Structural analysis of mathematical formulae with verification based on formula description grammar
Identifieur interne : 000309 ( PascalFrancis/Checkpoint ); précédent : 000308; suivant : 000310Structural analysis of mathematical formulae with verification based on formula description grammar
Auteurs : Seiichi Toyota [Japon] ; Seiichi Uchida [Japon] ; Masakazu Suzuki (mathématicien) [Japon]Source :
- Lecture notes in computer science [ 0302-9743 ] ; 2006.
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Abstract
In this paper, a reliable and efficient structural analysis method for mathematical formulae is proposed for practical mathematical OCR. The proposed method consists of three steps. In the first step, a fast structural analysis algorithm is performed on each mathematical formula to obtain a tree representation of the formula. This step generally provides a correct tree representation but sometimes provides an erroneous representation. Therefore, the tree representation is verified by the following two steps. In the second step, the result of the analysis step, (i.e., a tree representation) is converted into a one-dimensional representation. The third step is a verification step where the one-dimensional representation is parsed by a formula description grammar, which is a context-free grammar specialized for mathematical formulae. If the one-dimensional representation is not accepted by the grammar, the result of the analysis step is detected as an erroneous result and alarmed to OCR users. This three-step organization achieves reliable and efficient structural analysis without any two-dimensional grammars.
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type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Alarm</term><term>Algorithm analysis</term><term>Character recognition</term><term>Context free grammar</term><term>Document analysis</term><term>Document structure</term><term>Fast algorithm</term><term>Image processing</term><term>Mathematical formula</term><term>Optical character recognition</term><term>Pattern recognition</term><term>Step method</term><term>Structural analysis</term><term>Two dimensional analysis</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Traitement image</term><term>Reconnaissance forme</term><term>Analyse documentaire</term><term>Structure document</term><term>Analyse structurale</term><term>Grammaire CF</term><term>Reconnaissance caractère</term><term>Reconnaissance optique caractère</term><term>Alarme</term><term>Formule mathématique</term><term>Méthode à pas</term><term>Algorithme rapide</term><term>Analyse algorithme</term><term>Analyse bidimensionnelle</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In this paper, a reliable and efficient structural analysis method for mathematical formulae is proposed for practical mathematical OCR. The proposed method consists of three steps. In the first step, a fast structural analysis algorithm is performed on each mathematical formula to obtain a tree representation of the formula. This step generally provides a correct tree representation but sometimes provides an erroneous representation. Therefore, the tree representation is verified by the following two steps. In the second step, the result of the analysis step, (i.e., a tree representation) is converted into a one-dimensional representation. The third step is a verification step where the one-dimensional representation is parsed by a formula description grammar, which is a context-free grammar specialized for mathematical formulae. If the one-dimensional representation is not accepted by the grammar, the result of the analysis step is detected as an erroneous result and alarmed to OCR users. This three-step organization achieves reliable and efficient structural analysis without any two-dimensional grammars.</div></front></TEI><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0302-9743</s0></fA01><fA05><s2>3872</s2></fA05><fA08 i1="01" i2="1" l="ENG"><s1>Structural analysis of mathematical formulae with verification based on formula description grammar</s1></fA08><fA09 i1="01" i2="1" l="ENG"><s1>Document analysis systems VII : 7th international workshop, DAS 2006, Nelson, New Zealand, February 13-15, 2006 : proceedings</s1></fA09><fA11 i1="01" i2="1"><s1>TOYOTA (Seiichi)</s1></fA11><fA11 i1="02" i2="1"><s1>UCHIDA (Seiichi)</s1></fA11><fA11 i1="03" i2="1"><s1>SUZUKI (Masakazu)</s1></fA11><fA12 i1="01" i2="1"><s1>BUNKE (Horst)</s1><s9>ed.</s9></fA12><fA12 i1="02" i2="1"><s1>SPITZ (A. 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