An Approach for Recognition and Interpretation of Mathematical Expressions in Printed Document

In this paper, we propose an approach for understanding Mathematical Expressions (MEs) in a printed document. The system is divided into three main components: (i) detection of MEs in a document; (ii) recognition of the symbols present in each ME; and (iii) arrangement of the recognised symbols. The MEs printed in separate lines are detected without any character recognition whereas the embedded expressions (mixed with normal text) are detected by recognising the mathematical symbols in text. Some structural features of the MEs are used for both cases. The mathematical symbols are grouped into two classes for convenience. At first, the frequently occurring symbols are recognised by a stroke-feature analysis technique. Recognition of less frequent symbols involves a hybrid of feature-based and template-based technique. The bounding-box coordinates and the size information of the symbols help to determine the spatial relationships among the symbols. A set of predefined rules is used to form the meaningful symbol groups so that a logical arrangement of the mathematical expression can be obtained. Experiments conducted using this approach on a large number of documents show high accuracy.     

Unrestricted gapping grammars1

Since Colmerauer's introduction of metamorphosis grammars (MGs), with their associated type-O-like grammar rules, there has been a desire to allow more general rule formats in logic grammars. Gap symbols were added to the MG rule by Pereira, resulting in extraposition grammars (XGs). Gaps, which are referenced by gap symbols, are sequences of zero or more unspecified symbols which may be present anywhere in a sentence or in a sentential form. However, XGs imposed restrictions on the position of gap symbols and on the contents of gaps. With the introduction of gapping grammars (GGs) by Dahl, these restrictions were removed but the rule was still required to possess a nonterminal symbol as the first symbol on the left-hand side. This restriction is removed with the introduction of unrestricted gapping grammars. FIGG, a flexible implementation of gapping grammars, possesses a bottom-up parser which can process a large subset of unrestricted gapping grammars. It can be used to examine the usefulness of unrestricted GGs for describing phenomena of natural languages such as free word order and partially free word/constituent order. Unrestricted gapping grammars, as implemented in FIGG, can also be used to describe grammars (or metagrammars) that utilize the gap concept, such as Gazdar's generalized phrase structure grammars.     

面向通信态势的三维标号生成

传统标绘以二维为基础,在平面上绘制标号再放到三维球上,使得表示复杂联系关系时,贴地存在明显遮挡问题且绘制性能低以及不同高度的空间联系难以表达。本文引入球面细分曲线和贝塞尔曲线,对传统标绘中坐标转换进行修改,采取分割出子线绘制图元的方法,利用子图元模拟网络攻击、电子干扰等真实效果提高视觉辨识,并由de Casteljau算法证明并计算得出三段贝塞尔曲线,加速图元计算过程。新生成的标号能够解决标号贴地遮挡和空间标绘的问题,大大提升贴地绘制效率,使得联系关系态势展示具备实用性。     

Recognition of online handwritten mathematical expressions

This paper aims at automatic understanding of online handwritten mathematical expressions (MEs) written on an electronic tablet. The proposed technique involves two major stages: symbol recognition and structural analysis. Combination of two different classifiers have been used to achieve high accuracy for the recognition of symbols. Several online and offline features are used in the structural analysis phase to identify the spatial relationships among symbols. A context-free grammar has been designed to convert the input expressions into their corresponding T(E)X strings which are subsequently converted into MathML format. Contextual information has been used to correct several structure interpretation errors. A new method for evaluating performance of the proposed system has been formulated. Experiments on a dataset of considerable size strongly support the feasibility of the proposed system.     

一种中文文档的数学公式定位方法

为了从中英文混排的中文文档中定位数学公式,提出了一种基于中文字符识别和公式符号识别的数学公式定位方法。该方法主要由中文字符提取、内嵌公式提取和独立公式定位三个部分组成。在中文字符提取中,首先提取字符块信息中文字符识别结果、公式符号识别结果和字符块的几何特征,然后使用决策树的方法区分中文字符和非中文字符。在内嵌公式提取中,使用公式符号的语义信息、符号间的角标关系和公式的语义信息等从非中文字符中定位内嵌公式。在独立数学公式定位中,对包含较多内嵌公式符号且不包含中文字符的文字行提取版式结构特征,并使用高斯混合模型区分独立公式和普通文字行。在148幅文档图像共包含3 690个公式组成的测试集上取得了91.19%的公式定位正确率。     

基于多候选的数学公式识别系统

提出了一种基于多候选方法的数学公式识别系统.该系统主要包括公式图像预处理,多候选公式符号分割和多候选公式结构分析3个部分.在公式符号切分中,使用3次动态规划方法对公式图像进行多候选公式符号切分.在公式结构分析中,采用层次结构方法多候选分析公式符号间的结构关系,然后使用LaTex格式和MathType格式表示数学公式的识别结果.为了确定符号间的空间位置关系,建立了符号的空间关系模型.在3268个公式图像组成的测试集上取得了78.2%的公式分析正确率.     

Computation is just interpretable symbol manipulation; cognition isn't

Computation is interpretable symbol manipulation. Symbols are objects that are manipulated on the basis of rules operating only on theirshapes, which are arbitrary in relation to what they can be interpreted as meaning. Even if one accepts the Church/Turing Thesis that computation is unique, universal and very near omnipotent, not everything is a computer, because not everything can be given a systematic interpretation; and certainly everything can't be givenevery systematic interpretation. But even after computers and computation have been successfully distinguished from other kinds of things, mental states will not just be the implementations of the right symbol systems, because of the symbol grounding problem: The interpretation of a symbol system is not intrinsic to the system; it is projected onto it by the interpreter. This is not true of our thoughts. We must accordingly be more than just computers. My guess is that the meanings of our symbols are grounded in the substrate of our robotic capacity to interact with that real world of objects, events and states of affairs that our symbols are systematically interpretable as being about.     

