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Mathematical Expression Recognition: A Survey
, 2000
"... . Automatic recognition of mathematical expressions is one of the key vehicles in the drive towards transcribing documents in scientific and engineering disciplines into electronic form. This problem typically consists of two major stages, namely, symbol recognition and structural analysis. In this ..."
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. Automatic recognition of mathematical expressions is one of the key vehicles in the drive towards transcribing documents in scientific and engineering disciplines into electronic form. This problem typically consists of two major stages, namely, symbol recognition and structural analysis. In this survey paper, we will review most of the existing work with respect to each of the two major stages of the recognition process. In particular, we try to put emphasis on the similarities and differences between systems. Moreover, some important issues in mathematical expression recognition will be addressed in depth. All these together serve to provide a clear overall picture of how this research area has been developed to date. Key words: error detection and correction  mathematical expression recognition  performance evaluation  structural analysis  symbol recognition 1
Error Detection, Error Correction and Performance Evaluation in Online MATHEMATICAL EXPRESSION RECOGNITION
 PATTERN RECOGNITION
, 2001
"... Automatic recognition of online mathematical expressions is difficult especially when there exist errors. In this paper, we incorporate an error detection and correction mechanism into a parser developed previously by us based on definite clause grammar (DCG). The resulting system can handle lexica ..."
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Cited by 22 (1 self)
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Automatic recognition of online mathematical expressions is difficult especially when there exist errors. In this paper, we incorporate an error detection and correction mechanism into a parser developed previously by us based on definite clause grammar (DCG). The resulting system can handle lexical, syntactic and some semantic errors. The recognition speed for 600 commonly seen expressions is quite acceptable, ranging from 0.73 to 6 s per expression on a modest workstation. In addition, we propose a performance evaluation scheme which can be used to demonstrate the effectiveness of both the symbol recognition and structural analysis stages by a single measure.
Mathematical Sketching: A New Approach to Creating and Exploring Dynamic Illustrations
, 2005
"... Diagrams and illustrations are frequently used to help explain mathematical concepts. Students often create them with pencil and paper as an intuitive aid in visualizing relationships among variables, constants, and functions, and use them as a guide in writing the appropriate mathematics to solve ..."
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Cited by 19 (4 self)
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Diagrams and illustrations are frequently used to help explain mathematical concepts. Students often create them with pencil and paper as an intuitive aid in visualizing relationships among variables, constants, and functions, and use them as a guide in writing the appropriate mathematics to solve the problem. However, such static diagrams generally assist only in the initial formulation of the required mathematics, not in “debugging ” or problem analysis. This can be a severe limitation, even for simple problems with a natural mapping to the temporal dimension or problems with complex spatial relationships. To overcome these limitations we present mathematical sketching, a novel, penbased, gestural interaction paradigm for mathematics problem solving. Mathematical sketching derives from the familiar pencilandpaper process of drawing supporting diagrams to facilitate the formulation of mathematical expressions; however, with mathematical sketching, users can also leverage their physical intuition by watching their handdrawn diagrams animate in response to continuous or discrete parameter changes in their written formulas. Diagram animation is driven by implicit associations that are inferred, either automatically or with gestural guidance, from mathematical expressions, diagram labels and drawing elements. We describe
PenCalc: A Novel Application of OnLine Mathematical Expression Recognition Technology
 In Proceedings of the Sixth International Conference on Document Analysis and Recognition
, 2001
"... Most of the calculator programs found in existing penbased mobile computing devices, such as personal digital assistants (PDA) and other handheld devices, do not take full advantages of the pen technology offered by these devices. Instead, input of expressions is still done through a virtual keypad ..."
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Cited by 14 (0 self)
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Most of the calculator programs found in existing penbased mobile computing devices, such as personal digital assistants (PDA) and other handheld devices, do not take full advantages of the pen technology offered by these devices. Instead, input of expressions is still done through a virtual keypad shown on the screen, and the stylus (i.e., electronic pen) is simply used as a pointing device. In this paper, we propose an intelligent handwritingbased calculator program with which the user can enter expressions simply by writing them on the screen using a stylus. In addition, variables can be defined to store intermediate results for subsequent calculations, as in ordinary algebraic calculations. The proposed software is the result of a novel application of online mathematical expression recognition technology which has mostly been used by others only for some mathematical expression editor programs. 1.
