Enhancing Offline Tamil Handwritten Character Recognition using Optimal Newton Algorithm based Deep Convolution Extreme Learning Model

: At present, recognizing Tamil characters is considered as one of the most provoking and challenging taskssince there exist discontinuities, slanting, huge differences as well as free-style property characters. In such cases, the error value is enhanced and most of the error arises due to the chaos between the characters having analogous shapes. In addition to this, the time required for processing is also increased. To overcome such shortcomings, recognition of Tamil characters is proposed comprising of four principal stages namely Pre-processing, Segmentation, Feature extraction and classification phase. In the initial data pre-processing phase, the input images are pre-processed by employing thresholding binarization, adaptive filter for noise elimination as well as cropping. Secondly, segmentation is employed typically for verifying an object as well as various boundaries like lines, curves, bends, etc. For optimal segmentation, this paper utilizes Tsallis entropy-based atom search (TEAS) optimization algorithm. Then the segmented features are fed to extract the features and finally in the classification phase, the Tamil characters are recognized effectively. Here, this paper utilizes deep convolution extreme learning-based Newton Metaheuristic (DCELM-NM) approach for both feature extraction and classification. The performances of the proposed approach are evaluated using various simulation measures to visualize the effectiveness. In addition to this, the comparative analyses are carried out and the results reveal that the proposed approach provides superior performance when compared with existing approaches.


Introduction
Over the past few decades, handwritten documents are considered as the most valuable tool to record and communicate information of everyday lives even after the establishment of various modern technologies in the fastgrowing world (Singh et al. 2020).In general, recognizing a handwritten character is the most complicated task, since there exist discontinuities, slanting, huge differences as well as free-style property characters.Numerous research works have been conducted and have succeeded with significantly good performances in both offline and online works based on character recognition (Vellingiriraj and Balasubrmanie, 2020).Among various languages, the Tamil language is used widely and creates a huge demand for recognizing characters.Numerous researches based on both online and offline Tamil character recognition is developed and has accomplished high performances.In addition to this, the Tamil handwritten characters are well analyzed and identified that they depend highly on writer.The Tamil characters also consist of various structural complications that include variation in directions, mismatch of locations, styles, shape differences, discontinuities in structures, etc (Vinotheni et al. 2020).Also, the portions of every character are analyzed by employing two diverse approaches: structural analysis and statistical analysis in other terms referred to as qualitative and pixel based processes (Prakash and Preethi, 2018).Generally, the Tamil script alphabet comprises of 247 characters (12 vowels, 1 aaydham, 18 consonants as well as 216 consonant vowels).The style of writing the Tamil script is begins from left and ends in right.In addition to this, majority of the Tamil characters are in circular form containing the matrix format 3 3 .Since the way and style of writings differ from each other, recognizing the characters of Tamil handwriting is considered as a complicated task (Suriya et al. 2021).Also, numerous errors arise because of similar shaped Tamil structures that make the recognition task more complex.On the other hand, every sound expressed and pronounced in the Tamil language comprises of individual Tamil syllable (Subramani et al. 2021).There are various junction points in Tamil characters that decide the characters and irrelevant junction points sometimes provide amorphous disorganized shapes that further result in misclassification.Tamil handwritten character recognition encounters two different levels of complexity namely the writer complexity and character complexity (Kavitha and Srimathi, 2019).
The writer's complexity affects the overall formation of the characters.Such types of complexities are due to discontinuation of structures, unnecessary and over loops, variation in shapes as well as irregular curves (Ahlawat et al. 2020).On the other hand, the character complexities occur because of its cursive characteristics.Similar to all other languages, the Tamil language also faces few troubles that are challenging and highly trustworthy.Few complexities are orientation angle, varying writing styles, mismatching of locations, curves and slants in characters, complicated structures in styles, as well as total number of holes and strokes (Velmurugan et al. 2018).Numerous researches based on offline Tamil recognition deals only with few Tamil characters since it becomes extremely complicated in distinguishing small variations in large handwritten document (Bala et al. 2018).This paper proposes four stages for optimal recognition of Tamil characters namely the data pre-processing phase, segmentation phase, feature extraction phase and classification phase.In the data pre-processing phase, the input image is pre-processed by using three steps: thresholding binarization, noise elimination using a bilateral adaptive filter as well as cropping.In the segmentation phase, TEAS approach is employed for optimal segmentation of the features.The feature extraction and classification phase utilizes DCELM-NM approach to extract and recognize the Tamil characters optimally.The major contributions of the proposed approach are discussed in the following section.
 Proposing four principal phases namely data preprocessing phase, segmentation phase, feature extraction phase and classification phase for optimal recognition of Tamil characters. Proposing TEAS approach for optimal segmentation of features and DCELM-NM approach to extract and recognize the Tamil characters optimally. Enhancing the rate of recognition accuracy by utilizing DCELM where the value of weight is optimized by NM optimization algorithm.
The rest of the paper is structured as follows: The existing studies based on Tamil character recognition are described in section 2. The problem formulation and motivation of this paper is discussed in section 3.In section 4, four major phases involved in the proposed approach are deliberated.The performance evaluation and the comparative analysis of the proposed approach are discussed in section 5. Section 6 concludes the research article.

