FAsT-Match: Fast Affine Template Matching

Simon Korman, Daniel Reichman, Gilad Tsur, Shai Avidan

CVPR 2013

Presented by Lee, YoonSeok

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Review : Boundary Preserving Dense Local Regions

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Overview

● Template Matching : Related Work

● Main Idea

● Algorithm

● Result

● Summary

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Generalized Template Matching

● Find the best …/Translation/Euclidean/Similarity/Affine/Projec-

tive/…

transformation between two given im-ages:

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

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Generalized Template Matching

● The algorithm:1. Take a sample of the Affine transformations

2. Evaluate each transformation in the sample

3. Return the best

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

● Questions:● Which sample to use?

● How does is guarantee a bound?

6 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]

Related Work : Direct methods

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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]

Related Work : Indirect methods

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The Main Idea

template image

Transformation space (e.g. affine)

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

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Formal Problem Statement

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

● 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 find a transformation in for which:

),(min),( 2121 IIII TT

),(),( 21*21 IIII T

1I 2I

T

)( 111 nnI 2I

T

*T

1

))(()(1

),( 2121

21Ip

T pTIpIn

II

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Simple Algorithm

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

For each affine transformation Compute the distance

Return with smallest distance

transformations – need to discretize “Combinatorial bounds and algorithmic aspects of image

matching under projective transformations” [Hundt & Liskiewicz MFCS, 2008] Enumerate affine transformations (for images)

Guarantee: best possible transformation

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Algorithm – take2

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

For each affine transformation Compute the distance

Return with smallest distance

in a Net

Sample transformation space build a Net of transformations

Guarantee ‘ – away’ from best possible distance

𝑇 ∗

)(O

𝑇 𝑂𝑃𝑇

|∆𝑇 𝑂𝑃𝑇 ( 𝐼 1 , 𝐼 2 )−∆𝑇∗(𝐼 1 , 𝐼 2)|=𝑂 (𝛿)

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Algorithm – take3

For each affine transformation Compute the distance

Return with smallest distanceEstimate

estimate

in a Net

|∆𝑇 𝑂𝑃𝑇 ( 𝐼 1 , 𝐼 2 )−∆𝑇∗(𝐼 1 , 𝐼 2)|=𝑂 (𝛿)

Estimate the SAD to within O( By sampling pixels Thus – total runtime is:

)/1( 2)/1(|| 2 A ))(( 21

1

28 n

n

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

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The net ● Transformations T1 and T2 are x-close

● The Net ● Any affine transformation is δn1-close to

some trans. in ● ( is a δn1-cover of affine transformations)

● Possible construction with size:

T1

T2

<x

xpTpTTTLIp

22121 )()(max),(1

))(( 211

26 n

n

h𝑇 𝑒𝑛𝑒𝑡 𝐴𝛿

x = δn1

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

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Fast-Match: a Branch-and-Bound Scheme

● Iteratively increase Net-precision (decrease δ)

● Throw away irrelevant transformation regions

● is guaranteed to move to next round

● (off-net neighbors of above- threshold points are worse

than )

h𝑇 𝑒𝑛𝑒𝑡 𝐴𝛿

𝑇 ∗𝑇 𝑂𝑃𝑇 𝑇 𝐶𝑙𝑜𝑠𝑒𝑠𝑡

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

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● 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}

Result

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

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Fast-Match vs. ASIFT – template dimension 50%

Result

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

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Fast-Match vs. ASIFT – template dimension 20%

Result

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

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● Runtimes

Result

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

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Template Dim: 45%

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

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Template Dim: 35%

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

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Template Dim: 25%

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

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Template Dim: 15%

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

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Template Dim: 10%

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

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Bad overlap due to ambiguity

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

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High SAD due to high TV and ambiguity

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

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Fast-Match: Summary

● Handles template matching under ar-bitrary Affine (6 dof) transformations with

● Guaranteed error bounds

● Fast execution

● Main ingredients● Sampling of transformation space (based on varia-

tion)

● Quick transformation evaluation (‘property test-ing’)

● Branch-and-Bound scheme

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

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Q&A