1. Introduction

Leukemia is a kind of cancer of the blood and bone marrow with subsequent medical implications when normal production of blood cells is compromised, resulting in impaired immunity, increased infections, anemia, and the possibility of internal bleeding. Prompt diagnosis is always a key component to successful therapy; however, methods of examination, such as blood smear analysis and biopsy of the bone marrow, are often quite time-consuming and labor-intensive as well as with possibilities of errors in human calculations. Other techniques also use experienced technologists that can interfere and are not convenient for screening purposes or surveillance procedures. Consequently, there exists a demand at present for techniques that are quick, accurate, and more accessible than those currently applied for early diagnostics of leukemia cases across the globe.

Medical image processing research for leukemia treatment is crucial because earlier diagnosis and better monitoring of all the disease stages are possible. Given that image processing can be employed to recognize leukemia cells and categorize them, diagnosis can be made much more efficient and available in regions without access to many specialists. Image processing also helps monitor disease stages and modify the treatment as soon as possible, which is essential in chronic cases. It may also help to decrease the number of invasive solutions, which can be done by providing non-invasive solutions to diagnose blood and bone marrow samples. In general, the advancement of medical image processing in leukemia benefits from advanced diagnostics, better treatment, and, of course, patients’ life expectancy.

Human blood includes a variety of white cell types, as shown in (Fig 1), which produces several diseases, including Leukemia. Leukemia is a type of blood cancer that arises due to the rapid increase of immature WBCs. The immature white blood cells kill other cells, causing diseases.

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Fig 1. Types of White Blood Cell.

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The severity of the disease depends on several factors, including the patient’s age and health, genetics, the kind of Leukemia (chronic or acute), and the time of diagnosis. Acute Leukemias like ALL and AML, for example, can quickly develop into life-threatening diseases in a matter of weeks if left untreated. Chronic Leukemias, CLL, and CML, on the other hand, have a more subtle onset, and symptoms appear years later. While older individuals or those with additional conditions may be at greater risk, younger people have the most significant prognosis. Genetic alterations also play a role in the disease’s stepwise progression; some, like the Philadelphia chromosome mutation linked to CML, respond to focused treatment, whereas CLL and CML, being chronic leukemias, are more insidious in basing, and patients develop symptoms after several years. Younger patients have the best prognosis, whereas older patients (age-wise) or patients with other illnesses may have more risks. Stepwise progression of the disease also involves genetic mutations; some respond to targeted treatment, like the Philadelphia chromosomal mutation found in CML, whereas other mutations may predispose patients to a poor outcome.

However, in every case, the body’s ability to produce blood cells is impaired due to a propensity to Leukemia, eventually compromising the person’s health and quality of life by causing weakness, infections, and bleeding issues.

In the late 1990s, leukemia was diagnosed using a time-consuming and laborious laboratory test, and then automated techniques were developed [1]. The details of existing manual and clinical methods for diagnosing malignant WBSs are given in the following.

• Patient Medical History
• Cytogenetic Analysis
• Blood Cell Counting
• Manual Microscopic blood smear image analysis
• Immunohistochemestry of Blood Sample
• Biopsy
• Catheter Drainage
• Percutaneous Aspiration
• Long Distance Inverse Polymerase Chain Reaction
• Molecular Cytogenetics

Leukemia malignancy is diagnosed using various techniques, including patient medical records that help to reveal risk factors and symptoms. Cytogenetic analysis has been used to detect the presence of chromosomal abnormalities in leukemia. A blood cell counter gives a preliminary count of WBCs, while a cell differential count using manual microscopic blood smear analysis is a visual check of blood samples under a microscope. Immunohistochemistry is employed to detect specific markers on blood cells, and biopsy gives the chance to take bone marrow or tissue samples for direct examination. Consequently, other non-invasive techniques, such as catheter drainage and percutaneous aspiration, are also used to get samples for analysis. Long-range PCR (LRCR-PCR) can be a method of specific genetic mutation detection related to leukemia, and molecular cytogenetics can be a tool that studies those alterations at the molecular level. In contrast to the automated methods, the manual and clinical ones still significantly provide extensive insight into the disease.

The white blood cell ratio in the human body is 1000:1. The ratio indicates 1000 red blood cells for one white blood cell [2]. Therefore, leukemia illnesses will develop if the white blood cell count rises clearly and severely. If immature white blood cells increase, they will start destroying other cells. The normal red and white blood cells are shown in (Fig 2).

