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blostein96recognition - Handbook on Optical Character...

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Handbook on Optical Character Recognition and Document Image Analysis, pp. 000-000 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 symbol-arrangement analysis. Symbol-arrangement analysis is particularly difficult for mathematics, due to the subtle use of space in this notation. We begin with a general discussion of the mathematics-recognition problem. This is followed by a review of existing approaches to mathematics recognition, including syntactic methods, projection-profile 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; Symbol-arrangement analysis; Syntactic methods; Projection-profile cutting; Graph rewriting. 1. Introduction Over the centuries, people have developed a specialized two-dimensional 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, two-dimensional mathematical notation can be generated by computers, but recognition facilities are not widely available: the task of translating mathematics into a computer-processable 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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2 Handbook on Optical Character Recognition and Document Image Analysis Manual conversion of notation: Person directly enters the structure of a mathematical expression, by Computer-processable mathematical expression Automatic conversion of notation: Computer recognizes the structure of an expression in two-dimensional mathematical notation. A person wanting to communicate mathematical notation to the computer Scanner (off-line data) Data Tablet (on-line 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 structure-based math editor.
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