2,197 research outputs found
Ein System für die Online-Erkennung handgeschriebener mathematischer Formeln
Title and Table of Contents
1.Introduction
2. Related Work
3. Preprocessing Techniques for On-Line Handwriting
4. Classification of On-Line Handwritten Symbols
5. Structural Analysis of Mathematical Expressions
6. An Editor for On-Line Handwritten Mathematical Expressions
7. Conclusion
BibliographyThis work presents a system for the recognition of on-line handwritten
mathematical formulas. The system consists of two main stages: Classification
of isolated on-line handwritten symbols and the analysis of spatial
relationships among them. We propose a system for the recognition of isolated
on-line handwritten characters which is based on support vector
classification. We also propose a suitable representation for strokes and
symbols which is used to improve the classification rates of the classifier.
Our experiments show that our classifier achieved better classification rates
in comparison to other popular classification techniques. This could be
accomplished by extensive preprocessing of the data and by parameter selection
for the support vector classification. We propose a new structural analysis
method for the recognition of on-line handwritten mathematical expressions
based on a minimum spanning tree construction and symbol dominance. Our method
addresses important layout problems frequently encountered in on-line
handwritten formula-recognition systems. Our method also aims to handle input
as naturally as possible, i.e. using the usual mathematical conventions,
without restrictions in the order the symbols are written. Our method handles
symbols with non-standard layout, like \sideset{^{*}_{*}}{^{*}_{*}}\prod, as
well as tabular layouts, e.g. matrices. Our system for the recognition of on-
line handwritten mathematical expressions is used in the Electronic Chalkboard
(E-Chalk), a multimedia system for distance-teaching.Die vorliegende Arbeit stellt ein System für die Online-Erkennung
handgeschriebener mathematischer Formeln vor. Das System besteht aus zwei
verschiedenen Komponenten, einem Klassifikator einzelner handgeschriebener
Online-Symbole und einem Analysator mathematischer Strukturen. Die Erkennung
der einzelnen Symbole erfolgt mittels Support-Vektor-Maschinen. Aus unserer
Experimenten ergab sich, dass unser Klassifikator gegenüber den klassischen
Techniken bessere Erkennungsraten erreichte. Diese Ergebnisse wurden durch
intensive Vorbearbeitung der Symbole und Suche optimaler Parameter ermöglicht.
Unsere Experimente lassen den Schluss zu, dass Support-Vektor-Maschinen den
Kompromiss zwischen Trainingszeit und Klassifikationsrate optimieren. In der
Arbeit wird eine neue Methode für die Online-Strukturanalyse handgeschriebener
mathematischer Ausdrücke besprochen, die sich auf der Aufbau eines minimalen
spannenden Baums und Symboldominanz basiert. Diese Technik ermöglicht eine
natürliche Eingabe der mathematischen Formeln, d.h., die Symbole und Formeln
werden ohne Beschränkungen nach der üblichen mathematischen Notation
geschrieben. Unsere Methode lässt sich einfach erweitern, um andere
mathematische Strukturen zu erkennen, z.B. Matrizen und andere ungewöhnliche
Strukturen, wie die in der LaTeX-Sprache definierte Struktur
sideset{^{*}_{*}}{^{*}_{*}} Unser Erkennungssystem wurde in der
Programmiersprache Java implementiert und ist das Standard-
Formelerkennungssystem des E-Kreide Systems
Math Search for the Masses: Multimodal Search Interfaces and Appearance-Based Retrieval
We summarize math search engines and search interfaces produced by the
Document and Pattern Recognition Lab in recent years, and in particular the min
math search interface and the Tangent search engine. Source code for both
systems are publicly available. "The Masses" refers to our emphasis on creating
systems for mathematical non-experts, who may be looking to define unfamiliar
notation, or browse documents based on the visual appearance of formulae rather
than their mathematical semantics.Comment: Paper for Invited Talk at 2015 Conference on Intelligent Computer
Mathematics (July, Washington DC
Mathematical Expression Recognition based on Probabilistic Grammars
[EN] Mathematical notation is well-known and used all over the
world. Humankind has evolved from simple methods representing
countings to current well-defined math notation able to account for
complex problems. Furthermore, mathematical expressions constitute a
universal language in scientific fields, and many information
resources containing mathematics have been created during the last
decades. However, in order to efficiently access all that information,
scientific documents have to be digitized or produced directly in
electronic formats.