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Fig 2. Normal Red and White Blood Cell.

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Various leukemia subtypes can result in multiple issues. Early on, you might not see any symptoms. The condition cannot be diagnosed solely by its signs and symptoms, but it can serve as indicators for you and your doctor to identify the issue as soon as feasible. If you experience symptoms, these could include Poor blood clotting, Red spots on the skin, Frequent infections, and Anemia. Leukemia symptoms include shortness of breath, night sweats, weakness or exhaustion, fever or chills, discomfort in your bones or joints, weight loss, and swollen lymph nodes or organs like your spleen. Leukemia can also manifest as symptoms in organs where the cancer cells have already invaded the tissue. For instance, headaches, nausea, vomiting, confusion, and seizures may result from cancer spreading to the central nervous system. In addition, leukemia can spread to your lungs, digestive system, heart, and kidneys, among other body organs.

The main objective is to segment all White blood cells, which can be further used to identify immature cells. It can also be useful in any emergency, and there might be a technique that quickly segments the white blood cells for different diseases. The proposed method can also be integrated with different smart health Apps in pandemic situations [3]. The suggested approach distinguishes between other blood cell types as well. Furthermore, it is crucial to do an analytical study on the ability to differentiate between various cell types, classify them as undeveloped cells, and then utilize that information to identify leukemia. The immature blasts of lymphoid and myeloid cells result in Lymphocytic and Myeloblastic conditions, respectively. Medical image analysis is now a trend to efficiently diagnose different types of diseases from blood in nearly real-time, either using optimized machine learning or deep learning techniques [4,5].

Segmentation is the division of an image into different sections based on certain shared characteristics. In medical imaging, segmentation helps examine anatomical structures, diagnose patients, formulate treatment plans, and identify malignancies and other conditions [6].

This work presents a novel deep-learning method for pre-segmenting cells from the blood through the integration of UNet++ [7]. A marker-based watershed (MW) approach is used to improve the segmentation of WBCs. This research study’s primary contributions are:

• A novel segmentation technique, which is the combination of U-Net++, ResNet, Neural Ordinary Differential Equation, and Marker Watershed.
• The MW algorithm produces the concluding segmented image of WBCs using the probabilistic grayscale map.

2. Literature

Many segmentation techniques have been reported for the identification and segmentation of blood cells and vessels [8–11]. To segment peripheral blood smears, Using the (KTE) Teager Energy operator is advised by Kumar et al. [12]. Here, the white blood cell (WBC) cytoplasm is separated using a selective mathematical operator, and a cell’s nucleus is segmented using edges, which (KTE) operator efficiently recognizes.

Piuri and Scotti examine the effectiveness of edge determination and contrast stretching for the automated identification of leucocytes [13]. Coupling contrast stretching, a clever edge detector, and a selected morphological operator allow for the detection of leucocyte membranes and nuclei. Issues related to image collection criteria and smear discoloration throughout the process of creating blood smears could potentially hinder the effectiveness of any previously stated segmentations. In aberrant blood cells, the round geometry hypothesis for cell segmentation is inappropriate [14].

Researchers have recently created two categories of different blood cell segmentation approaches. The majority of current algorithms segment data using both conventional and deep learning-based methodologies. These methods are intended to improve the handling of overlapping and clustered cells. Graph theory [15,16], level sets [17,18], the watershed method [19,20], and the region-growing approach are examples of traditional segmentation techniques. Convolutional neural networks, U-Net, U-Net++, and fully convolutional networks are the main types of deep learning methods. Significant for irregularly shaped and sized cells. An approach for segmenting clustered cells in classical cell images developed by Wang et al. [21] combines mathematical, morphology, and graph theory. The algorithm is simple, but the segmentation impact could be more optimal for irregularly shaped and sized cells, and the mistake rate is high.

To distinguish overlapping cells, the authors of the research [22] combined the region-expanding technique with color space transformation. This method’s mean pixel accuracy is excellent. However, the accuracy decreases when there are no visible internal borders among the clustered cells. Miao et al. [23] described a marker-controlled watershed technique to segment RBCs; we apply this approach to WBCs instead. After removing the binary images of the cells, foreground and background markers were first acquired. The watershed approach was then applied to the regenerated gradient topographic map to obtain segmentation results. Although the segmentation technique is simple to use and inexpensive to compute, its accuracy may be impacted by low-quality images.

