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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 12 (3 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
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 4 (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.
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
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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Cited by 1 (0 self)
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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.
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
Towards Query by Sketch *
"... Contentbased retrieval has become a very popular and also powerful paradigm for searching in multimedia collections, especially in large collections of images. However, such queries require that one or even several reference images are available prior to the start of the search process. These refer ..."
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Contentbased retrieval has become a very popular and also powerful paradigm for searching in multimedia collections, especially in large collections of images. However, such queries require that one or even several reference images are available prior to the start of the search process. These reference images must be close to the final result so that the user can take them to express her information need. If such reference images are not available or if the information need is covered only by parts of the query object, the result usually does not meet the user’s expectation. Therefore, more flexible user interfaces are needed that allow users to sketch a query image by hand drawings and to dynamically select regions of interest from a given query image. In this paper, we present a novel approach to query by sketch where interactive paper and image similarity search are seamlessly combined. It is based on the iPaper/iServer system of ETH Zurich and the ISIS/OSIRIS contentbased image retrieval system of the University of Basel. The paper presents the integrated system which has already very successfully been applied to the development of an interactive museum catalogue. Moreover, it reports on ongoing activities that aim at extending the system to support handwritten sketches, gestures and/or dynamic region selection to make the retrieval process more flexible and less dependent from existing query objects.
2009 10th International Conference on Document Analysis and Recognition A Unified Framework for Recognizing Handwritten Chemical Expressions
"... Chemical expressions have more variant structures in 2D space than that in math equations. In this paper we propose a unified framework for recognizing handwritten chemical expressions including both inorganic and organic expressions. A set of novel statistical algorithms is presented in two key co ..."
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Chemical expressions have more variant structures in 2D space than that in math equations. In this paper we propose a unified framework for recognizing handwritten chemical expressions including both inorganic and organic expressions. A set of novel statistical algorithms is presented in two key components of this framework: symbol grouping and structure analysis. Nonsymbol modeling and intergroup modeling are proposed to achieve better grouping result, and bond modeling is proposed to group the special bond symbols in the unified framework. A graphbased representation (CESG) is defined for representing generic chemical expressions, and the structure analysis problem is formulated as a search problem for CESG over a weighted direction graph. Experiments on a database of more than 35,000 expressions were conducted and results are presented. 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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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