White blood cell detection and classification using Euler’s Jenks optimized multinomial logistic neural networks

Abstract

Due to the wide acceptance of White Blood Cells (WBCs) in disease diagnosis, detection and classification of WBC are hot topic. Existing methodologies have some drawbacks such as significant degree of error, higher accuracy, time bound and higher misclassification rate. A WBCs detection and classification called, Jenks Optimized Logistic Convolutional Neural Network (JO-LCNN) method has proposed. Initally, Eulers Principal Axis is used as a convolution model to obtain a rotation invariant form of image by differentiating the background and RBCs, then eliminating them which leaves only the WBCs. By eliminating the wanton features, inherent features are detected contributing to minimum misclassification rate. According to above, Jenks Optimization function is used as a pooling model to obtain feature map for lower resolution. Therefore JO-LCNN is used for removing tiny objects in image and complete nuclei. Finally, Multinomial Logistic classifier is used to classify five types of classes by means of loss function and updating weight according to the loss function, therefore classifying with higher accuracy rate. Using LISC database for WBCs with different parameters as classification accuracy, false positive rate and time complexity are performed. Result shows that JO-LCNN, efficiently improves accuracy with less time, misclassification rate than the state-of-art methods.

Keywords

White blood cell Eulers Principal Axis Jenks Optimization pooling Multinomial Logistic Classification

1 Introduction

Blood tests are especially utilized for assessing individual health. Blood test is used to evaluate blood cell categories. A complete blood count (CBC) is an estimation of cellular elements. Besides, CBC is the commonly used blood tests by clinicians. In WBC count, the information provided by the physicians is vital for identifying diverse sickness conditions.

A three layered approach was proposed in [8] that considerably partitions WBCs in the whole blood. This three layered approach provided a concentration dependent visual of WBC counts. Besides, readout ratio of granulocytes from the blood was presented in a significant manner. By integrating the three layered approach with smart phone optical detection, this approach ensured blood cell counting easily obtainable, particularly in resource poor, point-of-care (POC) settings in a more time and cost efficient manner. However, the results were obtained with maximum error. On the other view, a larger field of view was obtained for gathering various images and employs image post processing to stitch them together.

A computer-aided automated system, called, Regional Convolutional Neural Networks (R-CNN) was presented in [2] that easily identified which locates WBC types in blood images. Transfer learning and Resnet50 CNN architecture were developed to extract the features.

Advantage of R-CNN in WBC detector was to soothe the overlapping problem or partial visibility of object in the image and therefore contributing accuracy. Though the accuracy was found to be higher, the invariance to intra-class variability was not provided, therefore compromising the false positive rate. To overcome this drawback, in this work, a trainable scalar for sub-sampling by means of Jenks Optimization model provide more invariance to intra-class variability, contributes towards higher accuracy and lower false positive rate.

An accurate detection and classification method has introduced to collect the data about the distribution of samples and helps to analyze abnormal and early disease diagnosis is the need of the hour. Aim to develop and validate an algorithm that detects and classifies WBCs. The contribution of this work is summarized as:

WBCs detection in the microscope image, we apply the convolution by means of rotation matrix employs Euler’s Principal Axis. According to the principal axis characteristics of WBC is for separating WBCs in the background and red blood cells.

Then we propose optimization function for eliminating the tiny objects from image and complete the nuclei by means of computing trainable scalar values. This reduces the time consumption in process.

In classification, a Logistic CNN is employed that classifies five different WBCs by employing Jenks Optimization to improve the accuracy.

In experiments, the quantitative results are delivered to confirm accuracy.

2 Related works

The organization of the paper is described as follows: related work is summarized in Section 2. Section 3 provides a detailed note of proposed method. Section 4 provides the experimental evaluation and database description. Experimental Results are analyzed with various metrics in Section 5. Section 6 concludes the paper.

The differential count of WBCs forms vital assessment in clinical hematology which is specifically performed in peripheral blood. Due to higher variations in intra and inter cells within a patient and between patients, WBC classification is still considered as a need topic of research.

