Probabilistic mathematical formula recognition using a 2D context-free graph grammar

We present a probabilistic framework for the mathematical expression recognition problem. The developed system is flexible in that its grammar can be extended easily thanks to its graph grammar which eliminates the need for specifying rule precedence. It is also optimal in the sense that all possible interpretations of the expressions are expanded without making early commitments or hard decisions. In this paper, we give an overview of the whole system and describe in detail the graph grammar and the parsing process used in the system, along with some preliminary results on character, structure and expression recognition performances

Intelligent Combination of Structural Analysis Algorithms: Application to Mathematical Expression Recognition

Structural analysis is an important step in many document based recognition problem. Structural analysis is performed to associate elements in a document and assign meaning to their association. Handwritten mathematical expression recognition is one such problem which has been studied and researched for long. Many techniques have been researched to build a system that produce high performance mathematical expression recognition. We have presented a novel method to combine multiple structural recognition algorithms in which the combined result shows better performance than each individual recognition algorithms. In our experiment we have applied our method to combine multiple mathematical expression recognition parsers called DRACULAE. We have used Graph Transformation Network (GTN) which is a network of function based systems in which each system takes graphs as input, apply function and produces a graph as output. GTN is used to combine multiple DRACULAE parsers and its parameter are tuned using gradient based learning. It has been shown that such a combination method can be used to accentuate the strength of individual algorithms in combination to produce better combination result which higher recognition performance. In our experiment we were able to obtain a highest recognition rate of 74% as compared to best recognition result of 70% from individual DRACULAE parsers. Our experiment also resulted into a maximum of 20% reduction of parent recognition errors and maximum 37% reduction in relation recognition errors between symbols in expressions

The WOZ Recognizer: A Tool For Understanding User Perceptions of Sketch-Based Interfaces

Sketch recognition has the potential to be an important input method for computers in the coming years; however, designing and building an accurate and sophisticated sketch recognition system is a time consuming and daunting task. Since sketch recognition is still at a level where mistakes are common, it is important to understand how users perceive and tolerate recognition errors and other user interface elements with these imperfect systems. A problem in performing this type of research is that we cannot easily control aspects of recognition in order to rigorously study the systems. We performed a study examining user perceptions of three pen-based systems for creating logic gate diagrams: a sketch-based interface, a WIMP-based interface, and a hybrid interface that combined elements of sketching and WIMP. We found that users preferred the sketch-based interface and we identified important criteria for pen-based application design. This work exposed the issue of studying recognition systems without fine-grained control over accuracy, recognition mode, and other recognizer properties. In order to solve this problem, we developed a Wizard of Oz sketch recognition tool, the WOZ Recognizer, that supports controlled symbol and position accuracy and batch and streaming recognition modes for a variety of sketching domains. We present the design of the WOZ Recognizer, modeling recognition domains using graphs, symbol alphabets, and grammars; and discuss the types of recognition errors we included in its design. Further, we discuss how the WOZ Recognizer simulates sketch recognition, controlling the WOZ Recognizer, and how users interact with it. In addition, we present an evaluative user study of the WOZ Recognizer and the lessons we learned. We have used the WOZ Recognizer to perform two user studies examining user perceptions of sketch recognition; both studies focused on mathematical sketching. In the first study, we examined whether users prefer recognition feedback now (real-time recognition) or later (batch recognition) in relation to different recognition accuracies and sketch complexities. We found that participants displayed a preference for real-time recognition in some situations (multiple expressions, low accuracy), but no statistical preference in others. In our second study, we examined whether users displayed a greater tolerance for recognition errors when they used mathematical sketching applications they found interesting or useful compared to applications they found less interesting. Participants felt they had a greater tolerance for the applications they preferred, although our statistical analysis did not positively support this. In addition to the research already performed, we propose several avenues for future research into user perceptions of sketch recognition that we believe will be of value to sketch recognizer researchers and application designers

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

MECA: Mathematical Expression Based Post Publication Content Analysis

Mathematical expressions (ME) are critical abstractions for technical publications. While the sheer volume of technical publications grows in time, few ME centric applications have been developed due to the steep gap between the typesetting data in post-publication digital documents and the high-level technical semantics. With the acceleration of the technical publications every year, word-based information analysis technologies are inadequate to enable users in discovery, organizing, and interrelating technical work efficiently and effectively. This dissertation presents a modeling framework and the associated algorithms, called the mathematical-centered post-publication content analysis (MECA) system to address several critical issues to build a layered solution architecture for recovery of high-level technical information. Overall, MECA is consisted of four layers of modeling work, starting from the extraction of MEs from Portable Document Format (PDF) files. Specifically, a weakly-supervised sequential typesetting Bayesian model is developed by using a concise font-value based feature space for Bayesian inference of ME vs. words for the rendering units separated by space. A Markov Random Field (MRF) model is designed to merge and correct the MEs identified from the rendering units, which are otherwise prone to fragmentation of large MEs. At the next layer, MECA aims at the recovery of ME semantics. The first step is the ME layout analysis to disambiguate layout structures based on a Content-Constrained Spatial (CCS) global inference model to overcome local errors. It achieves high accuracy at low computing cost by a parametric lognormal model for the feature distribution of typographic systems. The ME layout is parsed into ME semantics with a three-phase processing workflow to overcome a variety of semantic ambiguities. In the first phase, the ME layout is linearized into a token sequence, upon which the abstract syntax tree (AST) is constructed in the second phase using probabilistic context-free grammar. Tree rewriting will transform the AST into ME objects in the third phase. Built upon the two layers of ME extraction and semantics modeling work, next we explore one of the bonding relationships between words and MEs: ME declarations, where the words and MEs are respectively the qualitative and quantitative (QuQn) descriptors of technical concepts. Conventional low-level PoS tagging and parsing tools have poor performance in the processing of this type of mixed word-ME (MWM) sentences. As such, we develop an MWM processing toolkit. A semi-automated weakly-supervised framework is employed for mining of declaration templates from a large amount of unlabeled data so that the templates can be used for the detection of ME declarations. On the basis of the three low-level content extraction and prediction solutions, the MECA system can extract MEs, interpret their mathematical semantics, and identify their bonding declaration words. By analyzing the dependency among these elements in a paper, we can construct a QuQn map, which essentially represents the reasoning flow of a paper. Three case studies are conducted for QuQn map applications: differential content comparison of papers, publication trend generation, and interactive mathematical learning. Outcomes from these studies suggest that MECA is a highly practical content analysis technology based on a theoretically sound framework. Much more can be expanded and improved upon for the next generation of deep content analysis solutions