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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 widespread availability of Optical Character Recognition (OCR) and textbased ..."
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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 widespread availability of Optical Character Recognition (OCR) and textbased 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.
Teaching With an Intelligent Electronic Chalkboard
 In Proceedings of ACM Multimedia 2004, Workshop on Effective Telepresence
, 2004
"... This paper presents EChalk, a software system which transforms a large touch sensitive screen into a smart teaching tool. The instructor writes on the screen using a special stylus and the software emulates a classical chalkboard. The lecturer can paste images to the board, can send queries to remo ..."
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Cited by 19 (8 self)
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This paper presents EChalk, a software system which transforms a large touch sensitive screen into a smart teaching tool. The instructor writes on the screen using a special stylus and the software emulates a classical chalkboard. The lecturer can paste images to the board, can send queries to remote web services, can activate a computer algebra system, and can paste interactive Java Applets on the board. A copy of the lecture’s audio, the board strokes (and an optional video) is stored on a server. The lecture is also transmitted live over the Internet and can be synchronized with teleconferencing systems for student feedback. The EChalk architecture is based on the metaphor of the classical chalkboard, enhanced by intelligent assistants running in the background. One assistant takes care of interpreting the handwritten input of the user. Another is a mathematical formula recognizer which processes handwritten queries for the algebraic server. A circuit simulator recognizes sketches of digital circuits and runs a simulation. An algorithm simulator accepts sketches of graphs as input data and runs graph algorithms, animating them on the screen. Further assistants can be incorporated using the EChalk API. EChalk is being used in our electronic classroom containing a 6 meter long by 1.15 meter wide rear projection “data wall”.
Developing Handwritingbased Intelligent Tutors to Enhance Mathematics Learning
, 2008
"... Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the NSF or PSLC. Keywords: Handwriting recognition, recognition accuracy, recognition evaluation, writerindependent training, averagerank sort, equat ..."
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Cited by 9 (1 self)
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Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the NSF or PSLC. Keywords: Handwriting recognition, recognition accuracy, recognition evaluation, writerindependent training, averagerank sort, equation entry, mathematics, algebra, intelligent tutoring systems, equation solving, handwritten mathematics, math learning, algebra learning, handwriting
Efficient search strategy in structural analysis for handwritten mathematical expression recognition
 PATTERN RECOGN
, 2009
"... Problems in local ambiguities in handwritten mathematical expressions are often resolved at the global level. For a well performing recognizer, multiple local hypotheses should be kept as long as possible until the ambiguities are resolved by a global analysis. We propose a layered search framework ..."
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Cited by 6 (1 self)
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Problems in local ambiguities in handwritten mathematical expressions are often resolved at the global level. For a well performing recognizer, multiple local hypotheses should be kept as long as possible until the ambiguities are resolved by a global analysis. We propose a layered search framework for handwritten mathematical expression (ME) recognition. From given handwritten input strokes, ME structures are constructed through adding a symbol hypothesis one by one, considering every possible symbol identity and spatial relationship with the existing structure. A cost reflecting the likelihood of a structure is estimated for each newly expanded layer so that a bestfirst search algorithm is applied to seek the most likely structure. The elegance of our method is in that while all the possibilities are examined, the search complexity is made manageable by applying admissible heuristics. Further complexity reduction is achieved by delaying the symbol identity decision. Unless a symbol identity causes structural alternatives for the remaining input strokes, the identity can be determined after the complete structure is fixed. Such a delayed decision reduces undesirable search space expansion. In an implementation targeting high school level MEs, our method achieved high speed with a high level of accuracy which resulted from the system’s capacity to examine a large number of possibilities.
OnLine Graphics Recognition: StateoftheArt
 in GREC 2003: 5th IAPR International Workshop on Graphics Recognition, 2003
, 2003
"... A brief survey on online graphics recognition is presented. We first present some common scenarios and applications of online graphics recognition and then identify major problems and subproblems at three levels: primitive shape recognition, composite graphic object recognition, and document ..."
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Cited by 4 (0 self)
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A brief survey on online graphics recognition is presented. We first present some common scenarios and applications of online graphics recognition and then identify major problems and subproblems at three levels: primitive shape recognition, composite graphic object recognition, and document recognition and understanding. Representative approaches to these problems are also presented. We also list several open problems at the end.
Online Recognition of Handwritten Mathematical Expressions with Support for Matrices
"... We present an online system for recognizing handwritten mathematical matrices in the context of an interactive computational tool called MathPaper. Automatic segmentation and recognition of multiple expressions are supported based on a spacing algorithm that leverages recognized symbol identities, s ..."