A Dual Stage CNN was proposed in [6] for automatic counting of WBC. Accuracy was found to be high using this dual stage due to the elimination of the time consuming feature selection and extraction process. However, with the technological advancements seen in the medical field, accurate analysis tool is said to be essential for early disease diagnosis. Feed forward back propagation neural network was used in [9] to classify the five types of WBCs. With the appropriate segmentation process, the classification accuracy was said to be high.

But, with the rise of high volumes of data, automatic systems have started to heighten. New unsupervised method for cell segmentation and counting called CSC in [3]. This in turn not only improved the classification accuracy but also minimized the time consumed in the classification process. A single-frame machine learning based super resolution processing was presented in [16] to address the automate detection and classification of WBCs for last few decades. But, an optimal model was not available as decision support system due to the complex composition of the cells.

In [15], the classification of WBCs was used with two approaches such as conventional image processing approach and deep learning approach. An automated high throughput classification of blood cells using Red Blood Cells shape quantification was presented in [10]. However, with the time consuming and tedious task involved, a modified configuration of detection and classification of WBC utilizing machine learning approach was proposed in [11].

Supervised machine learning approach was investigated in [20] depended on Morphological classification of cells to improve accuracy. Yet another method for segmentation using K-Means and CNN classification was introduced in [7], therefore improving the classification accuracy and reducing classification time when compared to conventional CNN classification.

The conventional CNN depends on the feature engineering is needed for obtaining the efficient segmentation models and also get particular amount of features for recognition. But, robustness of the conventional systems was poor. An automatic feature extraction was provided by classification method depending on the CNN to avoid the separate model for segmentation but hard for multiple object recognition.

In [13], a leukocyte recognition model was presented using Single Shot Multibox Detector and An Incremental Improvement Version, therefore resulting in the improvement of recognition performance. Fourier ptychographic microscopy (FPM) were accessed in [5] to count the WBCs and also an automatic counting algorithm was designed that proved to be both cost effective and resulted in accurate detection. However, with the need to enrich the existing CNNs, transfer model was used in [1] for fine tuning existing deep networks.

A neural network based approach involving feature extraction for three different features and training them to network was presented in [12] for WBC classification. Computation vision algorithms were employed in [2], therefore minimizing long access time.

Yet another different component was applied in [18] for online scanning of human blood smear that in turn segmented five different types of leukocyte at a quick speed. However, with the limitation involved in the selection of threshold, accuracy was compromised. To address this issue, a dual-threshold model was utilized in [17] based on golden section search model. An iterative structured circle detection algorithm was performed in [19] for segmentation and counting of WBCs and RBCs.

Though many methods and algorithms have been developed for WBC, the data detection and classification performance was not efficient. Due to presence of noise, different shapes of WBC, and similar color among stained cytoplasm and WBCs issues involved. Detection and classification accuracy of the existing methods cannot assemble the original clinical needs. To minimize the classification time in the field of WBC detection and classification is necessary.

The major issues identified from the mentioned existing methods are overcome by introducing a JO-LCNN for WBCs detection and classification. JO-LCNN is used to divide the densely adhered WBCs effectively with higher accuracy. Logistic CNN is employed to classify the different WBCs.

3 Methodology

White blood cell forms the central part of immune system that in turn safeguards the body from infections like, bacteria, viruses, fungi and so on. WBC consists of various types such as Lymphocytes, Monocytes, Eosinophils, Basophils and Neutrophils [14]. A surplus or insufficiency number of WBCs results in several types of diseases. Therefore detection and classification of WBCs can assists clinicians diagnosing diseases at the early stage.

In this section, JO-LCNN is proposed. Figure 1 shows the block diagram of the JO-LCNN method.

Fig. 1

Block diagram of the Jenks Optimized Logistic Convolutional Neural Network method.

