Handbook on Optical Character Recognition and Document Image Analysis, pp. 000000
Eds. P.S.P. Wang and H. Bunke
© World Scientific Publishing Company, 1996
CHAPTER 22
RECOGNITION OF MATHEMATICAL NOTATION
*
DOROTHEA BLOSTEIN
†
and
ANN GRBAVEC
Department of Computing and Information Science
Queen’s University, Kingston, Ontario, Canada
K7L 3N6
Recognition of mathematical notation involves two main components: symbol
recognition and symbolarrangement analysis.
Symbolarrangement analysis is
particularly difficult for mathematics, due to the subtle use of space in this notation.
We begin with a general discussion of the mathematicsrecognition problem.
This is
followed by a review of existing approaches to mathematics recognition, including
syntactic methods, projectionprofile cutting, graph rewriting, and procedurally
coded math syntax.
A central problem in all recognition approaches is to find a
convenient, expressive, and effective method for representing the notational
conventions of mathematics.
Keywords
:
Computer recognition of mathematical notation; Notational
conventions; Symbol recognition; Symbolarrangement analysis; Syntactic
methods; Projectionprofile cutting; Graph rewriting.
1. Introduction
Over the centuries, people have developed a specialized twodimensional notation for
communicating with each other about mathematics. The notation is designed to represent
ideas in a way that aids mathematical thinking and visualization.
It is natural and
convenient for people to communicate with computers using this same notation.
This
involves conversion between mathematical notation and internal computer
representations.
Under current technology, twodimensional mathematical notation can be
generated by computers, but recognition facilities are not widely available: the task of
translating mathematics into a computerprocessable form usually falls to a human user
(Fig. 1).
By relieving the user of the burden of translation, a mathematics recognition
system enhances the usefulness of computers as a tool for mathematics and document
handling.
*
This research is supported by Canada’s Natural Sciences and Engineering Research Council.
†
[email protected]
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Handbook on Optical Character Recognition and Document Image Analysis
Manual conversion
of notation:
Person directly enters the structure
of a mathematical expression, by
Computerprocessable
mathematical expression
Automatic conversion
of notation:
Computer recognizes the structure
of an expression in twodimensional
mathematical notation.
A person wanting to
communicate mathematical
notation to the computer
Scanner
(offline data)
Data Tablet
(online data)
(when output is desired)
Screen
Printer
Notation generator
Typing an ASCII form of the
mathematical expression, or
Issuing a sequence of commands
to a structurebased math editor.
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 Table of mathematical symbols, Mathematical notation

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