Kam Fai Chan

Mathematical expression recognition: a survey

Abstract. Automatic recognition of mathematical expressions is one of the key vehicles in the drive towards transcribing documents in scientific and engineering disciplines into electronic form. This problem typically consists of two major stages, namely, symbol recognition and structural analysis. In this survey paper, we will review most of the existing work with respect to each of the two major stages of the recognition process. In particular, we try to put emphasis on the similarities and differences between systems. Moreover, some important issues in mathematical expression recognition will be addressed in depth. All these together serve to provide a clear overall picture of how this research area has been developed to date.

An efficient syntactic approach to structural analysis of on-line handwritten mathematical expressions

Abstract Machine recognition of mathematical expressions is not trivial even when all the individual characters and symbols in an expression can be recognized correctly. In this paper, we propose to use definite clause grammar (DCG) as a formalism to define a set of replacement rules for parsing mathematical expressions. With DCG, we are not only able to define the replacement rules concisely, but their definitions are also in a readily executable form. However, a DCG parser is potentially inefficient due to its frequent use of backtracking. Thus, we propose some methods here to increase the efficiency of the parsing process. Experiments done on some commonly seen mathematical expressions show that our proposed methods can achieve quite satisfactory speedup, making mathematical expression recognition more feasible for real-world applications.

Recognizing on-line handwritten alphanumeric characters through flexible structural matching

Speed, accuracy, and flexibility are crucial to the practical use of on-line handwriting recognition. Besides, extensibility is also an important concern as we move from one domain to another which requires the character set to be extended. In this paper, we will propose a simple yet robust structural approach for recognizing on-line handwriting. Our approach is designed to achieve reasonable speed, fairly high accuracy and sufficient tolerance to variations. At the same time, it maintains a high degree of reusability and hence facilitates extensibility. Experimental results show that the recognition rates are 98.60% for digits, 98.49% for uppercase letters, 97.44% for lowercase letters, and 97.40% for the combined set. When the rejected cases are excluded from the calculation, the rates can be increased to 99.93%, 99.53%, 98.55% and 98.07%, respectively. On the average, the recognition speed is about 7.5 characters per second running in Prolog on a Sun SPARC 10 Unix workstation and the memory requirement is reasonably low. With this simple yet robust structural approach, we already have an effective and efficient on-line character recognition module. This module will be used as part of a larger system, a pen-based mathematical equation editor, which is being developed by the authors using a syntactical pattern recognition approach.

PenCalc: a novel application of on-line mathematical expression recognition technology

Most of the calculator programs found in existing pen-based mobile computing devices, such as personal digital assistants (PDA) and other handheld devices, do not take full advantages of the pen technology offered by these devices. Instead, input of expressions is still done through a virtual keypad shown on the screen, and the stylus (i.e., electronic pen) is simply used as a pointing device. In this paper we propose an intelligent handwriting-based calculator program with which the user can enter expressions simply by writing them on the screen using a stylus. In addition, variables can be defined to store intermediate results for subsequent calculations, as in ordinary algebraic calculations. The proposed software is the result of a novel application of on-line mathematical expression recognition technology which has mostly been used by others only for some mathematical expression editor programs.

Elastic structural matching for online handwritten alphanumeric character recognition

We propose a simple yet robust structural approach for recognizing online handwriting. Our approach is designed to achieve reasonable speed, fairly high accuracy and sufficient tolerance to variations. Experimental results show that the recognition rates are 98.60% for digits, 98.49% for uppercase letters, 97.44% for lowercase letters, and 97.40% for the combined set. When the rejected cases are excluded from the calculation, the rates can be increased to 99.93%, 99.53%, 98.55% and 98.07%, respectively. On the average, the recognition speed is about 7.5 characters per second running in Prolog on a Sun SPARC 10 Unix workstation and the memory requirement is reasonably low.

Mesh Simplification by Vertex Cluster Contraction

A novel 3D mesh model simplification algorithm that makes use of vertex cluster contraction is proposed. The proposed algorithm computes a distortion metrics that satisfy the volume preservation and shape preservation criterion. The simplification results are shown to have better visual quality than other algorithms in literature. Furthermore, the proposed algorithm can generate progressive mesh models.

Towards Efficient Structural Analysis of Mathematical Expressions

Machine recognition of mathematical expressions is not trivial even when all the individual characters and symbols in an expression can be recognized correctly. In this paper, we propose to use Definite Clause Grammar (DCG) as a formalism to define a set of replacement rules for parsing mathematical expressions. With DCG, we are not only able to define the replacement rules concisely, but their definitions are also in a readily executable form. However, backtracking parsers like Prolog interpreters, which execute DCG directly, are by nature inefficient. Thus we propose some methods here to increase the efficiency of the parsing process. Experiments done on some typical mathematical expressions show that our proposed methods can achieve speedup ranging from 10 to 70 times, making mathematical expression recognition more feasible for real-world applications.