Structure detection and segmentation of documents using 2D stochastic context-free grammars

[EN] In this paper we define a bidimensional extension of stochastic context-free grammars for structure detection and segmentation of images of documents. Two sets of text classification features are used to perform an initial classification of each zone of the page. Then, the document segmentation is obtained as the most likely hypothesis according to a stochastic grammar. We used a dataset of historical marriage license books to validate this approach. We also tested several inference algorithms for probabilistic graphical models and the results showed that the proposed grammatical model outperformed the other methods. Furthermore, grammars also provide the document structure along with its segmentation. & 2014 Elsevier B.V. All rights reserved.Work is partially supported by the Spanish MEC under the STraDA Research Project (TIN2012-37475-C02-01), the Spanish Project 2010-CONES-00029, the FPU Grant (AP2009-4363), and through the EU 7th Framework Programme Grant tranScriptorium (Ref: 600707).Álvaro Muñoz, F.; Cruz Fernández, F.; Sánchez Peiró, JA.; Ramos Terrades, O.; Benedí Ruiz, JM. (2015). Structure detection and segmentation of documents using 2D stochastic context-free grammars. Neurocomputing. 150:147-154. https://doi.org/10.1016/j.neucom.2014.08.076S14715415

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

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

Page Segmentation of Structured Documents Using 2D Stochastic Context-Free Grammars

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-38628-2_15n this paper we define a bidimensional extension of Stochastic Context-Free Grammars for page segmentation of structured documents. Two sets of text classification features are used to perform an initial classification of each zone of the page. Then, the page segmentation is obtained as the most likely hypothesis according to a grammar. This approach is compared to Conditional Random Fields and results show significant improvements in several cases. Furthermore, grammars provide a detailed segmentation that allowed a semantic evaluation which also validates this model.Work partially supported by the Spanish MEC under the STraDA research project (TIN2012-37475-C02-01), the MITTRAL (TIN2009- 14633-C03-01) project, the Spanish projects TIN2009-14633-C03-01/03 and 2010- CONES-00029, the FPU grant (AP2009-4363), by the Generalitat Valenciana under the grant Prometeo/2009/014, and through the EU 7th Framework Programme grant tranScriptorium (Ref: 600707)Álvaro Muñoz, F.; Cruz Fernández, F.; Sánchez Peiró, JA.; Ramos Terrades, O.; Benedí Ruiz, JM. (2013). Page Segmentation of Structured Documents Using 2D Stochastic Context-Free Grammars. En Pattern Recognition and Image Analysis. Springer. 133-140. https://doi.org/10.1007/978-3-642-38628-2_15133140Álvaro, F., Sánchez, J.A., Benedí, J.M.: Recognition of on-line handwritten mathematical expressions using 2d stochastic context-free grammars and hidden markov models. Pattern Recognition Letters (2012)An, C., Bird, H.S., Xiu, P.: Iterated document content classification. In: Proc. of ICDAR, Brazil, vol. 1, pp. 252–256 (2007)Antonacopoulos, A., Clausner, C., Papadopoulos, C., Pletschacher, S.: Historical document layout analysis competition. In: Proc. of ICDAR, pp. 1516–1520 (2011)Bulacu, M., Koert, R., Schomaker, L., Zant, T.: Layout analysis of handwritten historical documents for searching the archive of the cabinet of the dutch queen. In: Proc. of ICDAR, Brazil, vol. 1, pp. 23–26 (2007)Crespi Reghizzi, S., Pradella, M.: A CKY parser for picture grammars. Information Processing Letters 105(6), 213–217 (2008)Cruz, F., Ramos Terrades, O.: Document segmentation using relative location features. In: Proc. of ICPR, Japan, pp. 1562–1565 (2012)Esteve, A., Cortina, C., Cabré, A.: Long term trends in marital age homogamy patterns: Spain, 1992-2006. Population 64(1), 173–202 (2009)Gould, S., Rodgers, J., Cohen, D., Elidan, G., Koller, D.: Multi-class segmentation with relative location prior. Int. Journal of Computer Vision 80(3), 300–316 (2008)Handley, J.C., Namboodiri, A.M., Zanibbi, R.: Document understanding system using stochastic context-free grammars. In: Proc. of ICDAR, vol. 1, pp. 511–515 (2005)Jain, A.K., Namboodiri, A.M., Subrahmonia, J.: Structure in online documents. In: Proc. of ICDAR, vol. 1, pp. 844–848 (2001)Lafferty, J., McCallum, A., Pereira, F.: Conditional random fields: Probabilistic models for segmenting and labeling sequence data. In: Proc. of ICML, USA, pp. 282–289 (2001

Methods for Structural Pattern Recognition: Complexity and Applications

Katedra kybernetik

High-Level Bottom-Up Cues for Top-Down Parsing of Facade Images

International audienceWe address the problem of parsing images of building facades. The goal is to segment images, assigning to the resulting regions semantic labels that correspond to the basic architectural elements. We assume a top-down parsing framework is developed beforehand, based on a 2D shape grammar that encodes a prior knowledge on the possible composition of facades. The algorithm explores the space of feasible solutions by generating the possible configurations of the facade and comparing it to the input data by means of a local, pixel- or patch-based classifier. We propose new bottom-up cues for the algorithm, both for evaluation of a candidate parse and for guiding the exploration of the space of feasible solutions. The method that we propose benefits from detection-based information and leverages on the similar appearance of elements that repeat in a given facade. Experiments performed on standard datasets show that this use of more discriminative bottom-up cues improves the convergence in comparison to state-of-the-art algorithms, and gives better results in terms of precision and recall, as well as computation time and deviation

Stroke order normalization for improving recognition of online handwritten mathematical expressions

We present a technique based on stroke order normalization for improving recognition of online handwritten mathematical expressions (ME). The stroke order dependent system has less time complexity than the stroke order free system, but it must incorporate special grammar rules to cope with stroke order variations. The stroke order normalization technique solves this problem and also the problem of unexpected stroke order variations without increasing the time complexity of ME recognition. In order to normalize stroke order, the X-Y cut method is modified since its original form causes problems when structural components in ME overlap. First, vertically ordered strokes are located by detecting vertical symbols and their upper/lower components, which are treated as MEs and reordered recursively. Second, unordered strokes on the left side of the vertical symbols are reordered as horizontally ordered strokes. Third, the remaining strokes are reordered recursively. The horizontally ordered strokes are reordered from left to right, and the vertically ordered strokes are reordered from top to bottom. Finally, the proposed stroke order normalization is combined with the stroke order dependent ME recognition system. The evaluations on the CROHME 2014 database show that the ME recognition system incorporating the stroke order normalization outperforms all other systems that use only CROHME 2014 for training while the processing time is kept low

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