As illustrated in the Fig. 1, with the samples provided as input, convolution is performed by means of Eulers Principal Axis Convolution model to discard the background and red cells leaving only the white blood cells. Next, Jenks Optimized Pooling is applied for convolving feature map to lower resolution by means of a trainable scalar obtained through Jenks Optimization function. Finally, classification of WBC is performed in the fully connected layer by means of Multinomial Logistic Classification model, that classifies into five different classes (i.e., ‘B’ for basophils, ‘E’ for eosinophils, ‘L’ for lymphocytes, ‘M’ for monocytes and ‘N’ for neutrophils) therefore reducing the misclassification rate and correspondingly increasing the accuracy.

3.1 Eulers Principal Axis convolution

Blood sample consists of WBCs and RBCs along with certain amount of cells. Initially, JO-LCNN is used for identifying WBCs by differentiating with background and RBCs. In this work, Euler’s Principal Axis Convolution model is used that is based on the idea of eliminating the background and RBCs leaving only the WBCs. With samples provided as input, here, the sample input images are convolved by means of principal axis. The block diagram of Euler’s Principal Axis Convolution model is illustrated in Fig. 2.

Fig. 2

Block diagram of Eulers Principal Axis Convolution model.

As given in the Fig. 3(a), with the sample image provided as input, in this work, PCA is applied to identify principal axes of these pixels on original space and is shown in Fig. 3(b). The principal axes of the pixels are identified because most of the pixels are grouped inside a circumvolved ellipsoid. Then, the principal axes information is used to circumvolve the ellipsoid to be equidistant to the new coordinate system with the rotation invariant forms obtained as in Fig. 3(c). Finally, the eliminated region for white blood cell pixels (i.e. discarding the background and red blood cells) is shown in Fig. 3(d) is described by the following equations. $⌊ \begin{matrix} H^{'} \\ S^{'} \\ V^{'} \end{matrix} ⌋ = R [\begin{matrix} H \\ S \\ V \end{matrix}] = (\begin{matrix} R_{11} & R_{12} & R_{13} \\ R_{21} & R_{22} & R_{23} \\ R_{31} & R_{32} & R_{33} \end{matrix}) (\begin{matrix} H \\ S \\ V \end{matrix})$ (1)

Fig. 3

a) Input image b) Principal axes evaluation c) Rotation invariant form d) WBC detection.

From the Equation (1), ‘H′’, ‘S′’, ‘V′’ represent the rotated form of the original input vector image ‘H’, ‘S’ and ‘V’ respectively. A rotation matrix ‘R’ is applied to achieve a rotation invariant form of the feature. Based on the Eulers rotation theorem, the rotation matrix ‘R’ used in our work is provided as a formation of rotations about three axes, therefore denoted as a ‘3 * 3’ matrix,

$\begin{matrix} ⌊ \begin{matrix} H^{'} \\ S^{'} \\ V^{'} \end{matrix} ⌋ = (\begin{matrix} R_{11} & R_{12} & R_{13} \\ R_{21} & R_{22} & R_{23} \\ R_{31} & R_{32} & R_{33} \end{matrix}) \\ [\frac{{(H^{'} - {CA}_{H})}^{2}}{{SPA}_{H}} + \frac{{(S^{'} - {CA}_{S})}^{2}}{{SPA}_{S}} + \frac{{(V^{'} - {CA}_{V})}^{2}}{{SPA}_{V}}] \end{matrix}$ (2)

From the Equation (2), ‘CA_H’, ‘CA_S’ and ‘CA_V’ represents the central axis of the rotation matrix with ‘SPA_H’, ‘SPA_S’ and ‘SPA_V’ denotes the semi principal axis of the length ‘H’, ‘S’ and ‘V’ respectively.

3.2 Jenks optimized pooling

With the detected WBC, however, certain amount of small or negligible substance that are not nuclei of WBCs may be not completed. Certain amount of weighted sum of variances as a trainable scalar with sub-sampling, called Jenks Optimized Pooling model is designed to eliminate small objects from image and complete the nuclei, which results in a feature map of lower resolution. Figure 4 shows the block diagram of Jenks Optimized Pooling model.

Fig. 4

Block diagram of Jenks Optimized Pooling model.

