1. SURF: Speeded Up Robust Features
授課教授: 連震杰 教授
Group number: 20
Advisor: Tzuu-Hseng S. Li
Group members: E 何雅芳
E 蕭信揚
N 李佳樺
aiRobots Laboratory, Department of Electrical Engineering,
National Cheng Kung University, Tainan, Taiwan, R.O.C.

2. Outline Introduction Related Work Fast-Hessian Detector
SURF Descriptor
Orientation Assignment
Descriptor Components
Matching
Experiments
Conclusion

3. Outline Introduction Related Work Fast-Hessian Detector
SURF Descriptor
Orientation Assignment
Descriptor Components
Matching
Experiments
Conclusion

4. Introduction
The task of finding point correspondences between two images of the same scene or object is part of many computer vision applications.
This article presents a novel scale- and rotation-invariant detector and descriptor, coined SURF (Speeded-Up Robust Features).
SURF approximates or even outperforms previously proposed schemes with respect to repeatability, distinctiveness, and robustness, yet can be computed and compared much faster.

5. Introduction (cont’d)
The search for discrete image point correspondences can be divided into three main steps.
Step1. Detector
Interest points are selected
Most valuable property:
Repeatability
(whether it reliably finds the same interest points under different viewing condition.)
Step2. Descriptor
Extract the vector for matching
Focus on
scale and image
rotation invariant.
Step3. Match
Often based on a distance
between the vector

6. Outline Introduction Related Work Fast-Hessian Detector
SURF Descriptor
Orientation Assignment
Descriptor Components
Matching
Experiments
Conclusion

7. Related Work Interest Point Detection
Harris corner detector
‧most widely used
‧based on the eigenvalues
‧not scale-invariant
Automatic scale selection detector
‧experimented both the determinant of the
Hessian matrix as well as Laplacian.
Scale-invariant feature detectors
(Mikolajczyk , Schmid)
‧Harris-Laplace and Hessian-Laplace
‧The location is selected by the determinant
of Hessian matrix.
‧The scale is selected by the Laplacian.
SIFT
‧Approximated the LoG by a DoG filter.
=> (1) Using the determinant of the Hessian matrix rather than its trace
(the Laplacian) seems advantageous,
(2) approximations like the DoG can bring speed at a low cost in
terms of lost accuracy.

8. Related Work (cont’d) Interest Point Description
SIFT
‧computes a histogram of local oriented gradients around
the interest point and stores the bins in a 128-dimensional
vector.
PCA-SIFT
‧Yields a 36-dimensional descriptor (=>Fast)
‧To be less distinctive than SIFT
GLOH
‧More distinctive with the same number of dimensions.
‧Computationally more expensive.
=> The SIFT descriptor still seems to be the most appealing descriptor
for practical uses, and hence also the most widely used nowadays.

9. Related Work (cont’d) ★Question: Step1. Fast-Hessian detector
Our approach
Step1. Fast-Hessian detector
Based on the Hessian matrix but
use a very basic approximation – DoG
Integral image: +
Integral image
(reduce the computation time)
(x,y)
(1)Fast implementation of
box type convolution filters
(2)Independent of its size A B C D
B-D
C-D Σ
Property…
Step2. SURF Descriptor
Describes a distribution of Haar-wavelet
Responses within the interest point neighborhood
Answer… +
Integral image
(reduce the computation time)
★Question:
Why can this method
reduce the computation
time?
Step3. Match
Present a new indexing step based on
the sign of the Laplacian
(Speed up & increase the robustness)

10. Outline Introduction Related Work Fast-Hessian Detector
SURF Descriptor
Orientation Assignment
Descriptor Components
Matching
Experiments
Conclusion

11. Fast-Hessian Detector
Hessian matrix H( x , σ) in x at scale σ is defined as
Approximation LoG with box filters => DoG
Gaussian second order derivative
x-dir y-dir xy-dir
Box filters (instead of Gaussian)
x-dir y-dir xy-dir
9x9 box filter with σ=1.2

12. Fast-Hessian Detector (cont’d)
The scale space is analysed by up-scaling the filter size rather than iteratively reducing the image size.
The scale space is divided into octaves. An octave represents a series of increasing filter response maps.
scale
9 x 9 (σ=1.2)
15 x 15 (σ=2.0)
21 x 21 (σ=2.8)
27 x 27 (σ=3.6)
Octave1 (increase:6)
15 x 15 (σ=2.0)
27 x 27 (σ=2.8)
39 x 39 (σ=5.2)
51 x 51 (σ=6.8)
Octave2 (increase:12)
It is selected as the interest point only if it is larger than
all of these neighbors.
For each new octave, the filter size increase is doubled.
(going from 6 to 12 to 24…)

13. Q & A (Fast-Hessian Detector)
Question1. 以放大filter的size代替將圖片縮小，有什麼好處?
Answer1. 因為integral image的使用，使得計算量不會隨filter的size增加，且沒有將圖片縮小，圖片就不會失真。

14. Outline Introduction Related Work Fast-Hessian Detector
SURF Descriptor
Orientation Assignment
Descriptor Components
Matching
Experiments
Conclusion

15. SURF Descriptor Orientation Assignment Descriptor Components Interest
Fixing a reproducible orientation
based on information from a
circular region around the
interest point.
Descriptor
Components
Construct a square region aligned
to the selected orientation, and
extract the SURF descriptor
from it.
Interest
point
Features

16. Outline Introduction Related Work Fast-Hessian Detector
SURF Descriptor
Orientation Assignment
Descriptor Components
Matching
Experiments
Conclusion

17. Orientation Assignment
Haar Wavelet
Orientation A B C D E F
=A-B-D+E
=B-C-E+F
Σ=-A+2B-C+D-2E+F 4s
a-b a b dx dy dx dy 6s
Image
(dx1,dy1)
(dx2,dy2)
π/3
Orientation
Interest point

18. Outline Introduction Related Work Fast-Hessian Detector
SURF Descriptor
Orientation Assignment
Descriptor Components
Matching
Experiments
Conclusion

19. Descriptor Components
Constructing a square region centered around the interest point, and oriented along the orientation.
The region is split up regularly into smaller 4 × 4 square sub-regions.
(4x4)x4=> a 64 dimensional vector
Horizontal direction
Vertical direction
Haar wavelet
(filter size 2s)
20s

20. Q&A(SURF Descriptor) Question1. Why to use Σ|dx| and Σ|dy| ? Answer1.
Question2. Why to use Haar wavelet response?
Answer2.

21. Outline Introduction Related Work Fast-Hessian Detector
SURF Descriptor
Orientation Assignment
Descriptor Components
Matching
Experiments
Conclusion

22. Matching
For fast indexing during the matching stage, the sign of the Laplacian (i.e. the trace of the Hessian matrix) for the underlying interest point is included.
In the matching stage, we only compare features if they have the same type of contrast.

23. Outline Introduction Related Work Fast-Hessian Detector
SURF Descriptor
Orientation Assignment
Descriptor Components
Matching
Experiments
Conclusion

24. Experiments
Scale variant + rotation

25. Experiments (cont’d)
Rotation

26. Experiments (cont’d)
Blurred

27. Experiments (cont’d)
Photometric deformations

28. Outline Introduction Related Work Fast-Hessian Detector
SURF Descriptor
Orientation Assignment
Descriptor Components
Matching
Experiments
Conclusion

29. Conclusion
SURF outperforms previously proposed schemes with respect to repeatability, distinctiveness, and robustness, yet can be computed and compared much faster.
Future work will aim at optimizing the code for additional speed up.

30. ★ Thanks for your attention!!