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Overlapping and multi-touching text-line segmentation by Block Covering analysis

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Abstract

This paper presents a new approach for text-line segmentation based on Block Covering which solves the problem of overlapping and multi-touching components. Block Covering is the core of a system which processes a set of ancient Arabic documents from historical archives. The system is designed for separating text-lines even if they are overlapping and multi-touching. We exploit the Block Covering technique in three steps: a new fractal analysis (Block Counting) for document classification, a statistical analysis of block heights for block classification and a neighboring analysis for building text-lines. The Block Counting fractal analysis, associated with a fuzzy C-means scheme, is performed on document images in order to classify them according to their complexity: tightly (closely) spaced documents (TSD) or widely spaced documents (WSD). An optimal Block Covering is applied on TSD documents which include overlapping and multi-touching lines. The large blocks generated by the covering are then segmented by relying on the statistical analysis of block heights. The final labeling into text-lines is based on a block neighboring analysis. Experimental results provided on images of the Tunisian Historical Archives reveal the feasibility of the Block Covering technique for segmenting ancient Arabic documents.

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Correspondence to Laurence Likforman-Sulem.

Appendix 1. Composing density between and with clusters (CDbw) criterion

Appendix 1. Composing density between and with clusters (CDbw) criterion

CDbw is defined as the product:

$$ {CDbw(vsn)} = {intra}\_{{den}}({vsn})*{sep}(m{vsn})$$

intra_den expresses the quality of intra-class clustering. sep is the cluster separation measure.

We calculate now the terms of the product:

For a given number of vertical strips vsn = 1/r, let \( V_{i} \; = \;\left\{ {v_{{i1}} ,v_{{i2}} , \cdots ,v_{{in_{i} }} } \right\} \) be the set of blocks of the ith class, and n i be the number of blocks in this class. The standard deviation stddev (i) of the ith class is defined as:

$$ {stddev}(i) = \sqrt {\sum\limits_{{k = 1}}^{{n_{i} }} {\frac{{(h_{{ik}} - m_{i} )^{2} }}{{(n_{i} - 1)}}} } $$

with h ik being the height of the kth block of the ith class and m i being the average height of the blocks of the ith class.

The average stddev is:

$$ {stddev} = \sqrt {\sum\limits_{{i = 1}}^{3} {\frac{{\left\| {{stddev}(i)} \right\|^{2} }}{3}} } ; $$

The quality of intra-class clustering, denoted by intra_den is defined as:

$$ intra\_den(vsn) = \frac{1}{3}\sum\limits_{{i = 1}}^{3} {\sum\limits_{{j = 1}}^{{n_{i} }} {density(v_{{ij}} )} }; $$

with density(v ij ) defined as:

$$ density(v_{{ij}} ) = \sum\limits_{{l = 1}}^{{n_{i} }} {f(v_{{il}} ,v_{{ij}} )}; $$

and f (v il ,v ij ) defined as:

$$f(v_{{il}} ,v_{{ij}} ) = \left\{\begin{array}{*{20}l}1 &\quad {\text{if}}\;||h_{{il}} - h_{{ij}} ||\; \le stddev \\0 &\quad{\text{otherwise}}\\ \end{array}\right.$$

The interclass density Inter_den is defined as the number of blocks being in the close neighborhood of several classes. This density should be very low. It is defined as:

$$ Inter\_den(vsn) = \sum\limits_{{i = 1}}^{3} {\sum\limits_{\begin{subarray}{l} j = 1 \\ j \neq i \end{subarray} }^{3} {\frac{{\left\| {m_{i} - m_{j} } \right\|}}{{\| {{stddev}(i) + {stddev}(j)}\|}}} } \times density(u_{{ij}} ); $$

u ij is a virtual block of height h ij  = (m i +m j )/2

density (u ij ) is defined as:

$$ density(u_{{ij}} ) = \sum\limits_{{k = 1}}^{{n_{i} + n_{j} }} {f(v_{k} ,u_{{ij}} )} $$

with v k belonging to the union set of blocks of classes i and j.

f (v k ,u ij ) is defined as:

$$ f(v_{k} ,u_{{ij}} ) = \left\{ \begin{array}{*{20}l} 1&{\rm if}\ \| {h_{k} - h_{{ij}} } \| \le (\|{{stddev}(i)}\| + \| {{stddev}(j)} \|)/2, \\0& {\rm otherwise} \\ \end{array} \right. $$

The cluster separation measure is defined as:

$$ sep(vsn) = \sum\limits_{{i = 1}}^{3} {\sum\limits_{\begin{subarray}{l} j = 1 \\ j \ne i \end{subarray} }^{3} {\frac{{\left\| {m_{i} - m_{j} } \right\|}}{{1 + Inter\_den}}} } $$

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Zahour, A., Taconet, B., Likforman-Sulem, L. et al. Overlapping and multi-touching text-line segmentation by Block Covering analysis. Pattern Anal Applic 12, 335–351 (2009). https://doi.org/10.1007/s10044-008-0127-9

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