1. Interest Point Detectors (see CS485/685 notes for more details)
CS491Y/691Y Topics in Computer Vision
Dr. George Bebis

2. What is an Interest Point?
A point in an image which has a well-defined position and can be robustly detected.
Typically associated with a significant change of one or more image properties simultaneously (e.g., intensity, color, texture). 2

3. What is an Interest Point? (cont’d)
Corners is a special case of interest points.
However, interest points could be more generic than corners. 3

4. Why are interest points useful?
Could be used to find corresponding points between images which is very useful for numerous applications!
panorama stitching
stereo matching
left camera
right camera

5. How to find corresponding points?
( ) = ?
feature descriptor
Need to define local patches surrounding the interest points and extract feature descriptors from every patch.
Match feature descriptors to find corresponding points. 5

6. Properties of good features
Local: robust to occlusion and clutter.
Accurate: precise localization.
Covariant
Robust: noise, blur, compression, etc.
Efficient: close to real-time performance.
Repeatable

7. Interest point detectors should be covariant
Features should be detected in corresponding locations despite geometric or photometric changes. 7

8. Interest point descriptors should be invariant
( ) = ?
feature descriptor
Should be similar despite geometric
or photometric transformations 8 8

9. Interest point candidates
Use features with gradients in at least two, significantly
different orientations (e.g., corners, junctions etc)

10. Harris Corner Detector
Assuming a W x W window, it computes the matrix:
AW(x,y) is a 2 x 2 matrix called auto-correlation matrix.
fx, fy are the horizontal and vertical derivatives.
w(x,y) is a smoothing function (e.g., Gaussian)
C. Harris and M. Stephens. "A Combined Corner and Edge Detector”, Proceedings of the 4th Alvey Vision Conference: pages 147—151, 1988. 

11. Why is the auto-correlation matrix useful?
Describes the gradient distribution
(i.e., local structure) inside the
window!

12. Properties of the auto-correlation matrix
Aw is symmetric and can be decomposed :
We can visualize AW as an ellipse with axis lengths and directions determined by its eigenvalues and eigenvectors.
(max)1/2
(min)1/2 12

13. Harris Corner Detector (cont’d)
The eigenvectors of AW encode direction of intensity change.
The eigenvalues of AW encode strength of intensity change. v1 v2
direction of the slowest change
(max)1/2
(min)1/2
direction of the fastest change 13 13

14. Harris Corner Detector (cont’d)2
“Edge” 2 >> 1
“Corner” 1 and 2 are large, 1 ~ 2; intensity changes in all directions
Classification of pixels using the eigenvalues of AW :
1 and 2 are small; intensity is almost constant in all directions
“Edge” 1 >> 2
“Flat” region 1 14

15. Harris Corner Detector (cont’d)
To avoid computing the eigenvalues explicitly, the Harris detector uses the following function:
R(AW) = det(AW) – α trace2(AW)
which is equal to:
R(AW) = λ1 λ2- α (λ1+ λ2)2
α: is a const

16. Harris Corner Detector (cont’d)
“Corner” R > 0
“Edge” R < 0
“Flat” region
|R| small
Classification of image
points using R(AW):
R(AW) = det(AW) – α trace2(AW)
α: is usually between
0.04 and 0.06 16

17. Harris Corner Detector (cont’d)
Other functions:

18. Harris Corner Detector - Steps
Compute the horizontal and vertical (Gaussian) derivatives
σD is called the “differentiation” scale
2. Compute the three images involved in AW :

19. Harris Detector - Steps
3. Convolve each of the three images with a larger Gaussian
w(x,y) :
Gaussian
σI is called the “integration” scale
4. Determine cornerness:
R(AW) = det(AW) – α trace2(AW)
5. Find local maxima

20. Harris Corenr Detector - Example

21. Harris Detector - Example21

22. Compute corner response R22

23. Find points with large corner response: R>threshold23

24. Take only the points of local maxima of R

25. Map corners on the original image (for visualization)25

26. Harris Corner Detector (cont’d)
Rotation invariant
Sensitive to:
Scale change
Significant viewpoint change
Significant contrast change

27. Multi-scale Harris Detector
Detect interest points at varying scales.
R(AW) = det(AW(x,y,σI,σD)) – α trace2(AW(x,y,σI,σD))
scale x y
 Harris 
σn=knσ σn
σD= σn
σI=γσD

28. Multi-scale Harris Detector (cont’d)
The same interest point will be detected at multiple consecutive scales.
Interest point location will shift as scale increases (i.e., due to smoothing).
i.e., the size of each circle corresponds to the scale at which the interest point
was detected.