Due to noise, performance, and other factors, certain traditional segmentation approaches cannot achieve high segmentation robustness. Compared to conventional image segmentation, deep learning methods have a higher segmentation accuracy because they use a large number of samples to learn the characteristics of cell images. Consequently, deep learning algorithms can be used in conjunction with the traditional segmentation technique to achieve semantic segmentation [24–27]. A method for segmenting partially overlapping cells that coupled U-Net was developed by Huang et al. [27]. This method extracted the cell contour using an improved level set energy function and employed U-Net to identify the cytoplasm and nucleus. This function increased segmentation accuracy by first incorporating a shape and a distance map. Kowal et al. [28] proposed integrating CNN with a seeded watershed approach to segment cell nuclei. This method uses a CNN classifier to pre-segment the cell nuclei. A seeded watershed is used to manage overlapping nuclei. Despite the high computational complexity, their results outperform conventional watershed approaches.

In the paper [29] the authors segmentized images with the presence of noise. They used power mean in their approach to segmentize different types of images, including medical images. They claimed that the power mean function is robust in the presence of an outlier. They also used the fuzzy membership function and power means to strengthen the segmented process further. Another recent research work has been done by Makem et al. [30]. They segmentize the nuclei of WBC and can be further used for different types of diseases. Their proposed system uses the mean method to smooth the input image. They enhanced the texture of images using arithmetic operations with the fusion of Fourier transformation. The nuclei of WBCs are extracted using the k-mean technique. They claimed 97.35% accuracy on CellaVision and 93.48% ALL-IDB2 database. Resendiz et al. [31] use U-Net for WBC segmentation and ResNet50 for classification. Their system achieves a segmentation accuracy of 91% and a classification accuracy of 99.9%. Wei Liu [32] et al. investigate deep and traditional Machen learning models for bacterial pathogens diagnoses. They claimed that deep learning techniques, i.e., (CNN) are better than conventional machine learning techniques in bacteria detection. After detailed experimentation, they justify their claim by obtaining accuracies. According to their proposed architected, 99.6%, 98.9%, and 96.4% accuracy are achieved by CNN, SVM, and Random Forest, respectively.

Shoaib et al. [33] focus on automated segmenting of the left ventricle (LV) from 2D echocardiographic images, an essential task in medical imaging for diagnosing cardiovascular diseases. The performance of three advanced architectures of CNN, Fully Convolutional Network (FCN), SegNet, and Mask R-CNN for segmenting the LV are evaluated in this study. A key finding of this paper is the development of echocardiography images. In addition, the performance of each model in terms of segmentation is evaluated using several evaluation metrics: pixel accuracy, precision, recall, specificity, Jaccard index, and Dice similarity coefficient (DSC). They claimed that Mask R-CNN consistently outperformed SegNet and FCN across all metrics among the three models. The Mask R-CNN model showed a high DSC of 92.21%, a Jaccard index of 85.55%, and excellent values for other measures such as precision (93.15%) and recall (96.81%) while being trained with 4,000 images. However, the model’s performance becomes stable when the training data exceeds 4,000 images. The paper [34] explores the application of deep learning in interpreting SPECT scans, specifically for Parkinson’s Disease (PD), using DaTscan imaging. This research demonstrates the ability of deep understanding, transfer learning, and soft attention mapping to differentiate between normal versus PD cohorts with DaTscan SPECT images. The approach is not feasible for analyzing the motor outcomes of such scans. The paper employs DenseNet-121 as the main model with a soft attention block, achieving 99% AUC and 99.2% accuracy. This is greater than other CNN models, such as Xception and ResNet. The paper uses soft attention mapping rather than Grad-CAM because of its cost-effectiveness and the ability to point out the relevant features, even with a small sample size. The approach is semi-automatic and not fully automated; therefore, an even more significant 3D CNN could better capture features of the whole scan volume. Future studies should develop an end-to-end 3D CNN model for more effective feature extraction from 3D SPECT data while increasing the number of samples in the database for robust outcomes. The research paper [35] introduces a new federated epistasis detection framework, FedED-SegNAS, to handle the challenges of detecting disease-associated genetic variants in a privacy-preserving manner with improved communication efficiency in multi-institutional genome data sharing. This framework uses FL to allow several institutions to collectively analyze genomic data without having to share the data directly. Sequence perturbation privacy-preserving is used to ensure privacy. It protects the data during the parameter transfer by grouping and randomly perturbing parameters, making it hard for attackers to link parameters to specific groups. Fuzzy logic is incorporated into convolutional neural networks (CNNs) to improve the interpretability of deep learning models. The model can deal with the ambiguity of genomic data, maintaining high interpretability and accuracy. The framework uses a NAS method based on PSO to automatically search for the optimal neural network architecture at different stages of federated learning. This optimization reduces the communication cost between institutions and improves communication efficiency.

