of Harris detector

43. ) ( Now we know where features are • But, how to match them? • What is the descriptor for a feature? The simplest solution is the intensities of its spatial neighbors. This might not be robust to brightness change or small shift/rotation.

44. 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

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

46. Scale invariant detection • The problem: how do we choose corresponding circles independently in each image? • Aperture problem

47. SIFT (Scale Invariant Feature Transform)

48. SIFT • SIFT is an carefully designed procedure with empirically determined parameters for the invariant and distinctive features.

49. descriptor detector ( ) local descriptor SIFT stages: • Scale-space extrema detection • Keypoint localization • Orientation assignment • Keypoint descriptor matching A 500x500 image gives about 2000 features

50. 1. Detection of scale-space extrema • For scale invariance, search for stable features across all possible scales using a continuous function of scale, scale space. • SIFT uses DoG filter for scale space because it is efficient and as stable as scale-normalized Laplacian of Gaussian.