Probabilistic description

Let $I_1,\ \cdots I_n$ represent the n observed images, and let $L_1,\ \cdots L_n$ represent a word hypothesis, that is, a particular sequence of n letters whose likelihood of having generated the observed images is to be evaluated. Then using Bayes' theorem one may express the conditional probability that the given word hypothesis is correct given the observed images as follows:  

$$P(L_1,\ L_2,\ \cdots L_n \vert I_1,\ I_2 \cdots I_n) = C \cd... ...ts I_n \vert L_1,\ L_2,\ \cdots L_n ) P(L_1,\ L_2,\ \cdots L_n)$$ (1)

Here, C is a normalization constant (this just means that you want to make sure that all the probabilities add up to 1). The basic problem thus becomes a concrete optimization problem: maximize the right-hand side of the above equation over all possible word hypotheses $L_1,\ \cdots L_n$. The solution to this problem depends on the model that one assumes for image generation and letter co-occurrence as encoded in the two terms on the right-hand side above. Some comments on this statement follow.