Although most people is able to understand and produce mathematical
information, introducing math expressions into electronic devices
requires learning specific notations or using editors. Automatic
recognition of mathematical expressions aims at filling this gap
between the knowledge of a person and the input accepted by
computers. This way, printed documents containing math expressions
could be automatically digitized, and handwriting could be used for
direct input of math notation into electronic devices.
This thesis is devoted to develop an approach for mathematical
expression recognition. In this document we propose an approach for
recognizing any type of mathematical expression (printed or
handwritten) based on probabilistic grammars. In order to do so, we
develop the formal statistical framework such that derives several
probability distributions. Along the document, we deal with the
definition and estimation of all these probabilistic sources of
information. Finally, we define the parsing algorithm that globally
computes the most probable mathematical expression for a given input
according to the statistical framework.
An important point in this study is to provide objective performance
evaluation and report results using public data and standard
metrics. We inspected the problems of automatic evaluation in this
field and looked for the best solutions. We also report several
experiments using public databases and we participated in several
international competitions. Furthermore, we have released most of the
software developed in this thesis as open source.
We also explore some of the applications of mathematical expression
recognition. In addition to the direct applications of transcription
and digitization, we report two important proposals. First, we
developed mucaptcha, a method to tell humans and computers apart by
means of math handwriting input, which represents a novel application
of math expression recognition. Second, we tackled the problem of
layout analysis of structured documents using the statistical
framework developed in this thesis, because both are two-dimensional
problems that can be modeled with probabilistic grammars.
The approach developed in this thesis for mathematical expression
recognition has obtained good results at different levels. It has
produced several scientific publications in international conferences
and journals, and has been awarded in international competitions.[ES] La notación matemática es bien conocida y se utiliza en todo el
mundo. La humanidad ha evolucionado desde simples métodos para
representar cuentas hasta la notación formal actual capaz de modelar
problemas complejos. Además, las expresiones matemáticas constituyen
un idioma universal en el mundo científico, y se han creado muchos
recursos que contienen matemáticas durante las últimas décadas. Sin
embargo, para acceder de forma eficiente a toda esa información, los
documentos científicos han de ser digitalizados o producidos
directamente en formatos electrónicos.
Aunque la mayoría de personas es capaz de entender y producir
información matemática, introducir expresiones matemáticas en
dispositivos electrónicos requiere aprender notaciones especiales o
usar editores. El reconocimiento automático de expresiones matemáticas
tiene como objetivo llenar ese espacio existente entre el conocimiento
de una persona y la entrada que aceptan los ordenadores. De este modo,
documentos impresos que contienen fórmulas podrían digitalizarse
automáticamente, y la escritura se podría utilizar para introducir
directamente notación matemática en dispositivos electrónicos.
Esta tesis está centrada en desarrollar un método para reconocer
expresiones matemáticas. En este documento proponemos un método para
reconocer cualquier tipo de fórmula (impresa o manuscrita) basado en
gramáticas probabilísticas. Para ello, desarrollamos el marco
estadístico formal que deriva varias distribuciones de probabilidad. A
lo largo del documento, abordamos la definición y estimación de todas
estas fuentes de información probabilística. Finalmente, definimos el
algoritmo que, dada cierta entrada, calcula globalmente la expresión
matemática más probable de acuerdo al marco estadístico.
Un aspecto importante de este trabajo es proporcionar una evaluación
objetiva de los resultados y presentarlos usando datos públicos y
medidas estándar. Por ello, estudiamos los problemas de la evaluación
automática en este campo y buscamos las mejores soluciones. Asimismo,
presentamos diversos experimentos usando bases de datos públicas y
hemos participado en varias competiciones internacionales. Además,
hemos publicado como código abierto la mayoría del software
desarrollado en esta tesis.
