239 research outputs found
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
Applying Hierarchical Contextual Parsing with Visual Density and Geometric Features to Typeset Formula Recognition
We demonstrate that recognition of scanned typeset mathematical expression images can be done by extracting maximum spanning trees from line of sight graphs weighted using geometric and visual density features. The approach used is hierarchical contextual parsing (HCP): Hierarchical in terms of starting with connected components and building to the symbol level using visual, spatial, and contextual features of connected components. Once connected components have been segmented into symbols, a new set of spatial, visual, and contextual features are extracted. One set of visual features is used for symbol classification, and another for parsing. The features are used in parsing to assign classifications and confidences to edges in a line of sight symbol graph. Layout trees describe expression structure in terms of spatial relations between symbols, such as horizontal, subscript, and superscript. From the weighted graph Edmonds\u27 algorithm is used to extract a maximum spanning tree. Segmentation and parsing are done without using symbol classification information, and symbol classification is done independently of expression structure recognition. The commonality between the recognition processes is the type of features they use, the visual densities. These visual densities are used for shape, spatial, and contextual information. The contextual information is shown to help in segmentation, parsing, and symbol recognition.
The hierarchical contextual parsing has been implemented in the Python and Graph-based Online/Offline Recognizer for Math (Pythagor^m) system and tested on the InftyMCCDB-2 dataset. We created InftyMCCDB-2 from InftyCDB-2 as a open source dataset for scanned typeset math expression recognition. In building InftyMCCDB-2 modified formula structure representations were used to better capture the spatial positioning of symbols in the expression structures. Namely, baseline punctuation and symbol accents were moved out of horizontal baselines as their positions are not horizontally aligned with symbols on a writing line. With the transformed spatial layouts and HCP, 95.97% of expressions were parsed correctly when given symbols and 93.95% correctly parsed when requiring symbol segmentation from connected components. Overall HCP reached 90.83% expression recognition rate from connected components
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
Features and Algorithms for Visual Parsing of Handwritten Mathematical Expressions
Math expressions are an essential part of scientific documents. Handwritten math expressions recognition can benefit human-computer interaction especially in the education domain and is a critical part of document recognition and analysis.
Parsing the spatial arrangement of symbols is an essential part of math expression recognition. A variety of parsing techniques have been developed during the past three decades, and fall into two groups. The first group is graph-based parsing. It selects a path or sub-graph which obeys some rule to form a possible interpretation for the given expression. The second group is grammar driven parsing. Grammars and related parameters are defined manually for different tasks. The time complexity of these two groups parsing is high, and they often impose some strict constraints to reduce the computation.
The aim of this thesis is working towards building a straightforward and effective parser with as few constraints as possible. First, we propose using a line of sight graph for representing the layout of strokes and symbols in math expressions. It achieves higher F-score than other graph representations and reduces search space for parsing. Second, we modify the shape context feature with Parzen window density estimation. This feature set works well for symbol segmentation, symbol classification and symbol layout analysis. We get a higher symbol segmentation F-score than other systems on CROHME 2014 dataset. Finally, we develop a Maximum Spanning Tree (MST) based parser using Edmonds\u27 algorithm, which extracts an MST from the directed line of sight graph in two passes: first symbols are segmented, and then symbols and spatial relationship are labeled. The time complexity of our MST-based parsing is lower than the time complexity of CYK parsing with context-free grammars. Also, our MST-based parsing obtains higher structure rate and expression rate than CYK parsing when symbol segmentation is accurate. Correct structure means we get the structure of the symbol layout tree correct, even though the label of the edge in the symbol layout tree might be wrong. The performance of our math expression recognition system with MST-based parsing is competitive on CROHME 2012 and 2014 datasets.
For future work, how to incorporate symbol classifier result and correct segmentation error in MST-based parsing needs more research
A Symbol layout classification for mathematical formula using layout context
We describe a symbol classification technique for identifying the expected locations of neighboring symbols in mathematical expressions. We use the seven symbol layout classes of the DRACULAE math notation parser (Zanibbi, et al., 2002) to represent expected locations for neighboring symbols: Ascender, Descender, Centered, Open Bracket, Non-Scripted, Variable Range (e.g., integrals) and Root. A new feature based on the shape context (Belongie, et al., 2002), named layout context, is used to describe the arrangement of neighboring symbols relative to a reference symbol, and the nearest neighbor rule is used for classification. 1917 mathematical symbols from the University of Washington III document database are used in our experiments. Using a leave-one-out estimate, our best classification rate reaches nearly 80%. In our experiments, we find that the size of the reference symbol neighborhood area, the number and the sampling positions of the points of the key points model representing a symbol\u27s location, play important roles in the classification process
Exploiting Spatio-Temporal Coherence for Video Object Detection in Robotics
This paper proposes a method to enhance video object detection for indoor environments in robotics. Concretely, it exploits knowledge about the camera motion between frames to propagate previously detected objects to successive frames. The proposal is rooted in the concepts of planar homography to propose regions of interest where to find objects, and recursive Bayesian filtering to integrate observations over time. The proposal is evaluated on six virtual, indoor environments, accounting for the detection of nine object classes over a total of ∼ 7k frames. Results show that our proposal improves the recall and the F1-score by a factor of 1.41 and 1.27, respectively, as well as it achieves a significant reduction of the object categorization entropy (58.8%) when compared to a two-stage video object detection method used as baseline, at the cost of small time overheads (120 ms) and precision loss (0.92).</p
Content Recognition and Context Modeling for Document Analysis and Retrieval
The nature and scope of available documents are changing significantly in many areas of document analysis and retrieval as complex, heterogeneous collections become accessible to virtually everyone via the web. The increasing level of diversity presents a great challenge for document image content categorization, indexing, and retrieval. Meanwhile, the processing of documents with unconstrained layouts and complex formatting often requires effective leveraging of broad contextual knowledge.
In this dissertation, we first present a novel approach for document image content categorization, using a lexicon of shape features. Each lexical word corresponds to a scale and rotation invariant local shape feature that is generic enough to be detected repeatably and is segmentation free. A concise, structurally indexed shape lexicon is learned by clustering and partitioning feature types through graph cuts. Our idea finds successful application in several challenging tasks, including content recognition of diverse web images and language identification on documents composed of mixed machine printed text and handwriting.
Second, we address two fundamental problems in signature-based document image retrieval. Facing continually increasing volumes of documents, detecting and recognizing unique, evidentiary visual entities (\eg, signatures and logos) provides a practical and reliable supplement to the OCR recognition of printed text. We propose a novel multi-scale framework to detect and segment signatures jointly from document images, based on the structural saliency under a signature production model. We formulate the problem of signature retrieval in the unconstrained setting of geometry-invariant deformable shape matching and demonstrate state-of-the-art performance in signature matching and verification.
Third, we present a model-based approach for extracting relevant named entities from unstructured documents. In a wide range of applications that require structured information from diverse, unstructured document images, processing OCR text does not give satisfactory results due to the absence of linguistic context. Our approach enables learning of inference rules collectively based on contextual information from both page layout and text features.
Finally, we demonstrate the importance of mining general web user behavior data for improving document ranking and other web search experience. The context of web user activities reveals their preferences and intents, and we emphasize the analysis of individual user sessions for creating aggregate models. We introduce a novel algorithm for estimating web page and web site importance, and discuss its theoretical foundation based on an intentional surfer model. We demonstrate that our approach significantly improves large-scale document retrieval performance
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