Existing Studies Based On Tamil Character Recognition
Numerous research works have been carried out by various research scholars regarding the recognition of Tamil characters.In order to gain better understanding, the highlights of few research works are delineated in the following section.Lincy et al. (2020) demonstrated an optimal configuration of convolutional neural network for Tamil Handwritten Character Recognition using an improved lion optimization algorithm.The evaluation measures employed in recognizing the Tamil characters were Accuracy, sensitivity, specificity and precision.The experimental analysis was conducted and the results revealed that the accuracy rate was high but the time required for obtaining a high accuracy rate was very large.The structural representation-based on off-line Tamil handwritten character recognition was developed by Raj et al. (2020).This approach utilized two different types of algorithm namely the Q-Quad tree algorithm and the Zordering algorithm for the evaluation of various measures namely Accuracy, time consumption, precision.The overall performances obtained during evaluation were high.But this approach failed to analyze the shape and location was the major drawback of this approach.Raj et al. (2020) proposed a Junction Point Elimination approach for recognizing the Tamil characters.Accuracy, average features, variances were the evaluation measures employed for simulation.The experimental analyses were conducted and the results revealed that the accuracy rate was enhanced with a minimum error value rate.But the position and location of Tamil characters were inappropriate was the disadvantage of this approach.A novel nearest interest point classifier for offline Tamil handwritten character recognition was demonstrated by Deepa et al. (2020).Here, the experimental analysis was carried out to evaluate certain simulation metrics namelyThreshold, recognition accuracy and normalized distance.In this approach, the recognition accuracy obtained was very high.But this approach failed to demonstrate the recognition of online characters.Bhardwaj et al (2020) proposed a handwritten Devanagari character recognition using deep learning-convolutional neural network model.The measures employed for simulation wereTest accuracy, learning rate and total number poof epochs.Test accuracy, learning rate and a total number of epochs.The evaluation results revealed that the test accuracy was improved for most of the challenging datasets.But the implementation was a bit complex when compared with other approaches.Athisayamani et al. (2020) demonstrated Recognition of Ancient Tamil Palm Leaf Vowel Characters in Historical Documents using B-spline Curve Recognition.The performance measures employed in this approach wereRecognition accuracy, precision, specificity and sensitivity.However, this approach failed to extract image patches was the major drawback of this approach.
Jayakanthan et al. ( 2020) developed a handwritten Tamil character recognition using a residual neural network.Learning rate, loss, accuracy, time were the performance measures employed for simulation.The experimental analyses were carried out and the analysis revealed that the accuracy was high when compared with various other approaches.Moreover, this approach failed to recognize 256 characters of Tamil language was considered as the most significant drawback of this approach.The Devanagari Handwritten Character Recognition using deep Convolutional Neural Networks was developed by Gurav et al. (2020).Model accuracy, loss, true label, predicted label was the evaluation metrics employed for simulation and the simulation results revealed that the efficiency of this approach in terms of accuracy, precision was high when compared with other approaches.But the implementation time required was very large.Prakash et al. (2020) demonstrated a Tamil handwritten character recognition using convnet model.Training accuracy, validation accuracy, training loss, validation losses were the performance measures employed for simulation.The accuracy rate was very high when compared with various other neural network-based approaches.In few circumstances the characters were misclassified was the major drawback of this approach.The Tamil-Brahmi script character recognition system using deep learning technique was proposed by Subadivya et al. (2020).The evaluation measures employed in recognizing the Tamil characters were Accuracy, sensitivity, specificity and precision.The experimental analysis was conducted and the results revealed that the accuracy rate was high.However, this approach failed to recognize the image accurately.Table 1 describes the brief description of Tamil language character recognition.

