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![Page 1: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/1.jpg)
Likelihood Models for Template MatchingUsing the PDF Projection Theorem
Arasanathan Thayananthan
Ramanan Navaratnam
Dr. Phil Torr
Prof. Roberto Cipolla
![Page 2: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/2.jpg)
ProblemProblem
The correct template
The minimum chamfer score
Chamfer score 3.49 3.07
![Page 3: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/3.jpg)
OverviewOverview
1. Problem Motivation
2. PDF Projection Theorem
3. Likelihood Modelling for Chamfer Matching
4. Experiments
5. Conclusion
![Page 4: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/4.jpg)
MotivationMotivation
Template matching widely used in computer vision
Similarity measures are obtained from matching a template to a new image e.g. chamfer score, cross-correlation, etc.
A likelihood value need to be calculated from the similarity measures.
Chamfer score 3.58
Likelihood ?
![Page 5: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/5.jpg)
MotivationMotivation
Is the similarity measure alone enough to calculate the likelihood ?
What are the probabilities of matching to a correct image and an incorrect image at this specific matching measure ?
![Page 6: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/6.jpg)
Feature LikelihoodFeature Likelihood
Feature likelihood distributions, obtained by matching the templates to the real images they represent
They differ according to the shape and scale of the templates.
![Page 7: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/7.jpg)
Feature LikelihoodsFeature Likelihoods
chamfer 6.0
likelihood 0.14 likelihood 0.03
![Page 8: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/8.jpg)
Clutter LikelihoodsClutter Likelihoods
Clutter likelihood distributions are obtained by matching the template to the background clutter
![Page 9: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/9.jpg)
Likelihood RatiosLikelihood Ratios
The ratio of the feature and clutter likelihood provides a robust likelihood measure.
Likelihood Ratio Tests (LRT) are often used in many classification problems
Jones & Ray [99], skin-colour classification
Sidenbladh & Black [01], limb-detector
![Page 10: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/10.jpg)
Modelling the likelihoodModelling the likelihood
Need a principled framework for modelling the likelihood for template matching
Probability Distribution Function Projection Theorem ( Baggenstoss [99]) provides such a framework
![Page 11: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/11.jpg)
OverviewOverview
1. Problem Motivation
2. PDF Projection Theorem
3. Likelihood Modelling for Chamfer Matching
4. Experiments
5. Conclusion
![Page 12: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/12.jpg)
PDF Projection TheoremPDF Projection Theorem
Provides a mechanism to work in raw data space, I, instead of extracted feature space, z.
This is done by projecting the PDF estimates from the feature space back to the raw data space
![Page 13: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/13.jpg)
PDF Projection TheoremPDF Projection Theorem
Neyman-Fisher factorisation states that if is a sufficient statistic for H, p(I|H) can be factored as
Applying Eq(1) for a hypothesis, H, and a reference Hypothesis, H0,
![Page 14: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/14.jpg)
PDF Projection TheoremPDF Projection Theorem
Image space, I
I
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PDF Projection TheoremPDF Projection Theorem
Image space, I Feature space, z
I z
![Page 16: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/16.jpg)
PDF Projection TheoremPDF Projection Theorem
Image space, I Feature space, z
I z
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Class-specific featuresClass-specific features
PDF Projection Theorem extends to class-specific features
Each hypothesis or class can have its feature set
Yet, we get consistent and comparable raw image likelihoods
Reference hypothesis H0 remains the same for all hypothesis
![Page 18: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/18.jpg)
Class-specific featuresClass-specific features
I
![Page 19: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/19.jpg)
OverviewOverview
1. Problem Motivation
2. PDF Projection Theorem
3. Likelihood Modelling for Chamfer Matching
4. Experiments
5. Conclusion
![Page 20: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/20.jpg)
Chamfer MatchingChamfer Matching
Input image Canny edges
Distance transform Template
![Page 21: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/21.jpg)
Chamfer MatchingChamfer Matching
We apply PDF projection Theorem to model likelihood in a chamfer matching scheme
Each template chooses its own subset of edge features, zj
![Page 22: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/22.jpg)
Chamfer MatchingChamfer Matching
A common reference hypothesis is chosen for all templates
p(zj|H0) provides the probability of template matching to any image.
Difficulty is in learning p(zj|Hj) and p(zj|H0) for each template Tj
![Page 23: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/23.jpg)
Learning the PDFsLearning the PDFs
Time-consuming to obtain real images for learning the PDFs
Software like “Poser” can create “near” real images
Becoming popular for learning image statistics e.g. Shakhnarovich [03]
For each template Tj, we learn p(zj|Hj) and p(zj|H0) from synthetic images.
