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

Overview • Problem Motivation • PDF Projection Theorem • Likelihood Modelling for Chamfer Matching • Experiments • Conclusion

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 ?

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 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 chamfer 6.0 likelihood 0.14 likelihood 0.03

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

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 • Need a principled framework for modelling the likelihood for template matching • Probability Distribution Function Projection Theorem ( Baggenstoss [99]) provides such a framework

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 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 Theorem I Image space, I

PDF Projection Theorem z I Image space, I Feature space, z

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 features I

Chamfer Matching Input image Canny edges Template Distance transform

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 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 • 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 PDFs Example learning images for the template For learning the feature likelihood p(zj|Hj) For learning the reference likelihood p(zj|H0)

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.

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.

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

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

Likelihood Models for Template Matching Using the PDF Projection Theorem