Recognition of Equations Using a Two-Dimensional Stochastic Context-Free Grammar
01 Nov 1989-Vol. 1199, pp 852-865
TL;DR: This work proposes using two-dimensional stochastic context-free grammars for image recognition, in a manner analogous to using hidden Markov models for speech recognition, and demonstrates the value of the approach in a system that recognizes printed, noisy equations.
Abstract: We propose using two-dimensional stochastic context-free grammars for image recognition, in a manner analogous to using hidden Markov models for speech recognition. The value of the approach is demonstrated in a system that recognizes printed, noisy equations. The system uses a two-dimensional probabilistic version of the Cocke-Younger-Kasami parsing algorithm to find the most likely parse of the observed image, and then traverses the corresponding parse tree in accordance with translation formats associated with each production rule, to produce eqn I troff commands for the imaged equation. In addition, it uses two-dimensional versions of the Inside/Outside and Baum re-estimation algorithms for learning the parameters of the grammar from a training set of examples. Parsing the image of a simple noisy equation currently takes about one second of cpu time on an Alliant FX/80.
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Book•
01 Jan 1996TL;DR: Professor Ripley brings together two crucial ideas in pattern recognition; statistical methods and machine learning via neural networks in this self-contained account.
Abstract: From the Publisher:
Pattern recognition has long been studied in relation to many different (and mainly unrelated) applications, such as remote sensing, computer vision, space research, and medical imaging. In this book Professor Ripley brings together two crucial ideas in pattern recognition; statistical methods and machine learning via neural networks. Unifying principles are brought to the fore, and the author gives an overview of the state of the subject. Many examples are included to illustrate real problems in pattern recognition and how to overcome them.This is a self-contained account, ideal both as an introduction for non-specialists readers, and also as a handbook for the more expert reader.
5,632 citations
Cites methods from "Recognition of Equations Using a Tw..."
...There are very few working examples of structural pattern re cognition systems; an interesting demonstration system was provided by Chou (1989) to convert typeset mathematical formulae into a typesetting language....
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TL;DR: This survey paper will review most of the existing work with respect to each of the two major stages of the recognition process, and tries to put emphasis on the similarities and differences between systems.
Abstract: . 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.
327 citations
TL;DR: 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 problem in math recognition (detecting expressions, detecting and classifying symbols, analyzing symbol layout, and constructing a representation of meaning).
Abstract: 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 wide-spread availability of optical character recognition and text-based 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.
267 citations
Cites background from "Recognition of Equations Using a Tw..."
...Stochastic context-free grammars allow uncertainty in symbol recognition, layout, and/or content to be accommodated, by returning the maximum likelihood derivation for the input image [34] or symbols [104]....
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...Markov Model [34]....
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...In Chou’s [34] paper, the expression grammar is augmented to include symbols representing horizontal and vertical concatenation of adjacent regions in the input image....
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...describing the use of stochastic context-free string grammars for analysis of typeset images of mathematical notation [34]....
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...It is true that sequential implementations of stochastic context-free grammars are computationally intensive, but both probability-estimation algorithms and parsers may be parallelized [34]....
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TL;DR: A robust and efficient system for recognizing typeset and handwritten mathematical notation that allows robust handling of unexpected input, increases the scalability of the system, and provides the groundwork for handling dialects of mathematical notation.
Abstract: We describe a robust and efficient system for recognizing typeset and handwritten mathematical notation. From a list of symbols with bounding boxes the system analyzes an expression in three successive passes. The Layout Pass constructs a Baseline Structure Tree (BST) describing the two-dimensional arrangement of input symbols. Reading order and operator dominance are used to allow efficient recognition of symbol layout even when symbols deviate greatly from their ideal positions. Next, the Lexical Pass produces a Lexed BST from the initial BST by grouping tokens comprised of multiple input symbols; these include decimal numbers, function names, and symbols comprised of nonoverlapping primitives such as "=". The Lexical Pass also labels vertical structures such as fractions and accents. The Lexed BST is translated into L/sup A/T/sub E/X. Additional processing, necessary for producing output for symbolic algebra systems, is carried out in the Expression Analysis Pass. The Lexed BST is translated into an Operator Tree, which describes the order and scope of operations in the input expression. The tree manipulations used in each pass are represented compactly using tree transformations. The compiler-like architecture of the system allows robust handling of unexpected input, increases the scalability of the system, and provides the groundwork for handling dialects of mathematical notation.
