unified detection and recognition for reading text in scene images

An alternative method for prediction is called maximum posterior marginal (MPM)
estimation:
ŷ i = arg max
y i ∈Y i
p (y i | x, θ, I), ∀i ∈ V. (2.31)
It corresponds to choosing the label for each unknown that maximizes the probability
with all other labelings marginalized. This can often be a more effective way of considering
the probabilities of all the labelings, rather than simply the maximum (joint)
labeling, as in MAP. Marginalization, however, suffers from the same computational
complexity problems. Sum-product loopy belief propagation, described next, can be
used to approximate these marginals.
In practice, the MAP estimate tends to be conservative, trying to give the most
correct labels, while MPM tends to give higher detection rates. These methods are
used variously in our experiments.
2.3.2 Belief Propagation
Because they all involve combinatorial sums or search spaces, we require approximations
to compute the log partition function for the likelihood objective (2.15),
the marginal probabilities for its gradient (2.18), or to make predictions with MAP
or MPM, Fortunately, there is one family of algorithms that handles all of these.
Namely, the loopy sum-product or belief propagation algorithm. In short, it exploits
the nature in which the joint probability factorizes into a product of local functions.
Recall the bipartite “factor graph” between unknowns y, represented by nodes in
the graph, and the compatibility functions (or factors, when they are exponentiated)
over the unknowns, as shown in the example of Figure 2.1 on page 22. The algorithm
operates by iteratively passing messages between the nodes representing the unknowns
and the factors. When these messages converge to a stable fixed point, the results
are equivalent to minimizing the so-called Bethe free energy, a variational method for
approximate inference from statistical physics [136]. When the factor graph is a tree,
the sum-product algorithm [60] efficiently performs exact inference. In most cases,
our graphs are not trees, and thus the results are only approximate.
Let N (i) ≡ {C ∈ C | i ∈ C} be the family of indices for the factors that neighbor
the ith unknown. This corresponds to the set of factors having y i as an argument.
The set of edges in a factor graph are thus
E (C) ≡ {(i, C) | i ∈ V ∧ C ∈ N (i)}. (2.32)
For all edges in the factor graph (i, C) ∈ E (C), the node-to-factor messages have the
general form
∏
m i→C (y i ) ∝ m C ′ →i (y i ) (2.33)
C ′ ∈N(i)\C
so that the message from a node to a factor is the product of all the messages to
that node from all other neighboring factors. The resulting functional message is
normalized (i.e., sums to 1 over y i ) for numerical stability. Note that for parsimony,
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