Problem Definition And Motivation
In general, the Tamil characters are employed to recognize the characters into a machine editable format from the scanned digital image input.It becomes a tough task to recognize the handwritten characters of the Tamil language because of deviations in style, orientation angle and size.On the other hand, recognizing the handwritten Tamil character becomes more complex and hence the error is increased.The majority of the errors arise due to the chaos between the characters having analogous shapes.Few problems based on recognizing Tamil characters are listed in the following section.

Maximum accuracy rate
Failed to recognize the image accurately  It is necessary to tackle the problem based on the handwritten compound characters of Tamil language; since recognizing the compound characters is still at an initial stage.
 After binarization of pre-processing, the character often changes its shape and loses its information.Therefore, it is necessary to have appropriate pre-processing to maintain the style and shape of a particular character.
 It is important to utilize persistent and robust preprocessing approaches for maintaining the nature of the original character despite various background changes in ink and the width of the pen. The shapes of Tamil handwritten characters are to be taken into consideration during the extraction of features. Reprinting and editing of certain textual documents printed on paper require more time and thus the accuracy obtained was also very low and it needs to be solved.
So to overcome such drawbacks, it is recommended to capture the image photography of a particular document more optimally.Few significant disadvantages motivated us to do this research based on recognizing handwritten Tamil characters.

Proposed Methodology
The proposed approach comprises of four principal steps: Pre-processing, Segmentation, Feature extraction and classification for the optimal recognition of Tamil characters as described in fig. 1.In the initial data pre-processing phase, the input images (Tamil characters) are pre-processed by employing thresholding binarization, adaptive filter for noise elimination as well as cropping.Secondly, the segmentation process utilizes TEAS approach for optimal segmentation.During segmentation, initially the total numbers of text lines are recognized followed by the identification of characters.Feature extraction is the third phase that extracts the features for further classification of Tamil characters.Finally, in the classification phase, the Tamil characters are recognized effectively.Here, this paper utilizesDCELM-NM approach for both feature extraction and classification.The detailed description of every respective phase is illustrated as follows.

Data Pre-processing phase
In general, data pre-processing is employed to reduce or eliminate the noises of an input Tamil handwritten image.If recognition of Tamil characters is deeply influenced by the noise, then the efficiency of an input image reduces rapidly.Therefore it is necessary to minimize the noise to obtain an optimal pre-processed image (Kowsalya and Periasamy, 2019).This paper utilizes an adaptive bilateral filtering technique to eliminate the noise from an input image.Practically, filters are employed to sort out the unnecessary objects or things from the spatial surfaces.The input images are highly influenced by a mixture of noise signals in digital image processing.The main intention of the bilateral adaptive filters is to enhance the image quality thereby increasing the compatibility of the data found in the input images.Here, in this paper, an input image is preprocessed by using three steps: thresholding binarization, noise elimination using a bilateral adaptive filter as well as cropping.A brief description of each step is described as follows.