29. How do we match them?
Corresponding features might appear at different scales.
How do we determine these scales?
We need a scale selection mechanism!

30. Exhaustive Search
Simple approach for scale selection but not efficient!

31. Characteristic Scale
Find the characteristic scale of each feature (i.e., the scale revealing the spatial extent of an interest point).
characteristic scale
characteristic scale 31

32. Characteristic Scale (cont’d)
Only a subset of interest points are selected using the characteristic scale of each feature.
i.e., the size of the circles is related to the scale at which the interest points were selected.
Matching can be simplified!

33. Automatic Scale Selection – Main Idea
Design a function F(x,σn) which provides some local measure.
Select points at which F(x,σn) is maximal over σn.
max of F(x,σn)
corresponds to
characteristic scale!
F(x,σn) σn
T. Lindeberg, "Feature detection with automatic scale selection" International Journal of Computer Vision, vol. 30, no. 2, pp , 1998.

34. Lindeberg et al, 1996
Slide from Tinne Tuytelaars

42. Automatic Scale Selection (cont’d)
Using characteristic scale, the spatial extent of interest points becomes covariant to scale transformations.
The ratio σ1/σ2 reveals the scale factor between the images. σ1 σ2
σ1/σ2 = 2.5 42

43. How to choose F(x,σn) ?
Typically, F(x,σn) is defined using derivatives, e.g.:
LoG (Laplacian of Gaussian) yielded best results in a recent evaluation study.
DoG (Difference of Gaussians) was second best.
C. Schmid, R. Mohr, and C. Bauckhage, "Evaluation of Interest Point Detectors",
International Journal of Computer Vision, 37(2), pp , 2000.

44. LoG and DoG
LoG can be approximated by DoG:

45. Harris-Laplace Detector
Multi-scale Harris with scale selection.
Uses LoG maxima to find characteristic scale. σn
scale
 LoG  y
 Harris  x

46. Harris-Laplace Detector (cont’d)
Find interest points at multiple scales using Harris detector.
- Scales are chosen as follows: σn =knσ
- At each scale, choose local maxima assuming 3 x 3 window
(i.e., non-maximal suppression)
where
(σD =σn, σI =γσD )

47. Harris-Laplace Detector (cont’d)
(2) Select points at which the normalized LoG is maximal across scales and the maximum is above a threshold.
σn+1 σn
where:
σn-1
K. Mikolajczyk and C. Schmid, “Indexing based on scale invariant interest points" IEEE Int. Conference on Computer Vision, pp , 2001.

48. Example Interest points detected at each scale using Harris-Laplace
Few correspondences between levels corresponding to same σ.
More correspondences between levels having a ratio of σ = 2.
images differ by a scale factor of 1.92
σ=1.2
σ=2.4
σ=4.8
σ=9.6
σ=1.2
σ=4.8
σ=9.6
σ=2.4

49. Example (cont’d)
(same viewpoint – change in focal length and orientation)
More than 2000 points would have been detected without scale selection.
Using scale selection, 190 and 213 points were detected in the left and right images, respectively.

50. Example (cont’d)
58 points are initially matched (some were not correct)

51. Example (cont’d)
Reject outliers (i.e., inconsistent matches) using RANSAC
Left with 32 matches, all of which are correct.
Estimated scale factor is 4:9 and rotation angle is 19 degrees.

52. Harris-Laplace Detector (cont’d)
Repeatability
Invariant to:
Scale
Rotation
Translation
Robust to:
Illumination changes
Limited viewpoint changes

53. Harris-Laplace using DoG
Look for local maxima
in DoG pyramid
DoG pyramid
David G. Lowe, "Distinctive image features from scale-invariant keypoints.” Int. Journal of Computer Vision, 60 (2), pp , 2004.

