Capturing Abstract Matrices from Paper

  • Toshihiro Kanahori
  • Alan Sexton
  • Volker Sorge
  • Masakazu Suzuki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4108)

Abstract

Capturing and understanding mathematics from print form is an important task in translating written mathematical knowledge into electronic form. While the problem of syntactically recognising mathematical formulas from scanned images has received attention, very little work has been done on semantic validation and correction of recognised formulas. We present a first step towards such an integrated system by combining the Infty system with a semantic analyser for matrix expressions. We applied the combined system in experiments on the semantic analysis of matrix images scanned from textbooks. While the first results are encouraging, they also demonstrate many ambiguities one has to deal with when analysing matrix expressions in different contexts. We give a detailed overview of the problems we encountered that motivate further research into semantic validation of mathematical formula recognition.

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References

  1. 1.
    Anderson, R.: Syntax-Directed Recognition of Hand-Printed Two-dimensional Mathematics. PhD thesis, Harvard University, Cambridge (1968)Google Scholar
  2. 2.
    Blostein, D., Grbavec, A.: Recognition of mathematical notation. In: Handbook on OCR and Document Analysis, ch. 22, pp. 557–582. World Scientific Publishing, Singapore (1997)Google Scholar
  3. 3.
    Chan, K., Yeung, D.: Mathematical expression recognition: a survey. International Journal on Document Analysis and Recognition 3(1), 3–15 (2000)CrossRefGoogle Scholar
  4. 4.
    Ciarlet, P., Miara, B., Thomas, J.: Introduction to numerical linear algebra and optimisation. Cambridge Univ. Press, Cambridge (1989)Google Scholar
  5. 5.
    Heck, A.: Maple Manuals, 3rd edn. Springer, Heidelberg (2003)Google Scholar
  6. 6.
    Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge (1990)MATHGoogle Scholar
  7. 7.
    Kanahori, T., Suzuki, M.: A recognition method of matrices by using variable block pattern elements generating rectangular areas. In: Blostein, D., Kwon, Y.-B. (eds.) GREC 2001. LNCS, vol. 2390, pp. 320–329. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Kanahori, T., Suzuki, M.: Detection of matrices and segmentation of matrix elements in scanned images of scientific documents. In: ICDAR 2003, pp. 433–437 (2003)Google Scholar
  9. 9.
    Kaye, R., Wilson, R.: Linear Algebra. Oxford Univ. Press, Oxford (2003)Google Scholar
  10. 10.
    Sexton, A., Sorge, V.: Abstract matrices in symbolic computation. In: The International Symposium on Symbolic and Algebraic Computation (to appear, 2006)Google Scholar
  11. 11.
    Sexton, A., Sorge, V.: Semantic analysis of matrix structures. In: ICDAR 2005, pp. 1141–1145. IEEE Computer Society Press, Los Alamitos (2005)Google Scholar
  12. 12.
    Sexton, A., Sorge, V.: Processing textbook-style matrices. In: Kohlhase, M. (ed.) MKM 2005. LNCS (LNAI), vol. 3863, pp. 111–125. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Suzuki, M., Tamari, F., Fukuda, R., Uchida, S., Kanahori, T.: Infty: an integrated ocr system for mathematical documents. In: DocEng 2003, pp. 95–104. ACM, New York (2003)CrossRefGoogle Scholar
  14. 14.
    Twaakyondo, H., Okamoto, M.: Structure analysis and recognition of mathematical expressions. In: ICDAR 1995, pp. 430–437 (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Toshihiro Kanahori
    • 1
  • Alan Sexton
    • 2
  • Volker Sorge
    • 2
  • Masakazu Suzuki
    • 3
  1. 1.Tsukuba University of TechnologyJapan
  2. 2.School of Computer ScienceUniversity of BirminghamUK
  3. 3.Faculty of MathematicsKyushu UniversityJapan

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