As shown in the Fig. 5(a), with the detected image provided as input, a trainable scalar value is first measured using Jenks Optimization function as shown in Fig. 5(b). With the trainable scalar value, sub-sampled images are shown in Fig. 5 (c) and in Fig. 5 (d) shows the background and red blood cell eliminated image. The mathematically expression to first obtain the trainable scalar value is as shown in Equation 3. $σ_{w}^{2} (t) = w_{1} (t) σ_{1}^{2} (t) + w_{2} (t) σ_{2}^{2} (t)$ (3)

Fig. 5

a) WBC detected image b) Trainable scalar value c) sub-sampled output images d) Background and red blood cell eliminated image.

From the Equation (3), the weights ‘w₁’ and ‘w₂’ represents the probabilities of two classes (WBC and others) separated by a threshold ‘t’ with the variances of these two classes (WBC and others) represented by ‘ $σ_{1}^{2}$ ’ and ‘ $σ_{2}^{2}$ ’ respectively. The class probability ‘w₁ (t)’ and ‘w₂ (t)’ for the corresponding sample ‘s (i)’ is measured as given in Equation 4 and 5. $w_{1} (t) = \sum_{i = 0}^{t - 1} s (i)$ (4) $w_{2} (t) = \sum_{i = t}^{L - 1} s (i)$ (5)

Followed by which the average of each class (WBC and others) for the corresponding sample image ‘s (i)’ is measured using ‘μ₁ (t)’ and ‘μ₂ (t)’ and is expressed as given in Equation 6 and 7. $μ_{1} (t) = \sum_{i = 0}^{t - 1} \frac{is (i)}{w_{1} (t)}$ (6) $μ_{2} (t) = \sum_{i = t}^{L - 1} \frac{is (i)}{w_{2} (t)}$ (7)

Finally, with the average values, a trainable scalar ‘β’ is measured and mathematically written as given in Equation 8. $w_{1} μ_{1} (t) (t) + w_{2} μ_{2} (t) = β$ (8)

With the obtained trainable scalar ‘β’, pooling is performed by means of sub-sampling ‘SS’ to attain spatial invariance by minimizing the feature map resolution. This is mathematically expressed as given in Equation 9. ${SS}_{j} = tanh (β \sum_{i = 1}^{n} si + b)$ (9)

From the Equation (9), the average over the input samples are obtained and is multiplied with a trainable scalar ‘β’, adding a trainable bias ‘b’, resulting in a feature map of low resolution.

3.3 Multinomial Logistic Classification for white blood cell detection

After multiple layers of convolution and pooling, the output is finally required in the form of a class. With the aid of convolution and pooling, only features are extracted (i.e. WBCs are detected) with reduced number of parameters from the original sample images. However, fully connected layer is needed to get the outcome of image classification into the specific class. The output is then generated via fully connected layer and comparison is made for error generation. Figure 6 shows the Multinomial Logistic Classification for WBCs Detection.

Fig. 6

a) Input image b) Initial weight c) Classified results d) Classified results after weight update.

As given in the Fig. 6 initial weight is measured as in Fig. 6 (b) for which the classified results are shown in Fig. 6 (c), loss function is used in fully connected final layer to measure the average loss. Then the error is reverse propagated to update the weights and bias values. Finally, the classified result is shown in Fig. 6 (d). In this work, Multinomial Logistic Regressive value is applied that generalizes logistic regression to multi-class problem (i.e. five class WBC detection).

In Multinomial Logistic Regressive model, the dependent variable said to be categorical in nature rather than binary, i.e., ‘k’ probable outcomes are said to exist rather than just two.

