2D Grammar Extension of the CMP Mathematical Formulae On-line Recognition System

Projecte realitzat en col.laboració amb Czech Technical University in PragueIn the last years, the recognition of handwritten mathematical formulae has recieved an increasing amount of attention in pattern recognition research. However, the diversity of approaches to the problem and the lack of a commercially viable system indicate that there is still much research to be done in this area. In this thesis, I will describe the previous work on a system for on-line handwritten mathematical formulae recognition based on the structural construction paradigm and two-dimensional grammars. In general, this approach can be successfully used in the anaylysis of inputs composed of objects that exhibit rich structural relations. An important benefit of the structural construction is in not treating symbols segmentation and structural anaylsis as two separate processes which allows the system to perform segmentation in the context of the whole formula structure, helping to solve arising ambiguities more reliably. We explore the opening provided by the polynomial complexity parsing algorithm and extend the grammar by many new grammar production rules which made the system useful for formulae met in the real world. We propose several grammar extensions to support a wide range of real mathematical formulae, as well as new features implemented in the application. Our current approach can recognize functions, limits, derivatives, binomial coefficients, complex numbers and more

Off-line Recognition of Printed Mathematical Expressions Using Stochastic Context-Free Grammars

Off-line recognition of printed mathematical expressions consists of three major steps: segmentation, symbol recognition and structural analysis. In this work we study an approach based on a twodimensional extension of context-free grammars parsing. Finally, some experiments are reported to evaluate the developed system.Álvaro Muñoz, F. (2010). Off-line Recognition of Printed Mathematical Expressions Using Stochastic Context-Free Grammars. http://hdl.handle.net/10251/13732Archivo delegad

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

2D Grammar Extension of the CMP Mathematical Formulae On-line Recognition System

Projecte realitzat en col.laboració amb Czech Technical University in PragueIn the last years, the recognition of handwritten mathematical formulae has recieved an increasing amount of attention in pattern recognition research. However, the diversity of approaches to the problem and the lack of a commercially viable system indicate that there is still much research to be done in this area. In this thesis, I will describe the previous work on a system for on-line handwritten mathematical formulae recognition based on the structural construction paradigm and two-dimensional grammars. In general, this approach can be successfully used in the anaylysis of inputs composed of objects that exhibit rich structural relations. An important benefit of the structural construction is in not treating symbols segmentation and structural anaylsis as two separate processes which allows the system to perform segmentation in the context of the whole formula structure, helping to solve arising ambiguities more reliably. We explore the opening provided by the polynomial complexity parsing algorithm and extend the grammar by many new grammar production rules which made the system useful for formulae met in the real world. We propose several grammar extensions to support a wide range of real mathematical formulae, as well as new features implemented in the application. Our current approach can recognize functions, limits, derivatives, binomial coefficients, complex numbers and more

Recognition of on-line handwritten mathematical expressions using 2D stochastic context-free grammars and hidden Markov models

[EN] This paper describes a formal model for the recognition of on-line handwritten mathematical expressions using 2D stochastic context-free grammars and hidden Markov models. Hidden Markov models are used to recognize mathematical symbols, and a stochastic context-free grammar is used to model the relation between these symbols. This formal model makes possible to use classic algorithms for parsing and stochastic estimation. In this way, first, the model is able to capture many of variability phenomena that appear in on-line handwritten mathematical expressions during the training process. And second, the parsing process can make decisions taking into account only stochastic information, and avoiding heuristic decisions. The proposed model participated in a contest of mathematical expression recognition and it obtained the best results at different levels. 2012 Elsevier B.V. All rights reserved.Work supported by the EC (FEDER/ FSE) and the Spanish MEC/MICINN under the MIPRCV ‘‘Consolider Ingenio 2010’’ program (CSD2007-00018), the MITTRAL (TIN2009-14633-C03-01) project, the FPU Grant (AP2009-4363), and by the Generalitat Valenciana under the Grant Prometeo/2009/014.Álvaro Muñoz, F.; Sánchez Peiró, JA.; Benedí Ruiz, JM. (2014). Recognition of on-line handwritten mathematical expressions using 2D stochastic context-free grammars and hidden Markov models. Pattern Recognition Letters. 35:58-67. https://doi.org/10.1016/j.patrec.2012.09.023S58673