54. Handling Affine Changes
Similarity transformations cannot account for perspective distortions; affine could be used for planar surfaces.
Similarity transform
Affine transform

55. Harris Affine Detector
Use an iterative approach:
Extract approximate locations and scales using the Harris-Laplace detector.
For each point, modify the scale and shape of its neighborhood in an iterative fashion.
Converges to stable points that are covariant to affine transformations. .

56. Steps of Iterative Affine Adaptation
1. Detect initial locations and neighborhood using Harris-Laplace.
2. Estimate affine shape of neighborhood using 2nd order moment matrix μ(x, σI, σD).

57. Steps of Iterative Affine Adaptation (cont’d)
3. Normalize (i.e., de-skew) the affine region by mapping it to a circular one (i.e., “remove” perspective distortions).
4. Re-detect the new location and scale in the normalized image.
5. Go to step 2 if the eigenvalues of μ(x, σI, σD) for the new point are not equal (i.e., not yet adapted to the characteristic shape).

58. Iterative affine adaptation - Examples
Initial points
Example Example 2

59. Iterative affine adaptation – Examples (cont’d)
Iteration #1
Example Example 2

60. Iterative affine adaptation – Examples (cont’d)
Iteration #2
Example Example 2

61. Iterative affine adaptation – Examples (cont’d)
Iteration #3, #4, …
Example Example 2
K. Mikolajczyk and C. Schmid, “Scale and Affine invariant interest point detectors”,
International Journal of Computer Vision, 60(1), pp , 2004.

62. Iterative affine adaptation – Examples (cont’d)62

63. De-skewing Consider a point xL with 2nd order matrix ML
The de-skewing transformation is defined as follows: xL 63

64. De-skewing corresponding regions
Consider two points xL and xR which are related through an affine transformation: xL xR

65. De-skewing corresponding regions (cont’d)
Normalized regions
are related by pure
rotation R.

66. Resolving orientation ambiguity
Create histogram of local gradient directions in the patch.
Smooth histogram and assign canonical orientation at peak of smoothed histogram.
Dominant gradient
direction! 2 p
(36 bins) 66

67. Resolving orientation ambiguity (cont’d)
Resolve orientation ambiguity.
Compute R 67 67

68. Other Affine Invariant Blob/Region Detectors
There are many other techniques for detecting affine invariant blobs or regions, for example:
Intensity Extrema-Based Region (IER)
Maximally Stable Extremal Regions (MSERs)
No need to detect interest points.

69. Intensity Extrema-Based Region Detector
Take a local intensity extremum as initial point.
(2) Examine the intensity along “rays” from the local extremum.
(3) The point on each ray for which fI(t) reaches an extremum is selected (i.e., invariant).
(4) Linking these points together yields an affinely invariant region, to which an ellipse is fitted.
d>0: small const
Tuytelaars, T. and Van Gool, L. “Matching Widely Separated Views based on Affine Invariant Regions”, International Journal on Computer Vision, 59(1):61–85, 2004.

70. Intensity Extrema-Based Region Detector (cont’d)
The regions found may not exactly correspond, so we approximate them with ellipses using 2nd order moments.

71. Intensity Extrema-Based Region Detector (cont’d)
Double the size of the ellipse to make regions more distinctive.
Final ellipse is not necessarily centered at original anchor point.

72. Intensity Extrema-Based Region Detector (cont’d)

73. Intensity Extrema-Based Region Detector (cont’d)
Region extraction is fairly robust to inaccurate localization of intensity extremum.

74. Maximally Stable Extremal Regions (MSERs)
Consider all possible thresholdings of a gray-scale image:
If I(x,y) > It then I(x,y)=255; else I(x,y)=0
Matas, J., Chum, O., Urban, M. and Pajdla, T., “Robust wide-baseline stereo from maximally stable extremal regions”, British Machine Vision Conf, pp. 384–393, 2002.

75. Maximally Stable Extremal Regions (MSERs)
Extermal Regions
All regions formed using different thresholds.
Can be extracted using connected components.
Maximally Stable Extremal Regions
Regions that remain stable over a large range of thresholds.
Approximate MSER by an ellipse

76. Example
Extermal regions can be extracted in O(nlog(logn)) time where n is the number of pixels.
Sensitive to image blur.