Character recognition (CR) has been extensively studied in the last half century
and progressed to a level sufficient to produce technology driven applications. Now, the rapidly growing computational power enables the implementation of the present CR methodologies and creates an increasing demand on many emerging application domains, which require more advanced methodologies.
Character recognition (CR) covers all types of machine recognition of characters in various application domains. It has increasing needs in newly emerging areas, such as development of electronic libraries, multimedia databases, and systems which require handwriting data entry. It can be classified based upon two major criteria that are Data acquisition process (on-line or off-line) and Text type (machine-printed or handwritten) 23.
Now a day there is a lot of development in smart devices which are combination of human intelligence and machines. Character recognition is one of the example of smart device and Mathematical expression recognition is belongs to such device which is developed to recognize handwritten as well as printed mathematical symbols and expressions 4.
Over the centuries, people have developed a specialized two-dimensional notation for communicating with each other about mathematics. The notation is designed to represent ideas in a way that aids mathematical thinking and visualization. It is natural and convenient for people to communicate with computers using this same notation. This involves conversion between mathematical notation and internal computer representations. Under current technology, two-dimensional mathematical notation can be generated by computers, but recognition facilities are not widely
available.the task of translating mathematics into a computer-process able form usually falls to a human user 3.
With the very rapid increase of Internet users in recent years, there is a growing trend of disseminating and ex-changing information via this popular channel. Digital library and distance learning are becoming hot research areas that address issues arisen from the widespread use of the Internet. One of the key vehicles in the drive towards realizing these ideas is to develop cheap and efficient methods for transcribing existing knowledge in the form of paper documents into corresponding electronic form, which is the form that can be processed by today’s digital computers and transmitted through the Internet 6.
Mathematical expressions constitute an essential part in most scientific and engineering disciplines. The input of mathematical expressions into computers is often modified in order to accommodate all the keys needed. Another method is to make use of some extra keys in the keyboard (e.g., function keys) along with a set of unique key sequences for representing other special symbols. Yet another method is to simply define a set of keywords to represent special characters and symbols, as in LATEX 6.
Mathematical expression recognition is one of the research topics from several decades but it is still an area of research topic because there are lots of challenges in this system. It is very important regarding scientific document image analysis and this system have applications like scientific document digitization, information retrieval or accessibility for blind people 14. The input for this system is mathematical expressions and symbols. The input of mathematical expression into computers is very difficult than that of plain text because mathematical expression contains special symbols, Latin or Greek letters and different operators with digits 6.
For on-line approach system utilizes the temporal information about strokes input. Whereas off-line recognition deals with the image representation of mathematical expressions, which may be printed or handwritten. This system faces lots of difficulties because if consider handwritten mathematical expression then there are variations occur in the size, font of symbol, writing style varies person to person and quality of image also matters 5
shows the system architecture for mathematical expression recognition. The first step carried out is data acquisition. In this process data is acquired from optical scanners or an image is captured from paper by camera. Paper on which mathematical Expression has written is thus inputted to the system. The next step is pre-processing under which image cleaning takes place. Along with that size normalization, skeletonization and noise removal takes place. After pre-processing stage image is applied to segmentation.Optical Character Recognition OCR is the most crucial part of Electronic Document Analysis Systems. The solution lies in the intersection of the fields of pattern recognition image and natural language processing. Although there has been a tremendous research effort the state of the art in the OCR has only reached the point of partial use in recent years. Nowadays cleanly printed text in documents with simple layouts can be recognized reliably by off the shelf OCR software. There is only limited success in handwriting recognition, particularly for isolated and neatly hand printed characters and words for limited vocabulary.23The k-Nearest-Neighbor (k-NN) rule is a very popular pattern classification rule that provides good results when the number of prototypes is large. This is a usual classification technique that has also been tested for mathematical symbols classification. This classifier doesn’t need to be trained, because only it is necessary to have available a set of labeled samples. Given the vector representation of a mathematical symbol, each sample is interpreted as a point in a high-dimensional space. Therefore, given a test sample, the distance is computed to all the prototypes of the labeled set. Then, the k-NN classifier uses the k nearest prototypes to the test sample to determine its class, which is the most voted.
The Weighted Nearest Neighbor (WNN) technique is an improvement of the classical 1-NN. A discriminative technique is used to learn a weighted distance by using the 1-NN rule with a training set. A distance weighting scheme is proposed which can independently emphasize prototypes and/or features. In this work a different weight for each prototype combined with a different weight for each class and characteristic. The reason is that in a training set there are samples more representative than others, and also in symbol representation the importance of each
SVM is a discriminative classifier based on Vapnik’s structural risk minimization principle. The utilization of the Support Vector Machine (SVM) classifier has gained immense popularity in the past years. It can be implemented on flexible decision boundaries in high dimensional feature spaces. Generally, an SVM solves a binary (two-class) classification problem and multi-class classification is accomplished by combining multiple binary SVMs. Good results on handwritten numeral recognition by using SVMs can be found by J. X. Dong 13.
First practical implementation of SVM had been executed in early nineties. It is most efficient family of algorithms in Machine Learning and computationally efficient. Support Vector Machines (SVM) are learning systems that use a hypothesis space of linear functions in a high dimensional feature space, trained with a learning algorithm from optimization theory that implements a learning bias derived from statistical learning theory.A Neural Network is defined as a computing architecture that consists of massively parallel interconnection of simple neural processors. It can perform computations at a higher rate compared to the classical techniques because of its parallel nature. ANN is inspired by the way biological nervous system such as the brain process information. The key element of this paradigm is the novel structure of the information processing system. And it is composed of large number of highly
M.E. E (D.E.)
SSBT’s COET, Bambhori, Jalgaon
A Soft Computing Approach To Mathematical Expression Recognition
interconnected processing elements (neurons). ANN is configured for specific application, such as data classification.
When ANN processed data then there are two main stages that are training stage and classification stage. In classification stage samples are passed as input to the ANN, resulting an output representing what ANN believes to be the most correct output. To be a successful classification it must be preceded by a training stage 12.
There are various classifying methods are investigated such as template matching, ANN. A template matching method is used by some systems, however this method can be slow and time consuming. The MLP has been widely used in pattern recognition. The standard MLP is a supervised feed forward neural network, which consists of one input layer, a number of hidden layers and one output layer 1. Structural recognition methods are less used in mathematical expressions recognition. Systems as those in extract structural primitives and use them by comparing with the training data. On the other hand, artificial neural networks (ANN) are known to be better in terms of speed and recognition rate. Some methods perform a simultaneous segmentation and recognition such as hidden markov model (HMM) they are based on statistical models. Each symbol has its own model where recognition results are obtained as probabilities of different models 6.
Table 2.1 shows various methods used by different authors for symbol and mathematical expression recognition system. This comparison gives idea about recognition rate of the different systems.
The first step carried out is data acquisition. This data is then acquired from optical scanner. Next step is pre-processing image cleaning takes place. Along with that image is converted to form of suitable subsequent processing like size normalization, skeletonization and noise removal takes place. After pre-processing image is applied to segmentation as well as feature extraction. In next step the document is segmented in sub components and separating of each character is takes place. After segmentation the feature set which is useful for training of the system and recognition is extracted.