1. FAsT-Match: Fast Affine Template Matching
Simon Korman, Daniel Reichman, Gilad Tsur, Shai Avidan
CVPR 2013
Presented by Lee, YoonSeok
Today, I’m gonna talk about fast-match: fast affine template matching for my presentation. 1

2. Review : Boundary Preserving Dense Local Regions

3. Overview Template Matching : Related Work Main Idea Algorithm Result
Summary

4. Generalized Template Matching
Find the best …/Translation/Euclidean/Similarity/Affine/Projective/…
transformation between two given images:
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

5. Generalized Template Matching
The algorithm:
Take a sample of the Affine transformations
Evaluate each transformation in the sample
Return the best
Questions:
Which sample to use?
How does is guarantee a bound?
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

6. Related Work : Direct methods
Lucas, Kanade “An iterative image registration technique with an application to stereo vision” [ICAI 1981]
Baker, Matthews “Lucas-Kanade 20 years on: A unifying framework” [IJCV 04]

7. Related Work : Indirect methods
Lowe “Distinctive image features from scale-invariant key-points” [IJCV 04]
Morel, Yu “Asift: A new framework for fully affine invariant image comparison” [SIAM 09]
M.A. Fichler, R.C. Bolles “Random sample consensus” [Comm. of ACM 81]

8. Transformation space (e.g. affine)
The Main Idea
image
template
Transformation space (e.g. affine)
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

9. Formal Problem Statement
Input: Grayscale image (template) and image
Distance with respect to a specific transformation :
Distance with respect to any transformation in a family (affinities):
Goal: Given 𝛿>0, find a transformation in for which:
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

10. Simple Algorithm For each affine transformation 𝑇
Compute the distance ∆ 𝑇 ( 𝐼 1 , 𝐼 2 )
Return 𝑇 ∗ with smallest distance
∞ transformations – need to discretize
“Combinatorial bounds and algorithmic aspects of image matching under projective transformations” [Hundt & Liskiewicz MFCS, 2008]
Enumerate ≈ 𝑛 18 affine transformations (for 𝑛×𝑛 images)
Guarantee: best possible transformation
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

11. Algorithm – take2 ∆ 𝑇 𝑂𝑃𝑇 𝐼 1 , 𝐼 2 − ∆ 𝑇 ∗ ( 𝐼 1 , 𝐼 2 ) =𝑂(𝛿)
For each affine transformation 𝑇
Compute the distance ∆ 𝑇 ( 𝐼 1 , 𝐼 2 )
Return 𝑇 ∗ with smallest distance
in a Net 𝐴 𝛿
𝑇 ∗
𝑇 𝑂𝑃𝑇
Sample transformation space
build a Net 𝐴 𝛿 of transformations
Guarantee
‘𝛿 – away’ from best possible distance
∆ 𝑇 𝑂𝑃𝑇 𝐼 1 , 𝐼 2 − ∆ 𝑇 ∗ ( 𝐼 1 , 𝐼 2 ) =𝑂(𝛿)
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

12. Algorithm – take3 Estimate the SAD to within O(𝛿) By sampling pixels
For each affine transformation 𝑇
Compute the distance ∆ 𝑇 ( 𝐼 1 , 𝐼 2 )
Return 𝑇 ∗ with smallest distance
in a Net 𝐴 𝛿
Estimate
estimate
Estimate the SAD to within O(𝛿)
By sampling pixels
Thus – total runtime is:
∆ 𝑇 𝑂𝑃𝑇 𝐼 1 , 𝐼 2 − ∆ 𝑇 ∗ ( 𝐼 1 , 𝐼 2 ) =𝑂(𝛿)
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

13. The net 𝐴 𝛿 𝑇ℎ𝑒 𝑛𝑒𝑡 𝐴 𝛿 The Net 𝐴 𝛿
Transformations T1 and T2 are x-close
The Net 𝐴 𝛿
Any affine transformation is δn1-close to some tran s. in 𝐴 𝛿
( 𝐴 𝛿 is a δn1-cover of affine transformations)
Possible construction with size:
𝑇ℎ𝑒 𝑛𝑒𝑡 𝐴 𝛿 T1 T2
<x x
= δn1
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

14. Fast-Match: a Branch-and-Bound Scheme
Iteratively increase Net-precision (decrease δ)
Throw away irrelevant transformation regions
𝑇 𝐶𝑙𝑜𝑠𝑒𝑠𝑡 is guaranteed to move to next round
(off-net neighbors of above- threshold points are worse than 𝑇 ∗ )
𝑇ℎ𝑒 𝑛𝑒𝑡 𝐴 𝛿
𝑇 𝐶𝑙𝑜𝑠𝑒𝑠𝑡
𝑇 ∗
𝑇 𝑂𝑃𝑇
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

15. Result Pascal VOC 2010 data-set 200 random image/templates
Template dimensions of 10%, 30%, 50%, 70%, 90%
‘Comparison’ to a feature-based method - ASIFT
Image degradations (template left in-tact):
Gaussian Blur with STD of {0,1,2,4,7,11} pixels
Gaussian Noise with STD of {0,5,10,18,28,41}
JPEG compression of quality {75,40,20,10,5,2}
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

16. Result Fast-Match vs. ASIFT – template dimension 50%
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

17. Result Fast-Match vs. ASIFT – template dimension 20%
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

18. Result
Runtimes
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

19. Template Dim: 45%
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

20. Template Dim: 35%
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

21. Template Dim: 25%
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

22. Template Dim: 15%
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

23. Template Dim: 10%
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

24. Bad overlap due to ambiguity
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

25. High SAD due to high TV and ambiguity
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

26. Fast-Match: Summary
Handles template matching under arbitrary Affine (6 dof) transformations with
Guaranteed error bounds
Fast execution
Main ingredients
Sampling of transformation space (based on variation)
Quick transformation evaluation (‘property testing’)
Branch-and-Bound scheme
FAsT-Match: Fast Affine Template Matching [Simon Korman et al., CVPR 2013]

27. Q&A