Recognizing mathematical expressions using tree transformation
Top Cited Papers
- 1 November 2002
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 24 (11) , 1455-1467
- https://doi.org/10.1109/tpami.2002.1046157
Abstract
We describe a robust and efficient system for recognizing typeset and handwritten mathematical notation. From a list of symbols with bounding boxes the system analyzes an expression in three successive passes. The Layout Pass constructs a Baseline Structure Tree (BST) describing the two-dimensional arrangement of input symbols. Reading order and operator dominance are used to allow efficient recognition of symbol layout even when symbols deviate greatly from their ideal positions. Next, the Lexical Pass produces a Lexed BST from the initial BST by grouping tokens comprised of multiple input symbols; these include decimal numbers, function names, and symbols comprised of nonoverlapping primitives such as "=". The Lexical Pass also labels vertical structures such as fractions and accents. The Lexed BST is translated into L/sup A/T/sub E/X. Additional processing, necessary for producing output for symbolic algebra systems, is carried out in the Expression Analysis Pass. The Lexed BST is translated into an Operator Tree, which describes the order and scope of operations in the input expression. The tree manipulations used in each pass are represented compactly using tree transformations. The compiler-like architecture of the system allows robust handling of unexpected input, increases the scalability of the system, and provides the groundwork for handling dialects of mathematical notation.Keywords
This publication has 28 references indexed in Scilit:
- Baseline structure analysis of handwritten mathematics notationPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Mathematical formula recognition using virtual link networkPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Performance evaluation of a robust method for mathematical expression recognitionPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Error detection, error correction and performance evaluation in on-line mathematical expression recognitionPattern Recognition, 2001
- Equation entry and editing via handwriting and gesture recognitionBehaviour & Information Technology, 2001
- Empirical performance evaluation of graphics recognition systemsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1999
- A technique of mathematical expression structure analysis for the handwriting input systemPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1999
- A parsing methodology for the implementation of visual systemsIEEE Transactions on Software Engineering, 1997
- Understanding mathematical expressions using procedure-oriented transformationPattern Recognition, 1994
- A Syntactic Approach for Handwritten Mathematical Formula RecognitionPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1984