W-TSV: Weighted topological signature vector for lexicon reduction in handwritten Arabic documents

Abstract

This paper proposes a holistic lexicon-reduction method for ancient and modern handwritten Arabic documents. The word shape is represented by the weighted topological signature vector (W-TSV), which encodes graph data into a low-dimensional vector space. Three directed acyclic graph (DAG) representations are proposed for Arabic word shapes, based on topological and geometrical features. Lexicon reduction is achieved by a nearest neighbors search in the W-TSV space. The proposed framework has been tested on the IFN/ENIT and the Ibn Sina databases, achieving respectively a degree of reduction of 83.5% and 92.9% for an accuracy of reduction of 90%.

Introduction

Handwritten word recognition systems have improved in a number of ways in recent decades, across many applications, from the recognition of the legal amount on bank checks and of postal addresses [1], [2], [3], [4], [5] to the automated transcription of ancient documents [6], [7], [8], [9], [10]. While the vocabulary for a bank check application is small (fewer than 30 words), it is large for postal applications (1000 words) and unconstrained for historical documents (several thousand words). A vocabulary of valid words that are expected to be recognized by the system is called a lexicon [11]. A large lexicon generates a high computational complexity, as all the word hypotheses must be tested, and recognition performance decreases as the number of allowed hypotheses grows. To address this problem, lexicon-reduction methods are used. When a query word shape is submitted for recognition, the lexicon is pruned by keeping only the shapes that are most likely to correspond to the query word class [12], or by using application-dependent knowledge [13]. Then, the recognition system considers the word hypotheses remaining in the pruned lexicon. The performance of a lexicon-reduction method is classically evaluated based on its accuracy of reduction $\alpha$ (the probability that the query word class was included in the pruned lexicon), the degree of reduction $\rho$ (the decrease in the size of the lexicon after pruning), and the reduction efficacy $\eta$, which is a combination of the two previous criteria. Computational complexity is also a major factor in lexicon reduction, as one of its goals is to speed up the recognition process. In this paper, we propose a lexicon-reduction method for handwritten Arabic documents, both ancient and modern.

The Arabic language has an alphabet of 28 letters. The script is cursive and written from right to left. One important feature of Arabic letters is that their shapes are context-dependent, which means that a letter shape is usually determined by its position in a word, i.e. initial, medial or final. The letters have no cases and many share the same base shape. They are distinguishable by the addition of diacritical marks. The diacritics used in Arabic for this purpose are dots, one, two, or three of them appearing below or above the base shape. If we ignore the dots, we obtain the archigraphemes (Fig. 1), where a single grapheme (letter shape) can represent many letters. Four archigrapheme letter shapes (‘A’, ‘D’, ‘R’, ‘W’) can be connected only if they are in the final position. If they appear in the middle of a word, the word is divided into subwords, also known as pieces of Arabic word (PAW).

The goal of this paper is to provide a lexicon-reduction strategy for Arabic documents, based on the structure of Arabic subword shapes, which is described by their topology and geometry. First, the topological and geometrical properties of the subword shapes are extracted from the shape skeleton. Then these properties are encoded in a directed acyclic graph (DAG) in order to preserve information about their relationship in the skeleton. Finally, the subword DAG is transformed into a vector using the weighted topological signature vector (W-TSV), which is an extension of the TSV [14] for weighted DAGs. Like the classical TSV, the W-TSV is a powerful tool for encoding structured data, such as a DAG, mapping the DAG to a low-dimensional vector space for fast matching. Also, it has good discriminatory power for DAGs with different topologies, because it preserves their topological properties to some extent. Unlike the TSV, the W-TSV can also discriminate between DAGs sharing the same topology, but with different weights, and it is more robust to topological perturbation than the TSV under small weight perturbation. In this work, lexicon reduction is performed by pruning the reference database of subword/word shapes. This is achieved by selecting the i nearest shapes in the database to a query shape in the W-TSV space. First, the database is indexed by ordering its shapes in ascending order, based on their distance from the query shape; next, the lexicon is reduced by selecting the first i elements of the indexed lexicon as candidates. The value of i is evaluated during a training phase in order to reach the accuracy of reduction level selected for the application. The same i value is then applied for all the query shapes during the lexicon reduction process. From the reduced database of shapes, it is then possible to build a reduced lexicon of subwords/words from the labels of the selected shapes (Fig. 2).

This paper is organized as follows. The features of lexicon reduction for ancient and modern Arabic documents are described in Section 2. Related work on lexicon reduction is reviewed in Section 3. The details of the W-TSV scheme and of the formation of the Arabic subword DAG are respectively provided in 4 Weighted topological signature vector (W-TSV), 5 Proposed arabic subword graph representation. Finally, the details of our experiments and our results are given in Section 6, followed by the conclusion in Section 7.

This paper is an extension of the work published in [15]. The underlying methodology, as well as the experimental evaluation, has been significantly improved.