3. Proposed methodology

This section introduces UNet++ and the marker watershed-based approach to segmenting WBC images. (Fig 1) depicts the proposed framework conceptual structure. The WBC images are segmented using the deep learning network UNet++, and the model is trained using the labeled training set. The image is segmented using the learned model to create the probability grayscale image. The final segmentation findings of WBSs are achieved after further optimizing the pre-segmentation results using an MW method, as given in (Fig 3).

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Fig 3. The Proposed Framework.

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The proposed system uses ODE for error reduction. An ODE is a differential equation involving the derivative of one or more dependent variables with respect to a single independent variable.

(1)

In equation (1), is an independent variable, is an unknown function (dependent variable), and the derivative of the anonymous function is referred to as an ordinary differential equation (ODE). The left-hand side of equation (1) is the derivative of with respect to while the right-hand side of equation (1), is a function of g and k. It is more typical in engineering to solve the equation numerically. One simply needs to approach the unknown value gradually with a known value rather than trying to solve the general solution of the anonymous function. Euler’s method is a common technique for resolving the numerical value of differential equations, which is given in equation (2).

(2)

In equation (2) is a small step in . The small change or step causes changes in . Furthermore, it reduces the error in each convolution. As the process progresses, errors are produced at every step, mounted to solve differential equations, and the ODE solver is used. It travels with a defined step size as opposed to the Euler technique. It chooses an acceptable step size based on an established error tolerance to approach an unknowable value.

A deep learning technique called residual network (ResNet) is used in the proposed framework. The ResNet has two types of connection, i.e., residual and direct connection. The generic structure of ResNet having a dense layer is given in (Fig 4).

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Fig 4. Generic structure of ResNet.

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Fig 5 shows the residual block architecture, and a residual network (ResNet) [36] is a specific type of NODE.

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Fig 5. Residual block structure.

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(3)

Here, the resultant vector is from the layer the network parameters of the layer , and is the layer parameterized neural network (NN). In (3), in ResNet comprises convolutional processes. The ResNet can be observed as an Euler discretization if . As diminutions, a steady convergence with more layers added in smaller increments is the result. This limit state transforms into an ODE designated by the neural network, as shown in (Fig 6).

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Fig 6. ODE block Structure.

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(4)

An ODE solver may solve a continuous neural network in which the forward pass operations are very straightforward, and the ODE solver backpropagation, whose precise function can be found in [7].

B. UNET++

In a UNet++ architecture, the suggested pre-segmentation model takes advantage of the ODE solver, as shown in (Fig 7), which displays the model in detail. There are two primary ways to differentiate the proposed technique from traditional U-Net++. First, the shallow feature maps are extracted using convolutional and ODE blocks in the encoder stage. Another difference is the addition of several convolutional layers by the U-Net++ and momentary connections between the encoder and decoder layers. Long links are utilized throughout the U-Net feature extraction process to combine surface features calculated by the encoder, while the decoder module extracts deep features. U-Net++ uses skip connections in the proposed technique to lessen the semantic difference between deep and surface features. It is challenging for U-Net to combine superficial feature images and deep feature images. Using the skip connections technique in dense convolutional blocks of UNet++, which U-Net++ influenced, fills in the semantic gap between the encoder and decoder feature maps. Like traditional U-Net++, the proposed technique employs deep supervision and augments each output node with a convolutional layer and a sigmoid function. The sigmoid function transfers the output value to , with a value range of , as indicated in equation .

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Fig 7. Architecture of the proposed technique.

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(5)

The degree of discrepancy between the model’s true values and predictions is measured using the loss function. The more closely the predicted value of the model matches the actual value, and the more robust the model is, the smaller the loss value of the function is during the neural network training process. The challenge of white blood cell segmentation is binary. As a result, we use binary cross-entropy loss, which is given below.

(6)

In (6) stands for the total number of pixels in the image, for the training label, which indicates whether pixel is a white blood cell or not, and p() for the likelihood that labels will be produced.

