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

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.

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:

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