También hemos explorado algunas de las aplicaciones del reconocimiento
de expresiones matemáticas. Además de las aplicaciones directas de
transcripción y digitalización, presentamos dos propuestas
importantes. En primer lugar, desarrollamos mucaptcha, un método para
discriminar entre humanos y ordenadores mediante la escritura de
expresiones matemáticas, el cual representa una novedosa aplicación
del reconocimiento de fórmulas. En segundo lugar, abordamos el
problema de detectar y segmentar la estructura de documentos
utilizando el marco estadístico formal desarrollado en esta tesis,
dado que ambos son problemas bidimensionales que pueden modelarse con
gramáticas probabilísticas.
El método desarrollado en esta tesis para reconocer expresiones
matemáticas ha obtenido buenos resultados a diferentes niveles. Este
trabajo ha producido varias publicaciones en conferencias
internacionales y revistas, y ha sido premiado en competiciones
internacionales.[CA] La notació matemàtica és ben coneguda i s'utilitza a tot el món. La
humanitat ha evolucionat des de simples mètodes per representar
comptes fins a la notació formal actual capaç de modelar
problemes complexos. A més, les expressions matemàtiques
constitueixen un idioma universal al món científic, i s'han creat
molts recursos que contenen matemàtiques durant les últimes
dècades. No obstant això, per accedir de forma eficient a tota
aquesta informació, els documents científics han de ser
digitalitzats o produïts directament en formats electrònics.
Encara que la majoria de persones és capaç d'entendre i produir
informació matemàtica, introduir expressions matemàtiques en
dispositius electrònics requereix aprendre notacions especials o usar
editors. El reconeixement automàtic d'expressions matemàtiques
té per objectiu omplir aquest espai existent entre el coneixement
d'una persona i l'entrada que accepten els ordinadors. D'aquesta
manera, documents impresos que contenen fórmules podrien
digitalitzar-se automàticament, i l'escriptura es podria utilitzar per
introduir directament notació matemàtica en dispositius electrònics.
Aquesta tesi està centrada en desenvolupar un mètode per reconèixer
expressions matemàtiques. En aquest document proposem un mètode per
reconèixer qualsevol tipus de fórmula (impresa o manuscrita) basat en
gramàtiques probabilístiques. Amb aquesta finalitat, desenvolupem el
marc estadístic formal que deriva diverses distribucions de
probabilitat. Al llarg del document, abordem la definició i estimació
de totes aquestes fonts d'informació probabilística. Finalment,
definim l'algorisme que, donada certa entrada, calcula globalment
l'expressió matemàtica més probable d'acord al marc estadístic.
Un aspecte important d'aquest treball és proporcionar una avaluació
objectiva dels resultats i presentar-los usant dades públiques i
mesures estàndard. Per això, estudiem els problemes de l'avaluació
automàtica en aquest camp i busquem les millors solucions. Així
mateix, presentem diversos experiments usant bases de dades públiques
i hem participat en diverses competicions internacionals. A més, hem
publicat com a codi obert la majoria del software desenvolupat en
aquesta tesi.
També hem explorat algunes de les aplicacions del reconeixement
d'expressions matemàtiques. A més de les aplicacions directes de
transcripció i digitalització, presentem dues propostes
importants. En primer lloc, desenvolupem mucaptcha, un mètode per
discriminar entre humans i ordinadors mitjançant l'escriptura
d'expressions matemàtiques, el qual representa una nova aplicació del
reconeixement de fórmules. En segon lloc, abordem el problema de
detectar i segmentar l'estructura de documents utilitzant el marc
estadístic formal desenvolupat en aquesta tesi, donat que ambdós són
problemes bidimensionals que poden modelar-se amb gramàtiques
probabilístiques.
