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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
Recognition of Handwritten Mathematical Expressions
, 1999
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An Efficient Syntactic Approach to Structural Analysis of Online Handwritten Mathematical Expressions
, 2000
"... Machine recognition of mathematical expressions is not trivial even when all the individual characters and symbols in an expression can be recognized correctly. In this paper, we propose to use definite clause grammar (DCG) as a formalism to define a set of replacement rules for parsing mathematical ..."
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Cited by 25 (3 self)
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Machine recognition of mathematical expressions is not trivial even when all the individual characters and symbols in an expression can be recognized correctly. In this paper, we propose to use definite clause grammar (DCG) as a formalism to define a set of replacement rules for parsing mathematical expressions. With DCG, we are not only able to define the replacement rules concisely, but their definitions are also in a readily executable form. However, a DCG parser is potentially inefficient due to its frequent use of backtracking. Thus, we propose some methods here to increase the efficiency of the parsing process. Experiments done on some commonly seen mathematical expressions show that our proposed methods can achieve quite satisfactory speedup, making mathematical expression recognition more feasible for realworld applications.
A SoftDecision Approach For Structural Analysis Of Handwritten Mathematical Expressions
 In International Conference on Acoustics, Speech and Signal Processing
, 1995
"... In this paper an efficient system for structural analysis of handwritten mathematical expressions is proposed. To handle the problems caused by handwriting, this system is based on a softdecision approach. This means that alternatives for the solution are generated during the analysis process if th ..."
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In this paper an efficient system for structural analysis of handwritten mathematical expressions is proposed. To handle the problems caused by handwriting, this system is based on a softdecision approach. This means that alternatives for the solution are generated during the analysis process if the relation between two symbols within the expression is ambiguous. Finally a string containing the mathematical information is generated and syntactical verified for each alternative. Strings failing this verification are considered as invalid. 1 INTRODUCTION We are accustomed to writing mathematical expressions containing integrals, fractions, exponents or indices by hand. Entering these expressions into a computer is quite uncomfortable and expendable because we have to learn a notation such as T E X or we should be familiar with a graphical formulaeditor supplied with mouse and keyboard [1]. The humanadapted way is analysing the handwritten expressions. But there are two essential p...
C.: A practical approach for writerdependent symbol recognition using a writerindependent symbol recognizer
 IEEE Trans. Pattern Anal. Mach. Intell
"... Abstract—We present a practical technique for using a writerindependent recognition engine to improve the accuracy and speed while reducing the training requirements of a writerdependent symbol recognizer. Our writerdependent recognizer uses a set of binary classifiers based on the AdaBoost learn ..."
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Abstract—We present a practical technique for using a writerindependent recognition engine to improve the accuracy and speed while reducing the training requirements of a writerdependent symbol recognizer. Our writerdependent recognizer uses a set of binary classifiers based on the AdaBoost learning algorithm, one for each possible pairwise symbol comparison. Each classifier consists of a set of weak learners, one of which is based on a writerindependent handwriting recognizer. During online recognition, we also use the nbest list of the writerindependent recognizer to prune the set of possible symbols and, thus, reduce the number of required binary classifications. In this paper, we describe the geometric and statistical features used in our recognizer and our allpairs classification algorithm. We also present the results of experiments that quantify the effect incorporating a writerindependent recognition engine into a writerdependent recognizer has on accuracy, speed, and user training time. Index Terms—Handwriting recognition, AdaBoost, writer dependence, writer independence, pairwise classification, realtime systems. Ç 1
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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Cited by 6 (0 self)
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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.
Symbol segmentation and recognition for understanding handwritten mathematical expressions
 Progress in Handwriting Recognition
, 1997
"... This paper is focused on the symbol segmentation and recognition problem within online sampled handwritten expressions, the first stage of an overall system for understanding arithmetic formulas. Within our system a statistical approach is used tolerating ambiguities within the single decision stag ..."
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Cited by 5 (1 self)
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This paper is focused on the symbol segmentation and recognition problem within online sampled handwritten expressions, the first stage of an overall system for understanding arithmetic formulas. Within our system a statistical approach is used tolerating ambiguities within the single decision stages and resolving them either automatically by additional knowledge acquired during the following processing stages or by interaction with the user. At this state the interaction is done by displaying next to the recognition result, the most probable symbol sequence corresponding to the handwritten input, some recognition alternatives for selection by the user. 1
Multilayer Perceptrons versus Hidden Markov Models: Comparisons and Applications to Image Analysis and Visual Pattern Recognition
, 1995
"... this report we presented a survey and comparisons of multilayer perceptrons (MLPs) versus hidden Markov models (HMMs), illustrating some successful experimental results that have been reported in image analysis and visual pattern recognition. An important property of these models is their intrinsic ..."
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Cited by 2 (0 self)
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this report we presented a survey and comparisons of multilayer perceptrons (MLPs) versus hidden Markov models (HMMs), illustrating some successful experimental results that have been reported in image analysis and visual pattern recognition. An important property of these models is their intrinsic ways to incorporate context. For the sake of better understanding, HMMs were subdivided into 1D, pseudo 2D and 2D HMMs.
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
Identifying Features via Homotopy on Handwritten Mathematical Symbols
"... Abstract—In handwritten mathematics, it is common to have characters in various sizes and for writing not to follow simple baselines. For example, subscripts and superscripts appear relatively smaller than normal text and are written slightly below or above it. Rather than use the location, feature ..."
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Abstract—In handwritten mathematics, it is common to have characters in various sizes and for writing not to follow simple baselines. For example, subscripts and superscripts appear relatively smaller than normal text and are written slightly below or above it. Rather than use the location, features and size to identify the character, it may be more effective to do the reverse — to use knowledge about specific characters to determine baseline, size, etc. In this approach, it is necessary to find the location of certain expected features that are determined by particular points. In earlier work, we have presented a method to derive the determining points for a new instance of a symbol from those on an average model for each symbol type. For those characters that are significantly different from the average instance, one can use a numerical homotopy between the average instance and the target character, and apply the determining point algorithm at each step. The present article studies the factors to be taken into account in performing such homotopies. We examine two strategies for possible starting points for the homotopy, and we examine the relation between the distance and the number of steps required. The first starting point strategy performs a homotopy from the average of samples of the same type. The second strategy uses a homotopy from the nearest neighbour with known determining points. Our experimental results show a useful relation between the homotopy distance and the number of steps usually required and improved strategies to find determining points for poorly written characters. I.