Thresholding Binarization
Binarization is a technique that transforms grayscale images to black and white images (two-tone images) using a thresholding approach.Here, the threshold value is employed in assigning the value (i.e.0 and 1) for the pixel position of an input image.The formula for assigning the pixel position using binarization approach is discussed in equation (1).
Therefore by employing the above formula, the input handwritten Tami character images are binarized (Suriya et al. 2021).

Adaptive Bilateral Filter for noise elimination
Generally, the adaptive filter is considered as a nonlinearly, noise-eliminating, edge-preserving smoothing filter.In an adaptive bilateral filter, the value of intensity is calculated initially and secondly the weighting range depending on both radiometric difference and Euclidean distance are evaluated.Consequently, the elimination of noises and preservation of sharp edges is ensured.The following expression provides the bilateral filtering of an input image (Yu et al. 2020).Thus, From equation ( 2), the adaptive bilateral filtering approach with normalization is represented as, From equations ( 2 From equations ( 4) and ( 5), D  and R  signifies the assigned value.Thus by employing an adaptive bilateral filter, the noise reduction is enhanced thereby obtaining a noise-free input image for recognizing characters.

Cropping
During the process of cropping, the images are cropped into a definite size that includes height and weight thereby eliminate the unnecessary parts present in the input image and enhances image framing.

Segmentation Phase
The segmentation process is considered as the most significant phase in system recognition; since it provides a consequential region for more analysis.The segmentation is employed typically for verifying an object as well as various boundaries like lines, curves, bends, etc.The accuracy of recognizing the characters depends highly on segmentation accuracy.Therefore, the segmentation process comprises of two major characteristics.The first to recognize the total number of text lines present on the respective page and the second to identify every character from respective words.In general, the segmentation is categorized into line and character segmentation.The characters and lines are segmented from the pre-processed Tamil handwritten document (Manigandan et al. 2017).For optimal segmentation, this paper utilizes Tsallis entropy approach based atom search (TEAS) optimization algorithm that is discussed as follows.

Tsallis Entropy Approach
Let us consider the image size is Q P  , the probability distribution is denoted by The mathematical expression for Tsallis entropy is related to both is defined in the respective section (Xing et al. 2020).
From the above equations, the nonextensivity is determined by the parameter Nand the total entropy value is obtained in equation (10).
The gray level is said to be known as the optimal threshold if ) (t S N reaches a maximum value.Thus,

 
) ( From equation ( 11), the optimal threshold value is represented by * T .On the other hand, the mathematical formulation for m-1 optimal threshold when ) (t In Tsallis entropy approach , the Atom search optimization algorithm is employed to optimize the weights that are discussed briefly in the following section.

Atom Search (AS) optimization algorithm
Atoms are typically small in size present in all substances moving all the time (Zhao et al. 2019).Based on Newton's second law of motion, the acceleration ) (J A cc significantly correlated with mass ) (J M is represented in equation ( 13).
) ( From equation ( 13), the interaction and the constraint force is represented as respectively.In accordance with Lennard-Jones potential, the force acting on both Jth and Kth atom with respect to dimension D and time T is written as From equation ( 14), the depth function for adjusting both the attraction and the repulsion regions are denoted by ) (t  and are determined as follows. From equation (15), t and  signifies the total number of iterations and the depth weight.The functional behaviour F consisting of the diverse values . The value of G can be determined as, Where, the upper and the lower boundary of G is represented as and From equation ( 17), the subset of the atom population is denoted by KBEST.In accordance with Newton's third law, the force acting upon both Jth and Kth atom are contradictory.Thus, The position and velocity of the atom with respect to (T+1) iteration for simplifying the algorithm can be written as, From equation ( 20), the position and velocity of the atom are represented as ) 1 (  T V J and ) 1 (  T Z J respectively.Thus by employing Tsallis entropy approach based atom search (TEAS) optimization algorithm the characters are segmented optimally and the segmented output is fed to extract the features.