$\begin{matrix} f (k, i) = α_{1, k} s_{1, i} + α_{2, k} s_{2, i} + α_{3, k} s_{3, i} + \dots + \\ α_{M, k} s_{M, i} \end{matrix}$ (10)

From the Equation (10), ‘α_1,k’ represent the regressive coefficient value for the sample ‘s_1,i’ and is said to be correlated to ‘M’ illustrative sample and the ‘kth’ outcome. $f (k, i) = α_{k} . s_{i}$ (11)

From the Equation (11), ‘α_k’ refers to the regressive coefficient associated with outcome ‘k’ and ‘s_i’ denotes the sample set associated with observation ‘i’. Here ‘k = 5’ represents five different classes. The pseudo code representation of Eulers Principal Jenks Optimized Logistic Convolutional Neural Network is given in Algorithm 1.

Algorithm 1

Eulers Principal Jenks Optimized Logistic Convolutional Neural Network

Input: Samples ‘S = s₁, s₂, …, s_n’
Output: Robust and optimized classification
1: Begin
2: For each samples ‘S’
//Convolution
3: Obtain rotated form of the original input vector image using Equations (1) and (2)
//Resultant convolved image
//Convolution and sub-sampling
4: For each classes (WBC and others)
5: Measure probabilities using equation (3)
6: Measure average using equations (6) and (7)
7: Evaluate trainable scalar using equation (8)
8: Evaluate sub-sampling using equation (9)
//Resultant pooled images
9: End for
//Fully connected layer
10: Evaluate Multinomial Logistic using equation (10)
11: Evaluate regressive coefficient associated with outcome ‘k’ using Equation (11)
12: End for
13: End

As given in the Algorithm 1 Eulers Principal Jenks Optimized Logistic Convolution Neural Network for WBCs detection and classification. Initially the sample input images are obtained from LISC dataset. First, the sample input images are convolved using Euler’s Principal Axis so as to eliminate the background and red blood cell pixels. Next, by applying Jenks Optimization function, a trainable scalar is said to be chosen that causes minimum within-class variance. With the minimization of within-class variance results more similarity of class samples are said to be evolved. Therefore, the accuracy of WBCs identification is enhanced. Finally, exact classification of WBCs into different categorizes is evolved by means of multinomial logistic regression, therefore contributing to higher accuracy and lower misclassification rate.

4 Experimental setup

The results of the JO-LCNN and existing methods namely three layered approach [8] and R-CNN [4] are discussed and compared in this section. Based on transfer learning, detection and classification of WBC is considered for the three layered approach and R-CNN. Transfer learning methods used adopted learning as a principle for similar types of data applicable for all types.

For example, the transfer learning models were designed with the assumption that solving one problem and applying it to a different related problem. However, classification results may change. On the other hand, JO-LCNN used in our work first detects and classifies into five different classes by means of CNN using MATLAB. Leukocyte Images for Segmentation and Classification (LISC) [14] was employed for fair comparison.

Hematological images are present in LISC database acquired from peripheral blood of healthy patients. LISC dataset was utilized for providing comparative evaluation on nucleus and cytoplasm detection and classification of various WBCs on hematological images. Samples were obtained from peripheral blood of 8 normal patients. 150 samples were collected in 100 microscope slides. The images comprises of 720 * 576 pixels. Experiments were conducted to measure the effectiveness of JO-LCNN in terms of ‘CT ’, ‘MR’ and ‘A’ with respect to different samples.

5 Discussion

In this section, comparative analysis is made for the proposed JO-LCNN, three layered approach [8] and R-CNN [4].

5.1 Confusion matrix evaluation

To start with, the confusion matrix obtained using JO-LCNN, [8] and [4] is evaluated. Simulations were conducted with 150 samples. Tables 1 –3 shows the confusion matrix results for JO-LCNN, three layered approach [8] and R-CNN [4].