El mètode desenvolupat en aquesta tesi per reconèixer expressions
matemàtiques ha obtingut bons resultats a diferents nivells. Aquest
treball ha produït diverses publicacions en conferències
internacionals i revistes, i ha sigut premiat en competicions
internacionals.Álvaro Muñoz, F. (2015). Mathematical Expression Recognition based on Probabilistic Grammars [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/51665TESI
Symbolic and Visual Retrieval of Mathematical Notation using Formula Graph Symbol Pair Matching and Structural Alignment
Large data collections containing millions of math formulae in different formats are available on-line. Retrieving math expressions from these collections is challenging. We propose a framework for retrieval of mathematical notation using symbol pairs extracted from visual and semantic representations of mathematical expressions on the symbolic domain for retrieval of text documents. We further adapt our model for retrieval of mathematical notation on images and lecture videos. Graph-based representations are used on each modality to describe math formulas. For symbolic formula retrieval, where the structure is known, we use symbol layout trees and operator trees. For image-based formula retrieval, since the structure is unknown we use a more general Line of Sight graph representation. Paths of these graphs define symbol pairs tuples that are used as the entries for our inverted index of mathematical notation. Our retrieval framework uses a three-stage approach with a fast selection of candidates as the first layer, a more detailed matching algorithm with similarity metric computation in the second stage, and finally when relevance assessments are available, we use an optional third layer with linear regression for estimation of relevance using multiple similarity scores for final re-ranking. Our model has been evaluated using large collections of documents, and preliminary results are presented for videos and cross-modal search. The proposed framework can be adapted for other domains like chemistry or technical diagrams where two visually similar elements from a collection are usually related to each other
An integrated grammar-based approach for mathematical expression recognition
This is the author’s version of a work that was accepted for publication in Pattern Recognition. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Pattern Recognition 51 (2016) 135–147. DOI 10.1016/j.patcog.2015.09.013.Automatic recognition of mathematical expressions is a challenging pattern recognition problem since there are many ambiguities at different levels. On the one hand, the recognition of the symbols of the mathematical expression. On the other hand, the detection of the two-dimensional structure that relates the symbols and represents the math expression. These problems are closely related since symbol recognition is influenced by the structure of the expression, while the structure strongly depends on the symbols that are recognized. For these reasons, we present an integrated approach that combines several stochastic sources of information and is able to globally determine the most likely expression. This way, symbol segmentation, symbol recognition and structural analysis are simultaneously optimized. In this paper we define the statistical framework of a model based on two-dimensional grammars and its associated parsing algorithm. Since the search space is too large, restrictions are introduced for making the search feasible. We have developed a system that implements this approach and we report results on the large public dataset of the CROHME international competition. This approach significantly outperforms other proposals and was awarded best system using only the training dataset of the competition. (C) 2015 Elsevier Ltd. All rights reserved.This work was partially supported by the Spanish MINECO under the STraDA research project (TIN2012-37475-C02-01) and the FPU Grant (AP2009-4363).Álvaro Muñoz, F.; Sánchez Peiró, JA.; Benedí Ruiz, JM. (2016). An integrated grammar-based approach for mathematical expression recognition. Pattern Recognition. 51:135-147. https://doi.org/10.1016/j.patcog.2015.09.013S1351475
Query-Driven Global Graph Attention Model for Visual Parsing: Recognizing Handwritten and Typeset Math Formulas
We present a new visual parsing method based on standard Convolutional Neural Networks (CNNs) for handwritten and typeset mathematical formulas. The Query-Driven Global Graph Attention (QD-GGA) parser employs multi-task learning, using a single feature representation for locating, classifying, and relating symbols. QD-GGA parses formulas by first constructing a Line-Of-Sight (LOS) graph over the input primitives (e.g handwritten strokes or connected components in images). Second, class distributions for LOS nodes and edges are obtained using query-specific feature filters (i.e., attention) in a single feed-forward pass. This allows end-to-end structure learning using a joint loss over primitive node and edge class distributions. Finally, a Maximum Spanning Tree (MST) is extracted from the weighted graph using Edmonds\u27 Arborescence Algorithm. The model may be run recurrently over the input graph, updating attention to focus on symbols detected in the previous iteration. QD-GGA does not require additional grammar rules and the language model is learned from the sets of symbols/relationships and the statistics over them in the training set.
We benchmark our system against both handwritten and typeset state-of-the-art math recognition systems. Our preliminary results show that this is a promising new approach for visual parsing of math formulas. Using recurrent execution, symbol detection is near perfect for both handwritten and typeset formulas: we obtain a symbol f-measure of over 99.4% for both the CROHME (handwritten) and INFTYMCCDB-2 (typeset formula image) datasets. Our method is also much faster in both training and execution than state-of-the-art
RNN-based formula parsers. The unlabeled structure detection of QDGGA is competitive with encoder-decoder models, but QD-GGA symbol and relationship classification is weaker. We believe this may be addressed through increased use of spatial features and global context
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