Feature Extraction Phase
The segmented features are then extracted where every character corresponds to the feature vector.The feature extraction plays a vital role during character recognition.The main intention of the feature extraction involves the extraction of a feature set that includes characters width, size, height, and the total number of horizontal and vertical lines, arcs, the total number of long and short horizontal and vertical lines that enhances the recognition rate.On the other hand, the feature extraction scales down the original document and distinguishes the characters.The resultant features are provided to the classification phase to recognize the Tamil characters from overlapping Tamil characters (Pragathi et al. 2019).In addition, this paper utilizes DCELM-NM to extract and classify the features for optimal recognition of Tamil characters.

Classification Phase
The process next to the extraction is the classification where the Tamil characters are recognized.For optimal recognition, this paper utilizes DCELM to classify the input images.In DCELM, the Newton Metaheuristic algorithm is employed to optimize the weights thus recognizing the Tamil characters more optimally.

Deep Convolutional Extreme Learning Machine (DCELM)
This section provides the concept of DCELM that utilizes to select the appropriate features and to solve classification tasks.Fig. 2 describes the basic architecture of DCLEM comprising of an input layer, numerous hidden layer and an output layer.Here the hidden layers arealternately arranged(i.e. one convolutional and one pooling layer).In general, the DCELM is calculated based on three certain considerations.Initially, the multiple pooling and convolution layer that are hidden extracts features of high level from the input handwritten Tamil images.Secondly, the local correlations are learned by employing the shared receptive weight.Finally, the batch training of ELM executes faster than various other deep learning approaches (Pang et al. 2016).The mathematical expressions involved in DCELM are discussed as follows.

Local / input weight initiation and orthogonalization
In general, the input weight among the initial convolution layer and the input layers are generated randomly by DCELM.Here, in this paper, the input sampling weights are determined Gaussian probability distribution function.Therefore, the input weight is evaluated by, From the above equation, the total size of the local receptive field is represented by S S  .The initial weight in matrix form is denoted as W I .In addition to this, the singular decomposition approach orthogonalizes the initial weight matrix.
Every J W i column of W I is further transformed to represent the respective input weight of Jth feature map.

Convolution layer
This layer is capable of extracting the features by means of convolution operation on the input Tamil handwritten images.The convolution node with respect to mth and nth coordinate of the Jth feature map is evaluated in the following equation.Thus, From the above equation, the input image is represented by Y.

Pooling layer
Generally, the two different strategies involved in determining the pooling layers are (a) square root pooling that comprises of summation and square operation thereby establishing the transitional invariance's and rectification nonlinearity (b) stochastic pooling where the maps to be pooled are evaluated by employing a multinomial distribution function.The mathematical terms involved in both types of pooling are derived as follows.
(a) Square pooling: From equation ( 24),the probability rate for the pooling rate with respect to the normalizing value K R is determined by m Pr .Then the value to be pooled in the stochastic pooling layer n V is determined in equation ( 25).
From the above equation, the nodal value at an appropriate location is represented as . On the other hand, the pooled map containing a very small size is obtained by stochastic pooling methods whereas in square root pooling, the size is bit large.The computational complexity is also minimum in case of stochastic pooling.

Evaluation of output weight
After the generation of features, the values obtained in stochastic pooling are concatenated into row vectors.Here, the regularized least square approach is employed in determining the optimal output weight.Thus, From equation ( 26),the sample input image label and the regularization parameter is represented as t and P R respectively.In DCELM, the Newton Metaheuristic algorithm is employed to optimize the weights in which the optimization processes are discussed briefly in the following section.

