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Recognition and Retrieval of Mathematical Expressions
- INTERNATIONAL JOURNAL ON DOCUMENT ANALYSIS AND RECOGNITION
"... 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 ..."
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Cited by 31 (10 self)
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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.
Logical Structure Recovery in Scholarly Articles with Rich Document Features
"... Scholarly digital libraries increasingly provide analytics to information within documents themselves. This includes information about the logical document structure of use to downstream components, such as search, navigation and summarization. We describe SectLabel, a module that further develops e ..."
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Cited by 15 (1 self)
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Scholarly digital libraries increasingly provide analytics to information within documents themselves. This includes information about the logical document structure of use to downstream components, such as search, navigation and summarization. We describe SectLabel, a module that further develops existing software to detect the logical structure of a document from existing PDF files, using the formalism of conditional random fields. While previous work has assumed access only to the raw text representation of the document, a key aspect of our work is to integrate the use of a richer representation of the document that includes features from optical character recognition (OCR), such as font size and text position. Our experiments reveal that using such rich features improves logical structure detection by a significant 9 F1 points, over a suitable baseline, motivating the use of richer document representations in other digital library applications.
D.: Mathbrush: a system for doing math on pen-based devices
- In: The Eighth IAPR Workshop on Document Analysis Systems (DAS
, 2008
"... Many on-line (interactive) mathematics recognition systems allow the creation of typeset equations, normally in LaTeX, but they do not support mathematical problem solving. In this paper, we present MathBrush, a system that allows users to draw math input using a pen-input device on a tablet compute ..."
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Cited by 14 (5 self)
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Many on-line (interactive) mathematics recognition systems allow the creation of typeset equations, normally in LaTeX, but they do not support mathematical problem solving. In this paper, we present MathBrush, a system that allows users to draw math input using a pen-input device on a tablet computer, recognizes the math expression, and then supports mathematical transformation and problem solving using back-end Computer Algebra Systems (CAS). We describe the architecture of the MathBrush system, which includes modules that support symbol recognition, semantic analysis, the transfer of recognized expressions to back-end CAS, and interface techniques for interacting with CAS output. We also identify unique challenges associated with recognition for math problem solving, such as the need for deeper semantic analysis than is required by LATEX, and the need to deal with ambiguities in user input. Our experiences serve to inform researchers seeking to design interactive mathematics recognition systems geared toward mathematical problem solving. 1.
Towards a parser for mathematical formula recognition
- In Carbonell and Siekmann [9
, 2006
"... Abstract. For the transfer of mathematical knowledge from paper to electronic form, the reliable automatic analysis and understanding of mathematical texts is crucial. A robust system for this task needs to combine low level character recognition with higher level structural analysis of mathematical ..."
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Abstract. For the transfer of mathematical knowledge from paper to electronic form, the reliable automatic analysis and understanding of mathematical texts is crucial. A robust system for this task needs to combine low level character recognition with higher level structural analysis of mathematical formulas. We present progress towards this goal by extending a database-driven optical character recognition system for mathematics with two high level analysis features. One extends and enhances the traditional approach of projection profile cutting. The second aims at integrating the recognition process with graph grammar rewriting by giving support to the interactive construction and validation of grammar rules. Both approaches can be successfully employed to enhance the capabilities of our system to recognise and reconstruct compound mathematical expressions. 1
Capturing Abstract Matrices from Paper
- In [6
, 2006
"... Abstract. Capturing and understanding mathematics from print form is an important task in translating written mathematical knowledge into electronic form. While the problem of syntactically recognising mathematical formulas from scanned images has received attention, very little work has been done o ..."
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Abstract. Capturing and understanding mathematics from print form is an important task in translating written mathematical knowledge into electronic form. While the problem of syntactically recognising mathematical formulas from scanned images has received attention, very little work has been done on semantic validation and correction of recognised formulas. We present a first step towards such an integrated system by combining the Infty system with a semantic analyser for matrix expressions. We applied the combined system in experiments on the semantic analysis of matrix images scanned from textbooks. While the first results are encouraging, they also demonstrate many ambiguities one has to deal with when analysing matrix expressions in different contexts. We give a detailed overview of the problems we encountered that motivate further research into semantic validation of mathematical formula recognition. 1
A Linear Grammar Approach to Mathematical Formula Recognition from PDF
"... Abstract. Many approaches have been proposed over the years for the recognition of mathematical formulae from scanned documents. More recently a need has arisen to recognise formulae from PDF documents. Here we can avoid ambiguities introduced by traditional OCR approaches and instead extract perfec ..."