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We present an online system for recognizing handwritten mathematical matrices in the context of an interactive computational tool called MathPaper. Automatic segmentation and recognition of multiple expressions are supported based on a spacing algorithm that leverages recognized symbol identities, sizes, and relative locations of individual symbols. Matrices with ellipses can be recognized and instantiated with nonellipsis elements. Both well and nonwellformed matrices can also be recognized. Matrix elements can be any general mathematical expressions including imbedded matrices. Our recognizer also addresses the poor column alignment problem of handwritten matrices, and allows for slight horizontal overlaps between elements in neighboring columns and different rows. 1
A paradigm for handwritingbased intelligent tutors
, 2012
"... Abstract This paper presents the interaction design of, and demonstration of technical feasibility for, intelligent tutoring systems that can accept handwriting input from students. Handwriting and pen input offer several affordances for students that traditional typingbased interactions do not. T ..."
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Abstract This paper presents the interaction design of, and demonstration of technical feasibility for, intelligent tutoring systems that can accept handwriting input from students. Handwriting and pen input offer several affordances for students that traditional typingbased interactions do not. To illustrate these affordances, we present evidence, from tutoring mathematics, that the ability to enter problem solutions via pen input enables students to record algebraic equations more quickly, more smoothly (fewer errors), and with increased transfer to noncomputerbased tasks. Furthermore our evidence shows that students tend to like pen input for these types of problems more than typing. However, a clear downside to introducing handwriting input into intelligent tutors is that the recognition of such input is not reliable. In our work, we have found that handwriting input is more likely to be useful and reliable when context is considered, for example, the context of the problem being solved. We present an intelligent tutoring system for algebra equation solving via penbased input that is able to use context to decrease recognition errors by 18% and to reduce recognition error recovery interactions to occur on one out of every four problems. We applied usercentered design principles to reduce the negative impact of recognition errors in the following ways: (1) though students handwrite their problemsolving process, they type their final answer to reduce ambiguity for tutoring purposes, and (2) in the small number of cases in which the system must involve the student in recognition error recovery, the interaction focuses on identifying the student's problemsolving error to keep the emphasis on tutoring. Many potential recognition errors can thus be ignored and distracting interactions are avoided. This work can inform the design of future systems for students using pen and sketch input for math or other topics by motivating the use of context and pragmatics to decrease the impact of recognition errors and put user focus on the task at hand.
OnLine Graphics Recognition: A Brief Survey
"... Abstract. A brief survey on online graphics recognition is presented. We first present some common scenarios and applications of online graphics recognition and then identify major problems and subproblems at three levels: primitive shape recognition, composite graphic object recognition, and doc ..."
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Cited by 1 (0 self)
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Abstract. A brief survey on online graphics recognition is presented. We first present some common scenarios and applications of online graphics recognition and then identify major problems and subproblems at three levels: primitive shape recognition, composite graphic object recognition, and document recognition and understanding. Representative approaches to these problems are also presented. We also list several open problems at the end. 1
ONLINE HANDWRITTEN MATHEMATICAL EXPRESSION RECOGNITION
, 2005
"... This thesis presents a system for online handwritten mathematical expression recognition that involves integrals, summation notation, superscripts and subscripts, squareroots, fractions, trigonometric and logarithmic functions; together with a userinterface for writing scientific articles. The aim ..."
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Cited by 1 (1 self)
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This thesis presents a system for online handwritten mathematical expression recognition that involves integrals, summation notation, superscripts and subscripts, squareroots, fractions, trigonometric and logarithmic functions; together with a userinterface for writing scientific articles. The aim
Representation, recognition and collaboration . . .
, 2013
"... Pen input for computing devices is now widespread, providing a promising interaction mechanism for many purposes. Nevertheless, the diverse nature of digital ink and varied application domains still present many challenges. First, the sampling rate and resolution of penbased devices keep improving ..."
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Pen input for computing devices is now widespread, providing a promising interaction mechanism for many purposes. Nevertheless, the diverse nature of digital ink and varied application domains still present many challenges. First, the sampling rate and resolution of penbased devices keep improving, making input data more costly to process and store. At the same time, existing applications typically record digital ink either in proprietary formats, which are restricted to single platforms and consequently lack portability, or simply as images, which lose important information. Moreover, in certain domains such as mathematics, current systems are now achieving good recognition rates on individual symbols, in general recognition of complete expressions remains a problem due to the absence of an effective method that can reliably identify the spatial relationships among symbols. Last, but not least, existing digital ink collaboration tools are platformdependent and typically allow only one input method to be used at a time. Together with the absence of recognition, this has placed significant limitations on what can be done.