FAsT-Match: Fast Affine Template Matching Simon Korman, Daniel Reichman, Gilad Tsur, Shai Avidan CVPR 2013 Presented by Lee, YoonSeok.

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


● 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)


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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 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


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



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


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


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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


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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


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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


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Fast-Match vs. ASIFT – template dimension 50%

Result


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Fast-Match vs. ASIFT – template dimension 20%

Result


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● Runtimes

Result


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Template Dim: 45%


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Template Dim: 35%


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Template Dim: 25%


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Template Dim: 15%


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Template Dim: 10%


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Bad overlap due to ambiguity


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High SAD due to high TV and ambiguity


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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


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Q&A

FAsT-Match: Fast Affine Template Matching Simon Korman, Daniel Reichman, Gilad Tsur, Shai Avidan CVPR 2013 Presented by Lee, YoonSeok.

Documents

affine fastmatch

best fastmatch

generalized template

overview template matching

yoonseok slide

affine transformations

shai avidan cvpr

algorithm take2