Optical character recognition for typeset mathematics

ABSTRACT

There is a wealth of mathematical knowledge that could be potentially very useful in many computational applications, but is not available in electronic form. This knowledge comes in the form of mechanically typeset books and journals going back more than a hundred years. Besides these older sources, there are a great many current publications, filled with useful mathematical information, which are difficult if not impossible to obtain in electronic form. What we would like to do is extract character information from these documents, which could then be passed to higher-level parsing routines for further extraction of mathematical content (or any other useful 2-dimensional semantic content). Unfortunately, current commercial OCR (optical character recognition) software packages are quite unable to handle mathematical formulas, since their algorithms at all levels use heuristics developed for other document styles. We are concerned with the development of OCR methods that are able to handle this specialized task of mathematical expression recognition.

REFERENCES

• 1: Gunilla Borgefors, Distance transformations in digital images, Computer Vision, Graphics, and Image Processing, v.34 n.3, p.344-371, June 1986 [doi>10.1016/S0734-189X(86)80047-0]
• 2: P. Chou, "Recognition of equations using a twodimensional stochastic context-free grammar", SPIE Conf. on Visual Communications and Image Processing, Philadelphia, PA, Nov. 1989.
• 3: D. Bierens de Haan. NouveUes Tables d'lnteOrales Definies edition of 1867 corrected, with an English Translation of the Introduction by J.F. Ritt. G. E. Stechert & Co. NY. 1939.
• 4: Richard J. Fateman. "Recognition and Parsing of Typeset Mathematics," UCB CS Division internal report, January 1994.
• 5: Richard J. Fateman and Theodore H. Einwohner. "Automated Integral Tables" U CB CS Division internal report, January 1994.
• 6: D.P. Huttenlocher, Gregory A. Klandermand, William J. Rucklidge. "Comparing Images Using the Hausdorff Distance," Cornell Univ. CS Dept. Tech. Rpt.
• 7: Melvin Klerer and Fred Grossman. "Error Rates in Tables of Indefinite Integrals." Industrial Math. 18 (1968) 31-62. See also, by the same authors, A new table of indefinite integrals; computer processed Dover, New York, 1971.
• 8: G. Kopec and P. Chou, "Automatic generation of custom document image decoders", Proc. Second lntl. Conf. on Doc. Anal. and Recog., Tsukuba Science City, Japan, Oct. 20-22, 1993.
• 9: Nicholas Mitchell. "A Parser for Two-Dimensional OCR of Mathematics," UCB progress report 1993.
• 10: David W. Paglieroni, Distance transforms: properties and machine vision applications, CVGIP: Graphical Models and Image Processing, v.54 n.1, p.56-74, Jan. 1992 [doi>10.1016/1049-9652(92)90034-U]

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems
          Subjects: Special-purpose algebraic systems

Additional Classification:
  B. Hardware
  B.4 INPUT/OUTPUT AND DATA COMMUNICATIONS
      B.4.2 Input/Output Devices

  I. Computing Methodologies
  I.5 PATTERN RECOGNITION
      I.5.4 Applications
          Subjects: Text processing

General Terms:
Algorithms