Mathematics recognition using graph rewriting

Grbavec, Ann; Blostein, Dorothea

doi:10.1109/icdar.1995.599026

Cited by 45 publications

(17 citation statements)

References 10 publications

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“…The earliest approach to recognizing symbol layout, by Anderson, is of this type: an operator tree is constructed top-down, and then a string representing the tree structure is synthesized bottom-up [5]. A number of different attributed grammar types have been used, including context-free string grammars [43] and graph grammars [58,87,137].…”

Section: Mathematical Content Interpretationmentioning

confidence: 99%

Recognition and retrieval of mathematical expressions

Zanibbi

Blostein

2011

IJDAR

234

112

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Document recognition and retrieval technologies complement one another, providing improved access to increasingly large document collections. While recognition and retrieval of textual information is fairly mature, with wide-spread availability of Optical Character Recognition (OCR) and text-based search engines, recognition and retrieval of graphics such as images, figures, tables, diagrams, and mathematical expressions are in comparatively early stages of research. This paper surveys the state of the art in recognition and retrieval of mathematical expressions, organized around four key problems in math retrieval (query construction, normalization, indexing, and relevance feedback), and four key problems in math recognition (detecting expressions, detecting and classifying symbols, analyzing symbol layout, and constructing a representation of meaning). Of special interest is the machine learning problem of jointly optimizing the component algorithms in a math recognition system, and developing effective indexing, retrieval and relevance feedback algorithms for math retrieval. Another important open problem is developing user interfaces that seamlessly integrate recognition and retrieval. Activity in these important research areas is increasing, in part because math notation provides an excellent domain for studying problems common to many document and graphics recognition and retrieval applications, and also because mature applications will likely provide substantial benefits for education, research, and mathematical literacy.

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Section: Mathematical Content Interpretationmentioning

confidence: 99%

Recognition and retrieval of mathematical expressions

Zanibbi

Blostein

2011

IJDAR

234

112

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“…A more complicated grammar-based approach, graph grammar rewriting technique (Grbavec and Blostein, 1995;Lavirotte and Pottier, 1997;Raja et al, 2006), was proposed by first creating an initial graph using compass point directions from each symbol. Then, hand-crafted grammar rules are used to specify a graph fragment for matching and a non-terminal graph fragment for replacing it with.…”

Section: Related Workmentioning

confidence: 99%

Progressive structural analysis for dynamic recognition of on-line handwritten mathematical expressions

Vuong

Hui

2008

Pattern Recognition Letters

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Structural analysis in handwritten mathematical expressions focuses on interpreting the recognized symbols using geometrical information such as relative sizes and positions of the symbols. Most existing approaches rely on hand-crafted grammar rules to identify semantic relationships among the recognized mathematical symbols. They could easily fail when writing errors occurred. Moreover, they assume the availability of the whole mathematical expression before being able to analyze the semantic information of the expression. To tackle these problems, we propose a Progressive Structural Analysis (PSA) approach for dynamic recognition of handwritten mathematical expressions. The proposed PSA approach is able to provide analysis result immediately after each written input symbol. This has an advantage that users are able to detect any recognition errors immediately and correct only the mis-recognized symbols rather than the whole expression. Experiments conducted Preprint submitted to Elsevier 14 September 2007on 57 most commonly used mathematical expressions have shown that the PSA approach is able to achieve very good performance results.

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“…For example, point size can be used to decide whether the configuration x i is a subscript (as in the expression x i y i ) or whether the spatial relationship is a byproduct of other operators (as in the expression a x i). As a result, the graph grammar uses simpler, more efficient interpretation strategies than are used in Grbavec's approach [GrBl95] discussed in Section 3. Lavirotte's work inspired the graph grammar used in the math recognition system by Smithies et al [SmNA01].…”

Section: Graph Grammar To Produce a Parse Treementioning

confidence: 98%

Graph Transformation in Document Image Analysis: Approaches and Challenges

Blostein

2005

Graph-Based Representations in Pattern Recognition

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Abstract. Graphs and graph transformation are versatile tools for representing and interpreting the contents of document images. Three main components are involved: a graph representing the contents of a document image at some level of interpretation, a set of graph transformation rules (graph productions), and a mechanism for controlling the application of the graph productions. We review existing document analysis systems that use graph transformation, and discuss challenges and research opportunities in this area.

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Mathematics recognition using graph rewriting

Cited by 45 publications

References 10 publications

Recognition and retrieval of mathematical expressions

Recognition and retrieval of mathematical expressions

Progressive structural analysis for dynamic recognition of on-line handwritten mathematical expressions

Graph Transformation in Document Image Analysis: Approaches and Challenges

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