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Grammatical Verification for Mathematical Formula Recognition Based on Context-Free Tree Grammar

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Abstract

This paper proposes the use of a formal grammar for the verification of mathematical formulae for a practical mathematical OCR system. Like a C compiler detecting syntax errors in a source file, we want to have a verification mechanism to find errors in the output of mathematical OCR. A linear monadic context-free tree grammar (LM-CFTG) is employed as a formal framework to define “well-formed” mathematical formulae. A cubic time parsing algorithm for LM-CFTGs is presented. For the purpose of practical evaluation, a verification system for mathematical OCR is developed, and the effectiveness of the system is demonstrated by using the ground-truthed mathematical document database InftyCDB-1 and a misrecognition database newly constructed for this study.

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Authors and Affiliations

  1. Department of Computer and Information Sciences, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki, 316-8511, Japan

    Akio Fujiyoshi

  2. Graduate School of Mathematics, Kyushu University, 6-10-1Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

    Masakazu Suzuki

  3. Graduate School of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Seiichi Uchida

Authors
  1. Akio Fujiyoshi
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  2. Masakazu Suzuki
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  3. Seiichi Uchida
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Correspondence to Akio Fujiyoshi.

Additional information

An earlier version of this article [1] was presented at the 7th International Conference on Mathematical Knowledge Management (MKM 2008).

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Fujiyoshi, A., Suzuki, M. & Uchida, S. Grammatical Verification for Mathematical Formula Recognition Based on Context-Free Tree Grammar. Math.Comput.Sci. 3, 279–298 (2010). https://doi.org/10.1007/s11786-010-0023-8

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  • DOI: https://doi.org/10.1007/s11786-010-0023-8

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