Table 1
Confusion matrix for JO-LCNN

Neutrophils Eosinophils Basophils Lympocytes Monocytes

Neutrophils 130 5 5 6 4

Eosinophils 5 120 10 10 5

Basophils 5 5 125 10 5

Lympocytes 10 20 10 100 10

Monocytes 20 25 25 0 80

	Neutrophils	Eosinophils	Basophils	Lympocytes	Monocytes
Neutrophils	130	5	5	6	4
Eosinophils	5	120	10	10	5
Basophils	5	5	125	10	5
Lympocytes	10	20	10	100	10
Monocytes	20	25	25	0	80

Table 2

Confusion matrix for three layered approach [8]

	Neutrophils	Eosinophils	Basophils	Lympocytes	Monocytes
Neutrophils	115	20	5	5	5
Eosinophils	10	100	15	15	10
Basophils	25	10	100	10	5
Lympocytes	25	5	20	90	10
Monocytes	30	30	10	10	70

Table 3

Confusion matrix for R-CNN [2]

	Neutrophils	Eosinophils	Basophils	Lympocytes	Monocytes
Neutrophils	120	5	10	10	5
Eosinophils	15	110	5	10	10
Basophils	0	25	115	5	5
Lympocytes	30	10	5	95	10
Monocytes	60	10	10	10	60

As given in Tables 1–3, the rows represent the correct classification. For each row, the columns on the other hand denote the classification made by the proposed JO-LCNN method, three layered approach [8] and R-CNN [2] respectively. Diagonal entries represents the correct classification made and are indicated in bold. From the simulation results, it is evident that the confusion matrix for the classifier presented for each type of WBC detection presents better results using JO-LCNN. Eulers Principal Jenks Optimized Logistic Convolution Neural Network algorithm is used in confusion matrix. By applying this algorithm, the classification results are obtained by learned features. Here, no manual feature extraction is being performed, therefore reducing the error or misclassification rate. Besides, by obtaining the trainable scalar by means of Jenks Optimization function, within-class variance is said to be reduced in a significant manner. Due to this, WBC identification accuracy for five different types is said to be improved.

5.2 Performance measure of accuracy

Performance measure of accuracy determined using JO-LCNN, [8] and [2]. The classifier made a total of ‘150’ predictions (e.g., 150 patients were used as samples). From the ‘150’ different samples the classifier predicted ‘yes’, ‘105’ times and ‘no’, ‘45’ times. In reality ‘100’ patients in the sample have the class and ‘50’ patients do not. With this scenario, both the accuracy and misclassification rate is measured.

Accuracy is measured as the percentage ratio of prediction which was true and they do have the class type ‘TP’ and the prediction with no certain type of class and they don’t have the class type ‘TN’ to the total samples ‘S_i’ provided as input. This is expressed as Equation 12. $A = \sum_{i = 1}^{n} \frac{TP + TN}{S_{i}} * 100$ (12)

From (12), the accuracy rate ‘A’ is determined using the true positive rate denotes ‘TP’ and true negative rate indicates ‘TN’ respectively. Table 4 shows the confusion matrix to measure accuracy and misclassification rate.

Table 4

Confusion matrix for accuracy, misclassification rate

	Predicted (NO)	Predicted (YES)	Total samples
Actual (NO)	TN = 40, 35[1], 25[2]	FP = 10, 15[1], 25[2]	50, 50[1], 50 [2]
Actual (YES)	FN = 5, 7[1], 8[2]	TP = 95, 93[1], 92[2]	100, 100[1], 100[2]
Total samples	45, 42[1], 33[2]	105, 108 [1], 117[2]	150, 150 [1], 150[2]

From the simulation results shown in Table 4, the accuracy rate was found to be improved by applying JO-LCNN when compared to three layered approach [8] and R-CNN [2]. The improvement result of accuracy is due to the application of Jenks Optimized Pooling model. By applying this model, an optimization function is used to obtain the trainable scalar value instead of using a threshold. With this trainable scalar, the weight and bias value are updated via back propagation, therefore minimizing the error rate. With the accuracy rate is observed to be 90% using JO-LCNN, 85.33% with three layered approach and 78% with R-CNN [2].

5.3 Performance measure of misclassification rate

Misclassification rate refers to the percentage ratio of the summation of predicted with certain type of class but done belong to that particular type of class ‘FP’ and did not predict class with certain type but they actually do have that particular type of class ‘FN’ to the samples ‘S_i’ provided as input. ‘MR’ is measured as follows, $MR = \sum_{i = 1}^{n} \frac{FP + FN}{S_{i}} * 100$ (13)

In Equation (13), misclassification rate ‘MR’ is computed in terms of percentage (%).

