### SURF: Speeded-Up Robust Features

```SURF: SPEEDED-UP ROBUST
FEATURES
Student : 劉彥廷
2011/10/17
Computer Vision and Image Understanding (CVIU) 2008.
OUTLINE
Introduction
Related Works
Speed-Up Robust Features
• Detection
• Description
Experiments
Conclusion
2
OUTLINE
Introduction
Related Works
Speed-Up Robust Features
• Detection
• Description
Experiments
Conclusion
3
Introduction
• Why do we care about feature matching?
 Object Recognition
 Wide baseline matching
 Tracking
4
Challenges
Types of variance
•
•
•
•
•
Illumination
Scale
Rotation
Affine
Perspective
We want to find
Repeatability、Distinctiveness
features
5
OUTLINE
Introduction
Related Works
Speed-Up Robust Features
• Detection
• Description
Experiments
Conclusion
6
Related Works
•
•
•
Harris Corner Detector - Harris 1988
Laplacian of Gaussian - Lindeberg 1998
Difference of Gaussian - Lowe 2004
7
Related Works
•
•
•
Harris Corner Detector - Harris 1988
Laplacian of Gaussian - Lindeberg 1998
Difference of Gaussian - Lowe 2004
flat
edge
corner
Illumination invariance !!!
8
Related Works
•
•
•
Harris Corner Detector - Harris 1988
Laplacian of Gaussian - Lindeberg 1998
Difference of Gaussian - Lowe 2004
characteristic scale
*
=
LoG can detect blob-like structures at locations
“Feature Detection with Automatic Scale Selection”, IJCV ‘98
9
Related Works
•
•
•
Harris Corner Detector - Harris 1988
Laplacian of Gaussian - Lindeberg 1998
Difference of Gaussian - Lowe 2004
Computational efficiency !
G ( x , y , k  )  G ( x , y ,  )  ( k  1)  G ( x , y ,  )
2
2
Compare to 26 neighbors
Keep the same keypoint in all scale !
10
Motivation
•
Lindeberg uses Laplacian of Gaussian, one could
obtain scale invariant features.
•
Lowe uses difference of Gaussian to approximate
Laplacian of Gaussian. (SIFT)
•
This paper uses Hessian - Laplacian to approximate
Laplacian of Gaussian, to improve calculation speed.
11
OUTLINE
Introduction
Related Works
Speed-Up Robust Features
• Detection
• Description
Experiments
Conclusion
12
Detection
Hessian-based interest point localization
•
Lxx(x,y,σ) is the Laplacian of Gaussian of the image.
•
It is the convolution of the Gaussian second order derivative
with the image.
•
This paper use Dxx to approximate Lxx.
13
Detection
Scale analysis with constant image size
(DoG)
Approximated second order derivatives with box filters.
14
Integral Images
Using integral images for major speed up
Integral Image (summed area tables) is an intermediate
representation for the image and contains the sum of gray
scale pixel values of image.
They can be evaluated at a very low computational cost using integral images with
box filters
15
Summary
 Keypoint detection
 Keypoint description
 Keypointmatching
16
Fourier v.s. Wavelet
• Fourier Transform (FT) is not a good tool –
gives no direct information about when an oscillation occurred.
• Wavelets can keep track of time and frequency information.
Fourier basis
Haar basis
17
Description
Orientation Assignment
•
The Haar wavelet responses are represented as vectors
•
Sum all responses within a sliding orientation window covering an angle of 60
degree
•
The longest vector is the dominant orientation
x response y response
interest point
scale = s
Haar
dx
r = 6s
dy
18
Description
•
Split the interest region (20s x 20s) up into 4 x 4 square subregions.
•
Calculate Haar wavelet
response dx and dy and
weight the response with
a Gaussian kernel.
•
Sum the response over
each sub-region for dx
and dy, then sum the
absolute value of response.
19
Matching
• Fast indexing through the sign of the Laplacian for the
underlying interest point
The sign of trace of the Hessian matrix
Trace = Lxx + Lyy
 can do match
 can do match
 not match
matching
20
OUTLINE
Introduction
Related Works
Speed-Up Robust Features
• Detection
• Description
Experiments
Conclusion
21
Experiments
• Test keypoint repeatability for
(Viewpoint Change), (Lighting Change) and(Zoom and Rotation)
22
Experiments
• Repeatability score for image sequences
23
Experiments
• Fix number of keypoints
24
Experiments
SIFT
SURF
25
Experiments
Image size
: 341x341
Running time : 2.411188 seconds
26
Experiments
Image size
: 800x600
Running time : 12.028462 seconds
27
Conclusion
•
SURF is faster than SIFT by 3 times, and has
recall precision not worse than SIFT.
•
SURF is good at handling image with blurring or
rotation.
•
SURF is poor at handling image with viewpoint .
28
Reference
• “Speeded-Up Robust Features”, CVIU ‘08 Herbert Bay
• “Distinctive Image Features from Scale-Invariant Features”,
IJCV ’04 David G. Lowe
• “A Combined Corner and Edge Detector” ‘88 Chris Harris
• “Feature Detection with Automatic Scale Selection”, IJCV ’98
Lindeberg
29
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