Segmentation of heterogeneous document images : an ... - Tel

• Problem 2: Given the observations and the model ψ = (f, λ), how do we
choose a corresponding label configuration y ∗ = y ∗ 1y ∗ 2...y ∗ s which is optimal
in some sense (i.e., best ”explains” the observations)? (Label decoding)
y ∗ = arg max p(y|x, ψ)
y
• Problem 3: Given the observations, the label configuration y = y 1 y 2 ...y S
and a model ψ = (f, λ), how do we adjust the model parameters λ to
maximize P (y|x, ψ)? (Training)
We can also view the first problem as one of scoring how well a given model
matches a given observation sequence. This viewpoint is useful for the purpose
of recognition where we are trying to choose among several competing models
the model that best matches the observations. Thus, it does not play any part
in our system where we want to segment regions by labeling the observations.
tel-00912566, version 1 - 2 Dec 2013
Problem 2 is the one in which we attempt to find the ”correct” label configuration.
Since we are using two labels text, non-text for each site, the problem
becomes to assign one of these labels to each site on the image. This is what
we want to do every time that we process a document for region detection. In
case of linear-chain conditional random fields, this operation is easily achieved
by using the Viterbi algorithm [97] that can assign the optimal labels using dynamic
programming. However, in two-dimensional random fields approximate
techniques should be used.
Problem 3 is the one in which we attempt to optimize the model parameters
to best describe how the given observations and label configuration come
about. It is called training, and various methods have been proposed for that.
Among these, Limited Memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS or
LM-BFGS) [20] and Collin’s Voted Perceptron [26] are two popular chooses.
4.2 Feature functions
Perhaps feature functions are the most important components of the model. The
general form of a feature function is f(y i,i∈N(s) , y s , x i,i∈N(s) , x s ), which looks at
a pair of adjacent sites to indicate how likely the given label configuration is
correct given the observations at both sites. Because this feature function depends
on two sites, it is called an edge feature function. However, if the feature
function only depends on the label and observation at one site, it is called a node
feature function. The value of the function is a real value that may depend on
labels and observations, including any non-linear combination of them.
The term ”feature function” is different from features and feature extraction
we are familiar with in image processing. Each feature function must be tied to
label configurations. For example, we can define a simple edge feature function
f 1 which produces binary values: it is 1 if the label of the current site is ”text”
and the label of the site on its left is ”non-text”.
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