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

the two children. The root node represents the entire text lines of the text
region.
• A set of features is extracted for each node of the binary tree. The cost to
preserve a node as a paragraph is a Gaussian weighted mixture of these
features. The cost to remove a node is equal to the sum of costs of preserving
both child nodes.
• At each node of the tree from root to the leaves, if the cost of preserving
a node is less than the cost of removing the node, that node is marked
to be preserved and the rest of the children for that particular node are
ignored. A dynamic programming framework is utilized to estimate these
costs.
tel-00912566, version 1 - 2 Dec 2013
• Training is performed using a training scheme similar to Collin’s voted
perceptron. It tunes weights to ensure that the cost of preserving a paragraph
(node) of the ground truth is less than that of its children. The
cost of removing a leaf node is ∞ which ensures that no leaf node can be
removed regardless of the cost for preserving the lead node.
6.1 Minimum spanning tree (MST)
All text lines in one text region are fully connected with links between them.
To compute the MST, first we need to compute a weight for each link. Consider
that all the text lines in figure 6.1 are part of one text region. The weight for
the link between the first text line (p) and the second line (q) is defined as:
W mst (p, q) = (1 + d(p, d))(1 + sin(∠ min (p, q))).
where d(p, q) is the Euclidean distances between the convex hull of the text
line p (red marks) and that of the text line q (blue marks). ∠ min (p, q) is the
minimum positive angle between the axis of p and axis of q. The second term
ensures that if accidentally a vertical line is included in the text region, it would
be the last text line to join the spanning tree.
6.2 Binary partition tree (BPT)
The goal of converting a minimum spanning tree to a binary partition tree is
illustrated in figure 6.2. The root node contains all the text lines. Then at each
node based on a criterion that we describe below, the algorithm chooses one of
the remaining links inside the MST. The link is removed and the MST ensures
that the tree breaks into two set of text lines that are not connected with any
other links. Each set of lines are assigned to a child node until we reach to the
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