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

Formalizing graphical notations

The thesis describes research into graphical notations for software engineering, with a principal interest in ways of formalizing them. The research seeks to provide a theoretical basis that will help in designing both notations and the software tools that process them. The work starts from a survey of literature on notation, followed by a review of techniques for formal description and for computational handling of notations. The survey concentrates on collecting views of the benefits and the problems attending notation use in software development; the review covers picture description languages, grammars and tools such as generic editors and visual programming environments. The main problem of notation is found to be a lack of any coherent, rigorous description methods. The current approaches to this problem are analysed as lacking in consensus on syntax specification and also lacking a clear focus on a defined concept of notated expression. To address these deficiencies, the thesis embarks upon an exploration of serniotic, linguistic and logical theory; this culminates in a proposed formalization of serniosis in notations, using categorial model theory as a mathematical foundation. An argument about the structure of sign systems leads to an analysis of notation into a layered system of tractable theories, spanning the gap between expressive pictorial medium and subject domain. This notion of 'tectonic' theory aims to treat both diagrams and formulae together. The research gives details of how syntactic structure can be sketched in a mathematical sense, with examples applying to software development diagrams, offering a new solution to the problem of notation specification. Based on these methods, the thesis discusses directions for resolving the harder problems of supporting notation design, processing and computer-aided generic editing. A number of future research areas are thereby opened up. For practical trial of the ideas, the work proceeds to the development and partial implementation of a system to aid the design of notations and editors. Finally the thesis is evaluated as a contribution to theory in an area which has not attracted a standard approach

Perbandingan Algoritma Sum of Squared Difference (Ssd) Dan Optimised Sum of Absolute Difference (Osad) Untuk Pengenalan Simbol Pada Citra Ekspresi Matematika Tercetak

The process of recognising printed mathematical expression consists of two general processes: symbol recognition and structural analysis which reads the expression structure and the relation between symbols within the structure, provide adequate labeling to preserve it, and finally be useful to reconstruct the whole expression.This research focused on comparing the effectivity of two correlation-based pattern matching algorithms: the well-established Sum of Squared Difference (SSD) and the relatively new Optimized Sum of Absolute Difference (OSAD) which is based on average face rather than mathing all trained symbols. Which one was better will be used on the next stage of a research on converting printed mathematical expression into LaTeX notation.. Results obtained from tests conducted shown that (1) the accuracy of OSAD is 85.6% and SSD is 70,6% on various test symbols, and (2) the USAge of average face in OSAD which was proposed to reduce time needed for matching, proven to have no negative effects on its matching performance. Therefore OSAD is well ahead in processing time and accuracy than SSD

On-Line Handwritten Formula Recognition using Hidden Markov Models and Context Dependent Graph Grammars

This paper presents an approach for the recognition of on-line handwritten mathematical expressions. The Hidden Markov Model (HMM) based system makes use of simultaneous segmentation and recognition capabilities, avoiding a crucial segmentation during pre-processing. With the segmentation and recognition results, obtained from the HMMrecognizer, it is possible to analyze and interpret the spatial two-dimensional arrangement of the symbols. We use a graph grammar approach for the structure recognition, also used in off-line recognition process, resulting in a general tree-structure of the underlying input-expression. The resulting constructed tree can be translated to any desired syntax (for example: Lisp, LaTeX, OpenMath . . . )

IMEGE: Image-based Mathematical Expression Global Error

Mathematical expression recognition is an active research eld that is related to document image analysis and typesetting. Several approaches have been proposed to tackle this problem, and automatic methods for performance evaluation are required. Mathematical expressions are usually represented as a coded string like LATEX or MathML for evaluation purpose. This representation has ambiguity problems given that the same expression can be coded in several ways. For that reason, the proposed approaches in the past either manually analyzed recognition results or they reported partial errors as symbol error rate. In this study, we present a novel global performance evaluation measure for mathematical expression based on image matching. In this way, using an image representation solves the representation ambiguity as well as human beings do. The proposed evaluation method is a global error measure that also provides local information about the recognition result.Álvaro Muñoz, F.; Sánchez Peiró, JA.; Benedí Ruiz, JM. (2011). IMEGE: Image-based Mathematical Expression Global Error. http://hdl.handle.net/10251/1308