Newton Metaheuristic (NM) Algorithm
The NM algorithm is considered as the most effective method in determining the optimal solution.Since the derivative tends to zero the local optima is found using the Newton method at an optimal point (Gholizadeh et al. 2020).In such an instance, an iterationvalue is obtained using the following equation.

Evaluation of numerical approximation
In general, it is impossible to determine the explicit derivative from the explicit from numerous real-world issues.Therefore, it is necessary to derive numerical approximation and it needs to be calculated.Let us assume three different points consisting of asymmetrical distance, From the above two equations, the positive parameter is represented by  .

Determination of second-order Taylor Expansion
The mathematical formulations to determine the second-order tailor expression of function f with respect to Using the equations of numerical approximation and second-order Taylor expansion, the values of Therefore on determining the above two equations, the function Therefore, on substituting the above to equations in In this paper, in order to extract and classify the Tamil characters optimally, a Newton metaheuristic algorithm is employed by modifying the above-mentioned equation.In addition to this, the particle positions are updated and the steps involved in the NM algorithm are delineated as follows.
Initially, the p-variables are designed and the population initialization using q particles is generated randomly.Therefore, From equations ( 36) and (37), the initial population and the discrete variables are represented by 0 M and D .Then the J th particle with respect to the initial population is denoted by J Y 0 .The Jth particle and I th design variables are selected randomly from the discrete variable based on uniform distribution is represented as J Y 1 0 .In addition to this, the fitness values based on particles are determined and the populations are arranged inincreasing order.Therefore, the sorted population with respect to the number of iterations is described in equation (38).
From the above two equations, the population sorted and the fitness function with respect to the iterations T is represented as respectively.
The NM algorithm converges prematurely to a local optimum value and the positions of the particles are updated using the following equation.Therefore,   From equation ( 40), ( 41) and ( 42) the round value near to the integer value and the vector norm is represented as ) ( Round and  respectively.The performances based on the position of the particles areenhanced and updated using equation ( 43).
From the above equation, the two random numbers with respect to the iterations are represented as T

DCELM-NM based Tamil character Recognition
The proposed approach utilizes 80% of the dataset for training and the rest 20% for testing.From NM optimization algorithm, the optimal weight value is obtained using NM algorithm and the obtained optimal value is considered in the DCELM network.Fig. 3 describes the proposed DCELM-NM based Tamil character recognition.

Experimental Discussions
This section describes the evaluation results of the proposed approach to recognize the Tamil characters.The experiments are carried out for numerous Tamil handwritten recognition based approaches.In addition to this, the comparative analyses for various approaches are discussed in the following equation.

Simulation Procedure
The proposed approach based on Tamil character recognition is executed under MATLAB platform done in windows machine containing 4GB RAM, 1.9GHz speed, Intel Core i3 processor.

Parameter Specifications
This section discusses the parameter details of AS optimization algorithm, DCELM and NM optimization algorithm.The parameters involved, their specifications and their respective ranges are set and discussed in Table 2. Depth weight 10 G 0.9-2

Dataset Description
In this paper, the proposed Tamil character recognition utilizes the datasets of Isolated Tamil handwritten character established by HP lab India.There are approximately 150 Tamil characters which are scripted and written by various local Tamil writers of South India.For every class, there are approximately 500 samples where 82500 samples are available freely.In addition to this, there are more than 50 styles of writing scripted by different writers (Kavitha and Srimathi, 2019).The proposed approach utilizes 80% of the dataset for training and the rest 20% for testing.

Simulation Metrics
The proposed approach requires various simulation metrics like accuracy, specificity, sensitivity, F1-score and rate of recognition are calculated to investigate the performances.The mathematical expressions for the metrics are determined as follows.

