# Constellation Model - The Method of Fergus Et Al. - Model Structure

Model Structure

Given a particular object class model with parameters, we must decide whether or not a new image contains an instance of that class. This is accomplished by making a Bayesian decision,

$R = frac{p(mbox{Object}|X,S,A)}{p(mbox{No object}|X,S,A)}$
$= frac{p(X,S,A|mbox{Object})p(mbox{Object})}{p(X,S,A|mbox{No object})p(mbox{No object})}$
$approx frac{p(X,S,A|Theta)p(mbox{Object})}{p(X,S,A|Theta_{bg})p(mbox{No object})}$

where is the background model. This ratio is compared to a threshold to determine object presence/absence.

The likelihoods are factored as follows:

$p(X,S,A|Theta) = sum_{h in H} p(X,S,A,h|Theta) =$
$sum_{h in H} underbrace{ p(A|X,S,h,Theta) }_{mbox{Appearance}} underbrace{ p(X|S,h,Theta) }_{mbox{Shape}} underbrace{ p(S|h,Theta) }_{mbox{Rel. Scale}} underbrace{ p(h|Theta) }_{mbox{Other}}$

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