One-sided random context grammars

The notion of a one-sided random context grammar is defined as a context-free-based regulated grammar, in which a set of permitting symbols and a set of forbidding symbols are attached to every rule, and its set of rules is divided into the set of left random context rules and the set of right random context rules. A left random context rule can rewrite a nonterminal if each of its permitting symbols occurs to the left of the rewritten symbol in the current sentential form while each of its forbidding symbols does not occur there. A right random context rule is applied analogically except that the symbols are examined to the right of the rewritten symbol. The paper demonstrates that without erasing rules, one-sided random context grammars characterize the family of context-sensitive languages, and with erasing rules, these grammars characterize the family of recursively enumerable languages. In fact, these characterization results hold even if the set of left random context rules coincides with the set of right random context rules. Several special cases of these grammars are considered, and their generative power is established. In its conclusion, some important open problems are suggested to study in the future.     

基于模糊理论的数学公式上下标关系判别

上下标关系数学公式中出现频繁又难于解决的特殊结构,容易与其它关系混淆.提出了基于模糊理论的数学公式上下标关系判别.运用模糊理论对数学公式中符号的空间区域关系进行划分,然后应用模糊识别的方法对上下标关系进行判别.实验结果表明,运用该方法能明显提高符号空间关系判别的识别率,尤其是能很好地判别手写数学公式中的空间关系,识别的正确率可达到96.4%.     

Distributed symbol formation and processing in connectionist networks

Abstract

Distributed connectionist (DC) systems offer a set of processing features which are distinct from those provided by traditional symbol processing (SP) systems. In general, the features of DC systems are derived from the nature of their distributed representations. Such representations have a microsemantics -i.e. symbols with similar internal representations tend to have similar processing effects. In contrast, the symbols in SP systems have no intrinsic microsemantics of their own; e.g. SP symbols are formed by concatenating ASCII codes that are static, human engineered and arbitrary. Such symbols possess only a macrosemantics - i.e. symbols are placed into structured relationships with other symbols, via pointers, and bindings are propagated via variables. The fact that DC and SP systems each provide a distinct set of useful features serves as a strong research motivation for seeking a synthesis. What is needed for such a synthesis is a method by which symbols can dynamically form their own microsemantics, while at the same time entering into structured, recursive relationships with other symbols, thus developing also a macrosemantics. Here, we describe a general method, called symbol recirculation, for allowing symbols to form their own microsemantics. We then discuss three techniques for implementing variables and bindings in DC systems. Finally, we describe a number of DC systems, based on these techniques, which perform a variety of high-level cognitive tasks.     

面向GIS 表达与分析的气象符号绘制库设计与实现

针对目前地理信息系统(GIS)软件中对气象符号支持的不足,通过对气象领域中所涉 及的符号进行特征分析及其逻辑分类,构建了对应的几何空间数据模型,并采用不同的“样式”表 征具体的气象符号,以“几何对象+样式”的形式完成气象符号对象的构建。在此基础上,基于GDI+ 实现各种气象符号的矢量绘制,并封装形成可供直接调用气象矢量符号绘制库,为基于GIS 的气 象数据信息的表达和分析提供支撑。最后实例验证了本气象符号绘制库的正确性与实用性。     

基于凸壳和模糊识别的数学公式识别

根据数学公式中字符或符号间空间关系特点,并针对目前用于数学公式字符空间关系判别的区域和质心方法所存在的不足,提出了基于字符凸壳和模糊识别的字符空间关系判别方法.首先,对数学公式中的字符或符号进行分类,对每一类运用字符凸壳判别其正上和正下关系,然后应用模糊识别的方法对常见关系进行识别.实验结果表明,运用该方法能明显提高字符空间关系判别的识别率,识别的正确率可达到93.5%.     

Interactive High-Level Language Direct-Execution Microprocessor System

It is our habit in writing an English composition that, as we write each word, each phrase, each sentence, and each paragraph, we consciously or unconsciously check the syntax and the semantics of the composition just written. Writing a computer program in a high-level language could be made similar to writing a composition in English. In this case, a highly interactive highlevel language system checks the syntax and the semantics of the highlevel language program as each symbol, each expression, and each statement are being entered at the terminal. When the source program is completely entered, the program could have been debugged and could have run once.     

A graph grammar programming style for recognition of music notation

Graph grammars are a promising tool for solving picture processing problems. However, the application of graph grammars to diagram recognition has been limited to rather simple analysis of local symbol configurations. This paper introduces the Build-Weed-Incorporate programming style for graph grammars and shows its application in determining the meaning of complex diagrams, where the interaction among physically distant symbols is semantically important. Diagram recognition can be divided into two stages: symbol recognition and high-level recognition. Symbol recognition has been studied extensively in the literature. In this work we assume the existence of a symbol recognizer and use a graph grammar to assemble the diagram's information content from the symbols and their spatial relationships. The Build-Weed-Incorporate approach is demonstrated by a detailed discussion of a graph grammar for high-level recognition of music notation. See Appendix A for an illustration of the terms for musical symbols used in this paper.