From the simulation results, it is evident that the misclassification rate is reduced using the JO-LCNN method when compared with the three layered approach [8] and R-CNN [2]. Here, the false positive rate and false negative rate was observed to be ‘10’ and ‘5’ when compared to [8] that had ‘15’, ‘7’ and [2] that had ‘25’ and ‘8’ respectively for ‘150’ different samples. From this result it is inferred that the misclassification rate is ‘10% ’ using JO-LCNN, ‘14.66% ’ using [8] and ‘22% ’ using [2]. Multinomial Logistic Regressive model is used to reduce the misclassification rate. Here, average loss is measured, followed by which error is then back propagated to update the weights and bias values. Due to this, the misclassification is reduced using JO-LCNN when compared with [8] and [2].

5.4 Performance measure of classification time

Finally, the classification time is used as a measure to evaluate the effectiveness of the WBC detection and classification. In other words, the classification time is determined as time utilized in classifying WBC into five different types. The formula for estimating ‘CT’ is given as follows. $CT = \sum_{i = 1}^{n} S_{i} * Time [f (k, i)]$ (14)

In Equation (14), classification time ‘CT’ is computed based on samples provided as input ‘S_i’ and time utilized in obtaining ‘k’ probable outcomes. ‘CT’ is computed in the unit of milliseconds (ms).

Table 5 shows the classification time involved in classifying 150 different samples carried out at different time intervals from LISC database.

Table 5

Classification time for JO-LCNN, three layered approach [8] and R-CNN [2]

Number of samples	Classification time (ms)
	JO-LCNN	Three layered approach	R-CNN
15	2.025	2.625	3.075
30	3.352	4.635	5.315
45	4.155	7.235	9.245
60	6.025	10.455	14.555
75	8.315	13.325	18.135
90	9.535	16.135	21.455
105	13.155	19.325	25.325
120	15.825	21.455	31.552
135	18.135	24.355	35.352
150	25.555	28.155	41.255

Table 5 depicts the classification time results obtained from three methods taking ten test sets (i.e. from 15 to 150 samples) and shows the average over the ten performance estimates.

Figure 7 demonstrates the ‘CT’ with respect to 150 different samples for three different methods, JO-LCNN, three layered approach [8] and R-CNN [2]. x axis denoting the sample images and y axis indicating the classification time, increasing the samples also causes an increase in the WBC detection time and therefore the WBC classification time also. But, comparatively, the classification time is found to be lesser using JO-LCNN than [8] and [2]. This is because of certain changes made in the traditional CNN method. First, images were convolved using Eulers principal axis is to obtain rotational invariant of features. Followed by which pooling was performed by means of sub-sampling that used trainable scalar values via Jenks Optimization, therefore reducing dimensionality. Only the optimized features were further utilized and classified into five different types of WBC by means of logistic regressive function. With this, the classification time was said to be reduced using JO-LCNN by 31% and 48% than compared to existing [8] and [2].

Fig. 7

Graphical representation of classification time.

6 Conclusion

An efficient algorithm called JO-LCNN is developed for automatic detection and classification of WBCs. JO-LCNN considering the entire process as a circumvolved ellipsoid problem. The proposed method uses the semi principal axis of the length as candidate ellipsoids of images. A rotation matrix permits to correctly determine the resemblance of a candidate circumvolved ellipsoid through an actual WBC on the sample. The set of feature map of low resolutions are examined with the help of Jenks Optimization model thereby robust into original WBC on the image. The method introduces a Multinomial Logistic Regression that can effectively classify leukocytes. The experimental result of research work is analyzed by comparing JO-LCNN method with two existing methods such as three layered approach and R-CNN based on accuracy, misclassification rate and classification time. The performance shows that the JO-LCNN method improves the results of accuracy with minimum classification time and misclassification error when compared to state-of-art methods.

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