Abstract
In spite of advances in the state of the art of analysis of mathematical and scientific documents, the field is significantly hampered by the lack of large open and copyright free resources for research on and cross evaluation of different algorithms, tools and systems.
To address this deficiency, we have produced a new, high quality scan of Abramowitz and Stegun’s Handbook of Mathematical Functions and made it available on our web site. This text is fully copyright free and hence publicly and freely available for all purposes, including document analysis research. Its history and the respect in which scientists have held the book make it an authoritative source for many types of mathematical expressions, diagrams and tables.
The difficulty of building an initial working document analysis system is a significant barrier to entry to this research field. To reduce that barrier, we have added intermediate results of such a system to the web site, so that research groups can proceed on research challenges of interest to them without having to implement the full tool chain themselves. These intermediate results include the full collection of connected components, with location information, from the text, a set of geometric moments and invariants for each connected component, and segmented images for all plots.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. US Government Printing Office, Washington, 10th printing, with corrections (December 1972)
Ashida, K., Okamoto, M., Imai, H., Nakatsuka, T.: Performance evaluation of a mathematical formula recognition system with a large scale of printed formula images. In: International Workshop on Document Image Analysis for Libraries, pp. 320–331 (2006), http://doi.ieeecomputersociety.org/10.1109/DIAL.2006.30
Boisvert, R.F., Lozier, D.W.: Handbook of mathematical functions. In: Lide, D.R. (ed.) A Century of Excellence in Measurements Standards and Technology, pp. 135–139. CRC Press (2001), http://nvl.nist.gov/pub/nistpubs/sp958-lide/135-139.pdf
Cheriet, M., Kharma, N., Liu, C.L., Suen, C.Y.: Character Recognition Systems — A Guide for Students and Practitioners. Wiley & Sons Ltd., Hoboken (2007)
Cornell University Library (2012), http://www.arxiv.org
Flusser, J., Suk, T., Zitová, B.: Moments and Moment Invariants in Pattern Recognition. Wiley & Sons Ltd., Chichester (2009)
Fuda, T., Omachi, S., Aso, H.: Recognition of line graph images in documents by tracing connected components. Trans. IEICE J86-D-II(6), 825–835 (2003)
Fujiyoshi, A., Suzuki, M., Uchida, S.: Verification of Mathematical Formulae Based on a Combination of Context-Free Grammar and Tree Grammar. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds.) AISC/Calculemus/MKM 2008. LNCS (LNAI), vol. 5144, pp. 415–429. Springer, Heidelberg (2008), http://dx.doi.org/10.1007/978-3-540-85110-3_35
Garain, U., Chaudhuri, B.B.: Ground truth datasets of mathematics, http://www.isical.ac.in/~utpal/resources.php
Garain, U., Chaudhuri, B.B.: A corpus for OCR research on mathematical expressions. IJDAR 7(4), 241–259 (2005), http://dx.doi.org/10.1007/s10032-004-0140-5
Hu, M.K.: Visual pattern recognition by moment invariants. IRE Transactions on Information Theory 8(2), 179–187 (1962)
Miller, B.: Personal communication (2011)
Mukundan, R., Ramakrishnan, K.: Moment Functions in Image Analysis. World Scientific, Singapore (1998)
Phillips, I., Chanda, B., Haralick, R.: UW-III english/technical document image database. University of Washington (2000), http://www.science.uva.nl/research/dlia/datasets/uwash3.html
Stamerjohanns, H., Kohlhase, M.: Transforming the arχiv to XML. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds.) AISC/Calculemus/MKM 2008. LNCS (LNAI), vol. 5144, pp. 574–582. Springer, Heidelberg (2008), http://dx.doi.org/10.1007/978-3-540-85110-3_46
Suzuki, M., Uchida, S., Nomura, A.: A ground-truthed mathematical character and symbol image database. In: Eighth International Conference on Document Analysis and Recognition (ICDAR 2005), pp. 675–679 (2005), http://doi.ieeecomputersociety.org/10.1109/ICDAR.2005.14
Takagi, N.: On consideration of a pattern recognition method for mathematical graphs with broken lines. In: International Workshop on Digitization and E-Inclusion in Mathematics and Science (DEIMS 2012), Tokyo, pp. 43–51 (2012)
The Infty Project: InftyCDB-1–3, InftyMDB-1 (2009), http://www.inftyproject.org/en/database.html
Theodoridis, S., Koutroumbas, K.: Pattern Recognition, 4th edn. Academic Press (2009)
Yampolskiy, R.: Feature Extraction Approaches for Optical Character Recognition. Briviba Scientific Press, Rochester (2007)
Zanibbi, R., Blostein, D.: Recognition and retrieval of mathematical expressions. International Journal on Document Analysis and Recognition, 1–27 (2012), http://dx.doi.org/10.1007/s10032-011-0174-4
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sexton, A.P. (2012). Abramowitz and Stegun – A Resource for Mathematical Document Analysis. In: Jeuring, J., et al. Intelligent Computer Mathematics. CICM 2012. Lecture Notes in Computer Science(), vol 7362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31374-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-31374-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31373-8
Online ISBN: 978-3-642-31374-5
eBook Packages: Computer ScienceComputer Science (R0)