Performance Evaluation
In this section, the performance analyses are carried out to determine the effectiveness of the proposed approach.Fig. 4 provides the graphical representation for various measures namely accuracy or recognition rate, sensitivity, specificity and F1-score for the dataset utilized in the proposed approach.The graph is plotted and from the graphical analysis, the recognition rate, sensitivity, specificity and F1-score achieves the percentage value of about 9.75%, 94.25%, 93.5% and 91.21% respectively.
The testing and training accuracy of the proposed approach with respect to the total number of epochs are displayed in fig. 5. Here, the testing dataset has been fed into the training dataset that provides the recognition accuracy rate of about 98% and the testing accuracy rate of about 96.23%.A total number of about 156 classes have been utilized for both training and testing of datasets.Thus from the graphical analysis, it is proven that the proposed approach provides a high rate of recognition accuracy.Fig. 6 provides the graphical representation for average processing time for every respective Tamil character image for the proposed approach with respect to the total number of training images.

Comparative Analysis
This section discusses the comparative results of various simulation metrics namely accuracy, sensitivity, specificity and F1-score for various existing Tamil character recognition approaches namely Neural network base Elephant herding optimization (NN-EHO) (Kowsalya and Periasamy, 2019), Convolution Neural Network-based Improved Lion optimization (CNN-ILO) (Lincy et al. 2020), Convolution neural networks (CNN) and Modified Convolution neural networks (MCNN).Fig. 7 (a) to (d) describes the graph plots for various measures; the experimental analysis is conducted and the analysis reveals that the recognition of Tamil characters provides better performances when compared with various other existing approaches.

Conclusion
Recognition of Tamil characters is considered as one of the most provoking and challenging tasks since there exist discontinuities, slanting, huge differences as well as free-style property characters.To overcome such drawbacks, this paper proposed four significant phases.In the initial data pre-processing phase, the input Tamil characters are pre-processed by employing thresholding binarization, adaptive filter for noise elimination as well as cropping.Secondly, the segmentation process utilizedTEAS approach for optimal segmentation.During segmentation, initially,the total number of text lines is recognized followed by the identification of characters.Feature extraction is the third phase that extracts the features for further classification of Tamil characters.Finally, in the classification phase, the Tamil characters are recognized effectively.This paper utilizedDCELM-NM approach for both feature extraction and classification.Here, the effectiveness of the proposed approach is determined by employing certain simulation measures namely the accuracy, sensitivity, specificity as well as F1-score.Finally, the comparative analysis is carried out for various approaches namely the proposed DCELM-NM approach, NN-EHO, CNN-ILO, CNN as well as MCNN.The analysis reveals that the recognition of Tamil characters provides better performances when compared with various other existing approaches.In the future, we planned to execute various other optimization approaches to determine the excellence of recognizing the Tamil characters.

Fig. 1 .
Fig.1.Proposed Flow Diagram ) and (3), the geometric closeness value among the limited region pointed at every point Y and the neighbouring point  is represented by ) function that evaluates the relationship among the adjacent and central pixel is represented by   is obtained as follows.

Fig. 3 .
Fig.3.Proposed DCELM-NM based Tamil character recognition From the above equation, the coordinate nodes with respect to Jth feature maps are represented as a and b respectively; where ) 1 ,...( 1 ,    S d b aand e signifies the pooling size. ), the value of J Y with respect toT and T+1 is represented by T first and the second-order derivative of a specific function is denoted

.
The global best solution and a maximum number of iterations are denoted by GB Y and v respectively.Thus from equation (43), the local and global both exploitation and exploration phases.Thus by employing the NM algorithm the features of Tamil characters are extracted and classified optimally.

Fig. 5 .
Fig.5.Training and testing accuracy rate of proposed approach

Fig. 6 .
Fig.6.Average processing time with respect to number of training images Comparison results for (a) accuracy (b) sensitivity (c) specificity (d) F1-score , when the pre-determined character is identified correctly.
Pos f:False positive, when the un-determined character is identified mistakenly as pre-determined.
, when the un-determined character is dropped out correctly as un-determined.Neg f:Falsenegative, True negative, when the predetermined character is dropped out mistakenly as an undetermined character.