![Page 24: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/24.jpg)
Learning the PDFsLearning the PDFs
Example learning images for the template
For learning the feature likelihood p(zj|Hj)
For learning the reference likelihood p(zj|H0)
![Page 25: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/25.jpg)
OverviewOverview
1. Problem Motivation
2. PDF Projection Theorem
3. Likelihood Modelling for Chamfer Matching
4. Experiments
5. Conclusion
![Page 26: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/26.jpg)
ExperimentsExperiments
35 hand templates from a 3D hand model with 5 gestures at 7 different scales
Hypothesis, Hj, is that the image contains a hand pose similar to Template Tj, (in scale and gesture).
The distributions p(zj|Hj) and p(zj|H0) were learned off-line for each template.
![Page 27: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/27.jpg)
ExperimentsExperiments
Aim of the experiment is to compare the matching performances of1. Zj, the chamfer score obtained by matching
the template Tj to the image
2. P(zj|Hj), the feature likelihood of Template Tj
3. P(I|Hj), the data likelihood value using the PDF projection theorem.
![Page 28: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/28.jpg)
ExperimentsExperiments
Template matching on 1000 randomly created synthetic images.
Each synthetic image contains a hand pose similar in scale and pose to a randomly chosen template.
Three ROC curves were obtained for each matching measure.
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ResultsResults
![Page 30: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/30.jpg)
ResultsResults
PDF ProjectionTheorem
Chamfer
Chamfer score 4.96 4.06
feature likelihood 14.59 x 10-2 8.62 x 10-2
reference likelihood 88.69 x 10-5 383.32 x 10-5
data likelihood 0.164 x 103 0.022 x 103
![Page 31: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/31.jpg)
ResultsResults
PDF ProjectionTheorem
Chamfer
Chamfer score 4.96 4.06
feature likelihood 14.59 x 10-2 8.62 x 10-2
reference likelihood 88.69 x 10-5 383.32 x 10-5
data likelihood 0.164 x 103 0.022 x 103
![Page 32: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/32.jpg)
ResultsResults
PDF ProjectionTheorem
Chamfer
Chamfer score 4.96 4.06
feature likelihood 14.59 x 10-2 8.62 x 10-2
reference likelihood 88.69 x 10-5 383.32 x 10-5
data likelihood 0.164 x 103 0.022 x 103
![Page 33: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/33.jpg)
ResultsResults
PDF ProjectionTheorem
Chamfer
Chamfer score 4.96 4.06
feature likelihood 14.59 x 10-2 8.62 x 10-2
reference likelihood 88.69 x 10-5 383.32 x 10-5
data likelihood 0.164 x 103 0.022 x 103
![Page 34: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/34.jpg)
ResultsResults
PDF ProjectionTheorem
Chamfer
Chamfer score 3.49 3.07
feature likelihood 24.94x 10-2 27.88 x 10-2
reference likelihood 4.73 x 10-5 24.7 x 10-5
data likelihood 5.27 x 103 1.126 x 103
![Page 35: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/35.jpg)
ResultsResults
PDF ProjectionTheorem
Chamfer
Chamfer score 3.49 3.07
feature likelihood 24.94x 10-2 27.88 x 10-2
reference likelihood 4.73 x 10-5 24.7 x 10-5
data likelihood 5.27 x 103 1.126 x 103
![Page 36: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/36.jpg)
ResultsResults
PDF ProjectionTheorem
Chamfer
Chamfer score 3.49 3.07
feature likelihood 24.94x 10-2 27.88 x 10-2
reference likelihood 4.73 x 10-5 24.7 x 10-5
data likelihood 5.27 x 103 1.126 x 103
![Page 37: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/37.jpg)
ResultsResults
PDF ProjectionTheorem
Chamfer
Chamfer score 3.49 3.07
feature likelihood 24.94x 10-2 27.88 x 10-2
reference likelihood 4.73 x 10-5 24.7 x 10-5
data likelihood 5.27 x 103 1.126 x 103
![Page 38: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/38.jpg)
ResultsResults
PDF ProjectionTheorem
Chamfer
Chamfer score 3.72 3.54
feature likelihood 13.15 x 10-2 20.5 x 10-2
reference likelihood 8.5 x 10-5 108.0 x 10-5
data likelihood 1.547 x 103 0.191 x 103
![Page 39: Likelihood Models for Template Matching Using the PDF Projection Theorem Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla.](https://reader030.fdocuments.in/reader030/viewer/2022013100/5515ea4a550346cf6f8b50ee/html5/thumbnails/39.jpg)
ConclusionConclusion
Depending on raw matching score is less reliable in template matching
PDF Projection theorem provides a principled framework for modelling the likelihood in raw image data space.
Consistent and comparable likelihoods obtained through PDF projection theorem improves the efficiency of template matching scheme