Likelihood models for template matching using the pdf projection theorem
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Likelihood Models for Template Matching Using the PDF Projection Theorem. Arasanathan Thayananthan Ramanan Navaratnam Dr. Phil Torr Prof. Roberto Cipolla. Problem. Overview. Problem Motivation PDF Projection Theorem Likelihood Modelling for Chamfer Matching Experiments Conclusion.

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Likelihood Models for Template Matching Using the PDF Projection Theorem

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Likelihood models for template matching using the pdf projection theorem

Likelihood Models for Template MatchingUsing the PDF Projection Theorem

Arasanathan Thayananthan

Ramanan Navaratnam

Dr. Phil Torr

Prof. Roberto Cipolla


Problem

Problem


Overview

Overview

  • Problem Motivation

  • PDF Projection Theorem

  • Likelihood Modelling for Chamfer Matching

  • Experiments

  • Conclusion


Motivation

Motivation

  • 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 ?


Motivation1

Motivation

  • 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 ?


Feature likelihood

Feature 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.


Feature likelihoods

Feature Likelihoods

chamfer 6.0

likelihood 0.14

likelihood 0.03


Clutter likelihoods

Clutter Likelihoods

  • Clutter likelihood distributions are obtained by matching the template to the background clutter


Likelihood ratios

Likelihood 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


Modelling the likelihood

Modelling the likelihood

  • Need a principled framework for modelling the likelihood for template matching

  • Probability Distribution Function Projection Theorem ( Baggenstoss [99]) provides such a framework


Overview1

Overview

  • Problem Motivation

  • PDF Projection Theorem

  • Likelihood Modelling for Chamfer Matching

  • Experiments

  • Conclusion


Pdf projection theorem

PDF 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


Pdf projection theorem1

PDF Projection Theorem

  • Neyman-Fisher factorisation states that if is a sufficient statisticfor H, p(I|H) can be factored as

  • Applying Eq(1) for a hypothesis, H, and a reference Hypothesis, H0,


Pdf projection theorem2

PDF Projection Theorem

I

Image space, I


Pdf projection theorem3

PDF Projection Theorem

z

I

Image space, I

Feature space, z


Pdf projection theorem4

PDF Projection Theorem

z

I

Image space, I

Feature space, z


Class specific features

Class-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


Class specific features1

Class-specific features

I


Overview2

Overview

  • Problem Motivation

  • PDF Projection Theorem

  • Likelihood Modelling for Chamfer Matching

  • Experiments

  • Conclusion


Chamfer matching

Chamfer Matching

Input image

Canny edges

Template

Distance transform


Chamfer matching1

Chamfer Matching

  • We apply PDF projection Theorem to model likelihood in a chamfer matching scheme

  • Each template chooses its own subset of edge features, zj


Chamfer matching2

Chamfer 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


Learning the pdfs

Learning 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.


Learning the pdfs1

Learning the PDFs

Example learning images for the template

For learning the feature likelihood p(zj|Hj)

For learning the reference likelihood p(zj|H0)


Overview3

Overview

  • Problem Motivation

  • PDF Projection Theorem

  • Likelihood Modelling for Chamfer Matching

  • Experiments

  • Conclusion


Experiments

Experiments

  • 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.


Experiments1

Experiments

Aim of the experiment is to compare the matching performances of

  • Zj, the chamfer score obtained by matching the template Tj to the image

  • P(zj|Hj), the feature likelihood of Template Tj

  • P(I|Hj), the data likelihood value using the PDF projection theorem.


Experiments2

Experiments

  • 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.


Results

Results


Results1

Results


Results2

Results


Results3

Results


Results4

Results


Results5

Results


Results6

Results


Results7

Results


Results8

Results


Results9

Results


Conclusion

Conclusion

  • 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


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