258 citations
Cites background from "Recognition of Equations Using a Tw..."
...However, these are not in a form that can be used as a specification for a mathematics recognition system....
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PARC1
TL;DR: The proposed approach is illustrated on the problem of decoding scanned telephone yellow pages to extract names and numbers from the listings by constructing a finite-state model for yellow page columns using a Viterbi-like dynamic programming algorithm.
Abstract: Document image decoding (DID) is a communication theory approach to document image recognition. In DID, a document recognition problem is viewed as consisting of three elements: an image generator, a noisy channel and an image decoder. A document image generator is a Markov source (stochastic finite-state automaton) that combines a message source with an imager. The message source produces a string of symbols, or text, that contains the information to be transmitted. The imager is modeled as a finite-state transducer that converts the 1D message string into an ideal 2D bitmap. The channel transforms the ideal image into a noisy observed image. The decoder estimates the message, given the observed image, by finding the a posteriori most probable path through the combined source and channel models using a Viterbi-like dynamic programming algorithm. The proposed approach is illustrated on the problem of decoding scanned telephone yellow pages to extract names and numbers from the listings. A finite-state model for yellow page columns was constructed and used to decode a database of scanned column images containing about 1100 individual listings. >
238 citations
Cites background from "Recognition of Equations Using a Tw..."
...One disadvantage of the region-based approach to image grammars is that the two-dimensional counterparts to regular (finite-state) string grammars are not particularly useful for image modeling [9]....
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...Previous attempts along these lines have generalized string grammar formalisms by replacing the notion of a one-dimensional phrase with that of a twodimensional rectangular region [9], [25]....
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References
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49,597 citations
Book•
01 Jan 1979
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Abstract: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity. The authors present the theory in a concise and straightforward manner, with an eye out for the practical applications. Exercises at the end of each chapter, including some that have been solved, help readers confirm and enhance their understanding of the material. This book is appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
13,779 citations
"Recognition of Equations Using a Tw..." refers background or methods in this paper
...852 / SPIE Vol 1199 Visual Communications and Image Processing IV (1989) - i ensional Stochastic t -Fre ra...
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...860 / SPIE Vol 1199 Visual Communications and Image Processing IV (1989) er s f {n l} to f er 2...
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...1199 Visual Communications and Image Processing IV (1989) t Younger-Kasami algorithm in conjunction with a t o-di ensional stoc ti -free gra r ize oisy images of equations that have be n generated by eqnlt co [ , ]....
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...856 / SPIE Vol 1199 Visual Communications and Image Processing IV (1989) ation: r 0, an all £...
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...1199 Visual Communications and image Processing IV (1989) / 853 ersing the r rs rtunately, such a tree lects nly ne ossible structure t rly t e, , i tion, r r i uity....
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01 Mar 1973
TL;DR: This paper gives a tutorial exposition of the Viterbi algorithm and of how it is implemented and analyzed, and increasing use of the algorithm in a widening variety of areas is foreseen.
Abstract: The Viterbi algorithm (VA) is a recursive optimal solution to the problem of estimating the state sequence of a discrete-time finite-state Markov process observed in memoryless noise. Many problems in areas such as digital communications can be cast in this form. This paper gives a tutorial exposition of the algorithm and of how it is implemented and analyzed. Applications to date are reviewed. Increasing use of the algorithm in a widening variety of areas is foreseen.
5,995 citations
4,618 citations
TL;DR: The purpose of this tutorial paper is to give an introduction to the theory of Markov models, and to illustrate how they have been applied to problems in speech recognition.
Abstract: The basic theory of Markov chains has been known to mathematicians and engineers for close to 80 years, but it is only in the past decade that it has been applied explicitly to problems in speech processing. One of the major reasons why speech models, based on Markov chains, have not been developed until recently was the lack of a method for optimizing the parameters of the Markov model to match observed signal patterns. Such a method was proposed in the late 1960's and was immediately applied to speech processing in several research institutions. Continued refinements in the theory and implementation of Markov modelling techniques have greatly enhanced the method, leading to a wide range of applications of these models. It is the purpose of this tutorial paper to give an introduction to the theory of Markov models, and to illustrate how they have been applied to problems in speech recognition.
4,546 citations