An interactive mathematical handwriting recognizer for the Pocket PC
, 2002
"... Handwriting is the primary input method for handheld computers because they are too small physically to have keyboards. To investigate the requirements for upcoming computer algebra systems on handheld computers, we designed and implemented an application for recognizing online handwritten mathema ..."
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Cited by 11 (3 self)
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Handwriting is the primary input method for handheld computers because they are too small physically to have keyboards. To investigate the requirements for upcoming computer algebra systems on handheld computers, we designed and implemented an application for recognizing online handwritten mathematical expressions on the pocket PC. The objective was to translate handwriting mathematical expressions into corresponding presentation MathML, which can be understood by computer algebra systems. This application consists of three components: 1) a handwriting recognizer for recognizing individual mathematical symbols, 2) a structural analyzer for interpreting and maintaining the relationship between symbols of the expression, and 3) a generator for generating MathML code. Currently it is able to recognize simple expressions including polynomial equations, fractions, trigonometric functions, allowing nested structures. This application could serve as a bridge for mathematical users to interact with the computer algebra systems on handheld computers.
Online recognition of handwritten mathematical expressions based on strokebased stochastic contextfree grammar
 In Proc. Int’l Work. Frontiers in Handwriting Recognition
, 2006
"... In this paper, we propose a new framework for online handwritten mathematical expression recognition. In this approach, we consider handwritten mathematical expressions as the output of stroke generation processes based on a stochastic contextfree grammar which generates handwritten expressions sto ..."
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In this paper, we propose a new framework for online handwritten mathematical expression recognition. In this approach, we consider handwritten mathematical expressions as the output of stroke generation processes based on a stochastic contextfree grammar which generates handwritten expressions stochastically. We estimate the most likely expression candidate derived from the grammar, rather than solving one by one the three major problems in mathematical expression recognition: symbol segmentation/recognition, 2D structure recognition, and expression syntax analysis. With this method, we can simultaneously recognize the symbols and structure of an expression within the grammatical constraint. Experiments revealed that this simultaneous estimation decreases errors in symbol segmentation and recognition, and that these errors are reduced as grammatical restriction is strengthened.
An Efficient Feature Extraction Algorithm for the Recognition of Handwritten Arabic Digits
 INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE
"... Abstract—In this paper, an efficient structural approach for recognizing online handwritten digits is proposed. After reading the digit from the user, the slope is estimated and normalized for adjacent nodes. Based on the changing of signs of the slope values, the primitives are identified and extr ..."
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Abstract—In this paper, an efficient structural approach for recognizing online handwritten digits is proposed. After reading the digit from the user, the slope is estimated and normalized for adjacent nodes. Based on the changing of signs of the slope values, the primitives are identified and extracted. The names of these primitives are represented by strings, and then a finite state machine, which contains the grammars of the digits, is traced to identify the digit. Finally, if there is any ambiguity, it will be resolved. Experiments showed that this technique is flexible and can achieve high recognition accuracy for the shapes of the digits represented in this work.
A Survey on Recognition of OnLine Handwritten Mathematical Notation
, 2007
"... This report describes recent advances in the area of the recognition of online 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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This report describes recent advances in the area of the recognition of online 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.
Probabilistic Mathematical Formula Recognition Using a 2D ContextFree Graph Grammar
 in Proc. ICDAR 2011
, 2011
"... AbstractWe present a probabilistic framework for the mathematical expression recognition problem. The developed system is flexible in that its grammar can be extended easily thanks to its graph grammar which eliminates the need for specifying rule precedence. It is also optimal in the sense that a ..."
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AbstractWe present a probabilistic framework for the mathematical expression recognition problem. The developed system is flexible in that its grammar can be extended easily thanks to its graph grammar which eliminates the need for specifying rule precedence. It is also optimal in the sense that all possible interpretations of the expressions are expanded without making early commitments or hard decisions. In this paper, we give an overview of the whole system and describe in detail the graph grammar and the parsing process used in the system, along with some preliminary results on character, structure and expression recognition performances.
Recognition of Online Handwritten Arabic Digits Using Structural Features and Transition Network
, 2006
"... processing, transition networks ..."
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