A Knowledge-Based Design for Structural Analysis of Printed Mathematical Expressions

  • Pavan Kumar P.
  • Arun Agarwal
  • Chakravarthy Bhagvati
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8875)

Abstract

Recognition of Mathematical Expressions (MEs) is a challenging Artificial Intelligence problem as MEs have a complex two dimensional structure. ME recognition involves two stages: Symbol recognition and Structural Analysis. Symbols are recognized in the first stage and spatial relationships like superscript, subscript etc., are determined in the second stage. In this paper, we have focused on structural analysis of printed MEs. For structural analysis, we have proposed a novel ternary tree based representation that captures spatial relationships among the symbols in a given ME. Proposed tree structure has been used for validation of generated ME structure. Structure validation process detects errors based on domain knowledge (mathematics) and the error feedback is used to correct the structure. Therefore, our validation process incorporates an intelligent mechanism to automatically detect and correct the errors. Proposed approach has been tested on an image database of 829 MEs collected from various mathematical documents and experimental results are reported on them.

Keywords

Mathematical expressions structural analysis ternary tree representation domain knowledge structure validation 
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References

  1. 1.
    Álvaro, F., Sánchez, J.A., Benedí, J.M.: Classification of on-line mathematical symbols with hybrid features and recurrent neural networks. In: International Conference on Document Analysis and Recognition (ICDAR), pp. 1012–1016 (2013)Google Scholar
  2. 2.
    Buchanan, B.G., Shortliffe, E.H.: Rule Based Expert Systems: The Mycin Experiments of the Stanford Heuristic Programming Project. Addison-Wesley (1984)Google Scholar
  3. 3.
    Chan, K.F., Yeung, D.Y.: An efficient syntactic approach to structural analysis of on-line handwritten mathematical expressions. Pattern Recognition 33(3), 375–384 (2000)CrossRefGoogle Scholar
  4. 4.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. The MIT Press and McGraw-Hill Book Company (1989)Google Scholar
  5. 5.
    Eto, Y., Suzuki, M.: Mathematical formula recognition using virtual link network. In: ICDAR 2001, pp. 762–767. IEEE Computer Society, Washington, DC (2001)Google Scholar
  6. 6.
    Garain, U., Chaudhuri, B.B.: Recognition of online handwritten mathematical expressions. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 34(6), 2366–2376 (2004)CrossRefGoogle Scholar
  7. 7.
    Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 2nd edn. Pearson Education Indian Reprint (2003)Google Scholar
  8. 8.
    Lee, H.J., Wang, J.S.: Design of a mathematical expression understanding system. Pattern Recognition Letters 18(3), 289–298 (1997)CrossRefGoogle Scholar
  9. 9.
    MacLean, S., Labahn, G.: A new approach for recognizing handwritten mathematics using relational grammars and fuzzy sets. IJDAR 16(2), 139–163 (2013)CrossRefGoogle Scholar
  10. 10.
    PACME: Printed Mathematical Expression Image Database (2010), http://dcis.uohyd.ernet.in/~pavanp/mathocr/PrintedMEs.zip
  11. 11.
    Pavan Kumar, P., Agarwal, A., Bhagvati, C.: A rule-based approach to form mathematical symbols in printed mathematical expressions. In: Sombattheera, C., Agarwal, A., Udgata, S.K., Lavangnananda, K. (eds.) MIWAI 2011. LNCS (LNAI), vol. 7080, pp. 181–192. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Pavan Kumar, P., Agarwal, A., Bhagvati, C.: A structure based approach for mathematical expression retrieval. In: Sombattheera, C., Loi, N.K., Wankar, R., Quan, T. (eds.) MIWAI 2012. LNCS (LNAI), vol. 7694, pp. 23–34. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  13. 13.
    Pavan Kumar, P., Agarwal, A., Bhagvati, C.: A string matching based algorithm for performance evaluation of mathematical expression recognition. Sadhana 39(1), 63–79 (2014)CrossRefGoogle Scholar
  14. 14.
    Suzuki, M., Tamari, F., Fukuda, R., Uchida, S., Kanahori, T.: Infty-an integrated OCR system for mathematical documents. In: Proceedings of ACM Symposium on Document Engineering 2003, pp. 95–104. ACM Press (2003)Google Scholar
  15. 15.
    Tapia, E., Rojas, R.: Recognition of on-line handwritten mathematical expressions using a minimum spanning tree construction and symbol dominance. In: Lladós, J., Kwon, Y.-B. (eds.) GREC 2003. LNCS, vol. 3088, pp. 329–340. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Tian, X., Fan, H.: Structural analysis based on baseline in printed mathematical expressions. In: PDCAT 2005, pp. 787–790 (2005)Google Scholar
  17. 17.
    Zanibbi, R., Blostein, D., Cordy, J.R.: Directions in recognizing tabular structures of handwritten mathematics notation. In: Proceedings of IAPR International Workshop on Graphics Recognition (2001)Google Scholar
  18. 18.
    Zanibbi, R., Blostein, D.: Recognition and retrieval of mathematical expressions. IJDAR 15(4), 331–357 (2012)CrossRefGoogle Scholar
  19. 19.
    Zanibbi, R., Blostein, D., Cordy, J.R.: Recognizing mathematical expressions using tree transformation. IEEE Transactions on PAMI 24(11), 1455–1467 (2002)CrossRefGoogle Scholar
  20. 20.
    Zwillinger, D.: CRC Standard Mathematical Tables and Formulae, 30th edn. CRC Press, Boca Raton (1996)MATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Pavan Kumar P.
    • 1
  • Arun Agarwal
    • 1
  • Chakravarthy Bhagvati
    • 1
  1. 1.School of Computer and Information SciencesUniversity of HyderabadHyderabadIndia

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