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Cited by 8 (3 self)
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Abstract. Many approaches have been proposed over the years for the recognition of mathematical formulae from scanned documents. More recently a need has arisen to recognise formulae from PDF documents. Here we can avoid ambiguities introduced by traditional OCR approaches and instead extract perfect knowledge of the characters used in formulae directly from the document. This can be exploited by formula recognition techniques to achieve correct results and high performance. In this paper we revisit an old grammatical approach to formula recognition, that of Anderson from 1968, and assess its applicability with respect to data extracted from PDF documents. We identify some problems of the original method when applied to common mathematical expressions and show how they can be overcome. The simplicity of the original method leads to a very efficient recognition technique that not only is very simple to implement but also yields results of high accuracy for the recognition of mathematical formulae from PDF documents. 1
Automated Tactile Graphics Translation: In the Field
"... We address the practical problem of automating the process of translating figures from mathematics, science, and engineering textbooks to a tactile form suitable for blind students. The Tactile Graphics Assistant (TGA) and accompanying workflow is described. Components of the TGA that identify text ..."
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We address the practical problem of automating the process of translating figures from mathematics, science, and engineering textbooks to a tactile form suitable for blind students. The Tactile Graphics Assistant (TGA) and accompanying workflow is described. Components of the TGA that identify text and replace it with Braille use machine learning, computational geometry, and optimization algorithms. We followed through with the ideas in our 2005 paper by creating a more detailed workflow, translating actual images, and analyzing the translation time. Our experience in translating more than 2,300 figures from 4 textbooks demonstrates that figures can be translated in ten minutes or less of human time on average. We describe our experience with training tactile graphics specialists to use the new TGA technology.
D.: A preliminary report on the MathBrush pen-math system
- In: Maple 2006 Conference
, 2006
"... In this paper we give a preliminary description of an experimental system, currently named MathBrush, for working with mathematics using pen-based devices. The system allows a user to enter mathematical expressions with a pen and to then do mathematical computation using a computer algebra system. T ..."
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Cited by 6 (1 self)
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In this paper we give a preliminary description of an experimental system, currently named MathBrush, for working with mathematics using pen-based devices. The system allows a user to enter mathematical expressions with a pen and to then do mathematical computation using a computer algebra system. The system provides a simple and easy way for users to verify the correctness of their handwritten expressions and, if needed, to correct any errors in recognition. Choosing mathematical operations is done making use of context menus, both with input and output expressions.
Mathematical Document Classification via Symbol Frequency Analysis
"... Abstract. Earlier work has examined the frequency of symbol and expression use in mathematical documents for various purposes including mathematical handwriting recognition and forming the most natural output from computer algebra systems. This work has found, unsurprisingly, that the particulars of ..."
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Abstract. Earlier work has examined the frequency of symbol and expression use in mathematical documents for various purposes including mathematical handwriting recognition and forming the most natural output from computer algebra systems. This work has found, unsurprisingly, that the particulars of symbol and expression vary from area to area and, in particular, between different top-level subjects of the 2000 Mathematical Subject Classification. If the area of mathematics is known in advance, then an area-specific information can be used for the recognition or output problem. What is more interesting is that although the specifics of which symbols are ranked as most frequent vary from area to area, the shape of the relative frequency curve remains the same. The present work examines the inverse problem: Given the relative frequencies of symbols in a document, is it possible to classify the document and determine the most likely area of mathematics of the work? We examine the symbol frequency “fingerprints ” for the different areas of the Mathematical Subject Classification. 1
A Survey on Recognition of On-Line Handwritten Mathematical Notation
, 2007
"... This report describes recent advances in the area of the recognition of on-line handwritten mathematical notation. We describe architectures, symbol classification methods, and techniques for the structural analysis of mathematical expressions. We also survey applications specialized for mathematica ..."
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Cited by 6 (0 self)
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This report describes recent advances in the area of the recognition of on-line handwritten mathematical notation. We describe architectures, symbol classification methods, and techniques for the structural analysis of mathematical expressions. We also survey applications specialized for mathematical notation.
