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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.
HMMBased Recognition of Online Handwritten Mathematical Symbols Using Segmental Kmeans Initialization and A Modified Penup/down Feature
"... Abstract—This paper presents a recognition system based on Hidden Markov Model (HMM) for isolated online handwritten mathematical symbols. We design a continuous left to right HMM for each symbol class and use four online local features, including a new feature: normalized distance to stroke edge. A ..."
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Abstract—This paper presents a recognition system based on Hidden Markov Model (HMM) for isolated online handwritten mathematical symbols. We design a continuous left to right HMM for each symbol class and use four online local features, including a new feature: normalized distance to stroke edge. A variant of segmental Kmeans is used to get initialization of the Gaussian Mixture Models ’ parameters which represent the observation probability distribution of the HMMs. The system obtains top1 recognition rate of 82.9 % and top5 recognition rate of 97.8 % on a dataset containing 20281 training samples and 2202 testing samples of 93 classes of symbols. For multistroke symbols, the top1 recognition rate is 74.7 % and the top5 recognition rate is 95.5%. For singlestroke symbols, the top1 recognition rate is 86.8 % and the top5 recognition rate is 98.9%. (MacLean et al., 2010) applied dynamic time warping algorithm on all the 70 classes of singlestroke symbols. Their top1 recognition rate is 85.8%, and top5 recognition rate is 97.0%. Our system gets top1 recognition rate of 85.5 % and top5 recognition rate of 99.1 % on the same 70 classes of singlestroke symbols. KeywordsHidden Markov Model; mathematical symbol recognition; segmental Kmeans
J.H.: 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 framew ..."
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Cited by 7 (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.
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.
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 new approach for recognizing handwritten mathematics using relational grammars and fuzzy sets
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Recognizing handwritten mathematics via fuzzy parsing
, 2010
"... We present a new approach to multidimensional parsing using relational grammars and fuzzy sets. A fast, incremental parsing algorithm is developed, motivated by the twodimensional structure of written mathematics. Our approach makes no hard decisions; recognized math expressions are reported to th ..."
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Cited by 2 (1 self)
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We present a new approach to multidimensional parsing using relational grammars and fuzzy sets. A fast, incremental parsing algorithm is developed, motivated by the twodimensional structure of written mathematics. Our approach makes no hard decisions; recognized math expressions are reported to the user in ranked order. A flexible correction mechanism enables users to quickly choose the correct math expression in case of recognition errors or ambiguity. 1
KECHADI T.: A purely online approach to mathematical expression recognition
 In Tenth International Workshop on Frontiers in Handwriting Recognition
, 2006
"... In this paper a new approach to handwritten mathematical expression recognition is presented. The approach is highly original in that the solution, an expression tree, is immediately updated whenever the user writes a new stroke. Fuzzy logic is used extensively, in both the symbol recognition and ..."
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In this paper a new approach to handwritten mathematical expression recognition is presented. The approach is highly original in that the solution, an expression tree, is immediately updated whenever the user writes a new stroke. Fuzzy logic is used extensively, in both the symbol recognition and structural analysis phases, which is appropriate given the amount of imprecision and ambiguity present in handwritten mathematics. The approach is highly efficient and encouraging results have been achieved.
A Study of Online Handwritten Chemical Expressions Recognition
 In Proc. of 19 th Intl. Conf. on Patten Recognition
, 2008
"... In this paper, we study the major modules of online handwritten chemical expressions recognition. We propose a novel twolevel algorithm to recognize expressions. In the first level, structural information is used to distinguish different parts and recognize substances. Then the algorithm segments ..."
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In this paper, we study the major modules of online handwritten chemical expressions recognition. We propose a novel twolevel algorithm to recognize expressions. In the first level, structural information is used to distinguish different parts and recognize substances. Then the algorithm segments expressions fatherly and recognizes isolated symbols. To meet the demand of actual applications, the paper also designs an XMLbased system to help users save, modify and search the recognition result. The experiment shows that the presented algorithm is reliable. 1.
A Template Matching Distance for Recognition of OnLine Mathematical Symbols
"... An online handwritten character recognition technique based on a template matching distance is proposed. In this method, the pendirection features are quantized using the 8level Freeman chain coding scheme and the dominant points of the stroke are identified using the first difference of the chai ..."
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Cited by 1 (0 self)
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An online handwritten character recognition technique based on a template matching distance is proposed. In this method, the pendirection features are quantized using the 8level Freeman chain coding scheme and the dominant points of the stroke are identified using the first difference of the chain code. The distance between two symbols results from the difference of the respective chain codes of the variable speed normalization of dominant points weighted by the local length proportions of the strokes. The proposed technique was tested on two datasets and showed a recognition rate of 92 % in the top 1 choice.