scispace - formally typeset
Search or ask a question
Proceedings Article

Ambiguity and constraint in mathematical expression recognition

01 Jul 1998-pp 784-791
TL;DR: A new lower bound estimate on the cost to goal that improves performance significantly is provided and the system limits the number of potentially valid interpretations by decomposing the expressions into a sequence of compatible convex regions.
Abstract: The problem of recognizing mathematical expressions differs significantly from the recognition of standard prose. While in prose significant constraints can be put on the interpretation of a character by the characters immediately preceding and following it, few such simple constraints are present in a mathematical expression. In order to make the problem tractable, effective methods of recognizing mathematical expressions will need to put intelligent constraints on the possible interpretations. The authors present preliminary results on a system for the recognition of both handwritten and typeset mathematical expressions. While previous systems perform character recognition out of context, the current system maintains ambiguity of the characters until context can be used to disambiguate the interpretation. In addition, the system limits the number of potentially valid interpretations by decomposing the expressions into a sequence of compatible convex regions. The system uses A-star to search for the best possible interpretation of an expression. We provide a new lower bound estimate on the cost to goal that improves performance significantly.

Content maybe subject to copyright    Report

Citations
More filters
Journal ArticleDOI
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


Cites background or methods from "Ambiguity and constraint in mathema..."

  • ...[6,16], Miller and Viola [46] Feature extraction and nearest neighbor classification Fateman et al....

    [...]

  • ...[6,16] and Miller and Viola [46] used Hausdorff distance....

    [...]

  • ...[35], Lavirotte and Pottier [37,38], Marzinkewitsch [45], Pfeiffer [55] Chart parsing associated with probability vectors Miller and Viola [46]...

    [...]

  • ...[32,43,64–67] and Miller and Viola [46]....

    [...]

  • ...Miller and Viola [46] took a relatively new approach for the recognition of mathematical expressions....

    [...]

Journal ArticleDOI
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 "Ambiguity and constraint in mathema..."

  • ...(a) Which division is performed first? (b) Is a superscripted? (c) What is the scope of the summation? (d) Is this symbol a 9 or a q? The perceived answer depends on context (from [103]) (e) What do s, t and · represent?...

    [...]

  • ...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 [103]....

    [...]

Journal ArticleDOI
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


Additional excerpts

  • ...Surveys are available in [1] and [2]....

    [...]

Journal ArticleDOI
01 Aug 2004
TL;DR: Initial feedback from a small user group of the mathematical sketching prototype application, MathPad2, suggests that it has the potential to be a powerful tool for mathematical problem solving and visualization.
Abstract: We present mathematical sketching, a novel, pen-based, modeless gestural interaction paradigm for mathematics problem solving Mathematical sketching derives from the familiar pencil-and-paper process of drawing supporting diagrams to facilitate the formulation of mathematical expressions; however, with a mathematical sketch, users can also leverage their physical intuition by watching their hand-drawn 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 The modeless nature of mathematical sketching enables users to switch freely between modifying diagrams or expressions and viewing animations Mathematical sketching can also support computational tools for graphing, manipulating and solving equations; initial feedback from a small user group of our mathematical sketching prototype application, MathPad2, suggests that it has the potential to be a powerful tool for mathematical problem solving and visualization

223 citations


Cites background from "Ambiguity and constraint in mathema..."

  • ...Finally, a number of systems let users enter 2D handwritten mathematics in the context of math recognition and parsing, such as those found in [Zanibbi et al. 2002; Chan and Yeung 2000a; Matsakis 1999; Miller and Viola 1998]....

    [...]

Journal ArticleDOI
TL;DR: Watch, Attend and Parse (WAP), a novel end-to-end approach based on neural network that learns to recognize HMEs in a two-dimensional layout and outputs them as one-dimensional character sequences in LaTeX format, significantly outperformed the state-of-the-art method.

182 citations

References
More filters
Book
01 Jan 1990
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Abstract: From the Publisher: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures. Like the first edition,this text can also be used for self-study by technical professionals since it discusses engineering issues in algorithm design as well as the mathematical aspects. In its new edition,Introduction to Algorithms continues to provide a comprehensive introduction to the modern study of algorithms. The revision has been updated to reflect changes in the years since the book's original publication. New chapters on the role of algorithms in computing and on probabilistic analysis and randomized algorithms have been included. Sections throughout the book have been rewritten for increased clarity,and material has been added wherever a fuller explanation has seemed useful or new information warrants expanded coverage. As in the classic first edition,this new edition of Introduction to Algorithms presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers. Further,the algorithms are presented in pseudocode to make the book easily accessible to students from all programming language backgrounds. Each chapter presents an algorithm,a design technique,an application area,or a related topic. The chapters are not dependent on one another,so the instructor can organize his or her use of the book in the way that best suits the course's needs. Additionally,the new edition offers a 25% increase over the first edition in the number of problems,giving the book 155 problems and over 900 exercises thatreinforcethe concepts the students are learning.

21,651 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


"Ambiguity and constraint in mathema..." refers background or methods in this paper

  • ...The Cocke-Younger-Kasami (CYK) algorithm (Hopcroft & Ullman 1979), a dynamic programming algorithm, is cubic in the number of characters....

    [...]

  • ...Mathematical expressions, which are collections of symbols arranged in two dimensions, do not have a straightforward decomposition into a polynomial number of subsets....

    [...]

  • ...Context-free grammars have proven to be very useful in the parsing of programming languages (Hopcroft & Ullman 1979)....

    [...]

Journal ArticleDOI
TL;DR: Efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model are presented and it is shown that the method extends naturally to the problem of comparing a portion of a model against an image.
Abstract: The Hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa. Thus, this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. Efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model are presented. The focus is primarily on the case in which the model is only allowed to translate with respect to the image. The techniques are extended to rigid motion. The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods. It is shown that the method extends naturally to the problem of comparing a portion of a model against an image. >

4,194 citations


"Ambiguity and constraint in mathema..." refers methods in this paper

  • ...A character recognizer based on the Hausdorff distance ( Huttenlocher, Klanderman, & Rucklidge 1993 ) is used to generate probabilities that each connected component or pair of connected components is a particular character....

    [...]

Book
01 Jan 1994
TL;DR: In this article, Charniak presents statistical language processing from an artificial intelligence point of view in a text for researchers and scientists with a traditional computer science background, which is grounded in real text and therefore promises to produce usable results.
Abstract: From the Publisher: Eugene Charniak breaks new ground in artificial intelligence research by presenting statistical language processing from an artificial intelligence point of view in a text for researchers and scientists with a traditional computer science background. New, exacting empirical methods are needed to break the deadlock in such areas of artificial intelligence as robotics, knowledge representation, machine learning, machine translation, and natural language processing (NLP). It is time, Charniak observes, to switch paradigms. This text introduces statistical language processing techniques -- word tagging, parsing with probabilistic context free grammars, grammar induction, syntactic disambiguation, semantic word classes, word-sense disambiguation -- along with the underlying mathematics and chapter exercises. Charniak points out that as a method of attacking NLP problems, the statistical approach has several advantages. It is grounded in real text and therefore promises to produce usable results, and it offers an obvious way to approach learning: "one simply gathers statistics." Language, Speech, and Communication

1,028 citations

Book
01 Jan 1968

224 citations