4. Experimental results

A. Results

The effectiveness and robustness of the recommended method are empirically assessed and proven using a large number of 256 × 256-pixel images. All of the Images can be found in the Leukemia dataset, i.e., ALL_IDB1 and ALL_IDB2. A total of 100 images were picked from the datasets and divided into two sections, i.e., training and validation sets, with a ratio of 80% and 20%, respectively. The primary research work is the semantic segmentation of white blood cells, but classification and validation are also performed to check whether the segmentation is useful. The proposed method comprises a deep learning architecture called ResNet, in which Adam optimizer is used for optimization, and the learning rate is set to 1e-. (Fig 8) exhibits the training loss, training accuracy, validation loss, and validation accuracy for each epoch during the training process. The proposed model is executed up to epochs on the training and validation set. (Fig 8) (a) shows the accuracy of training and validation, which is quite remarkable. (Fig 8) (b) shows training and validation losses up to 30 epochs.

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Fig8. (a) The accuracy of the training and validation set (b) The losses in the training and validation set.

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Three examples of WBC pre-segmentation using the proposed technique are shown in (Fig 9). The original image is shown in (Fig 9a) the label image is shown in (Fig 9b) and the grayscale image obtained from pre-segmentation is shown in (Fig 9c). The first step segmentation result is further segmentized using the MW algorithm, as shown in (Fig 10) where (Fig 10a) displays the foreground marker image, and (Fig 10b) displays the segmented WBCs.

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Fig 9. (a) Orignal Image (b) Label Images (c) Pre-segmentation using Unet++.

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Fig 10. (a)^‌‌ Foreground Marker (b) Segmented White Blood Cells.

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B. Experimental analysis

(Fig 11) shows the various conditions of blood smear images during segmentation. The original images from the dataset are shown in (Fig 11a) the label image is shown in (Fig 11b) and the segmentation image is showning (Fig 11e) using the fusion of UNet++, ODE, and MW algorithm.

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FIG 11. (a) Original ima ge (b) Label image (c) Final Result.

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(Fig 11) shows that the proposed method does an excellent job of extracting the contour of erythrocytes, but it significantly under-segments areas like clustering and overlapping WBCs. The MW algorithm may effectively tackle the erythrocytes problem, but it frequently results in missing extraction due to its sensitivity to weak edges and other interference factors. The Proposed technique can extract the majority of erythrocytes with various sizes, clusterings, and overlaps by combining the benefits of the two approaches, i.e., UNet ++ and MW. The erythrocytes hold a more consistent structure than WBCs, which display a more distinct appearance by most likely taking the form of tapered or irregular shapes. Additionally, there is a tendency for them to lump together as well instead of existing separately. The new approach that has been proposed in this paper is able to detect overlapping or clustered WBCs and regard them as a single object in the image. Though this technique is used specifically for WBC cell segmentation, with slight modifications, it can be used for red blood cell detection and diseases associated with red blood cells. The experimental findings are studied qualitatively and quantitatively to assess the proposed technique’s segmentation results further.

The segmentation accuracy of the proposed technique for WBCs is computed using various evaluation methods. This study has evaluated the segmentation outcomes of three methods using DSM, MPA, and MIoU. The DSM is a dice similarity measure, MPA is mean pixel accuracy, and MIoU is the mean intersection over union (MIoU). Measurements are based on the confusion matrix, as indicated in Table 1.

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Table 1. Confusion matrix.

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DSM is a predetermined similarity metric frequently used to compare two samples. Its value might be 0,1 or between 0 and 1. When the DSM value approaches 1, the performance increases. The DCM value near 1 indicates better segmentation outcomes. The Dice similarity measure (DSM) is given in (7).

(7)

Pixel accuracy (PA) is another technique used for performance measurement. It is the percentage of pixels correctly identified as erythrocytes and the number of pixels correctly identified as non-erythrocytes concerning the total number of pixels. In short, PA is the number of correctly predicted pixels as a percentage of the total number of pixels, as given in (8).

(8)

The proposed system is also evaluated using mean pixel accuracy (MPA) (9). Mean pixel accuracy across all categories relates to the average pixel accuracy for white and non-red cells.

(9)

One recurrent metric used in semantic segmentation is intersection over union (IU). It refers to the intersection and union ratio between a class of models’ true and predicted values, which is given in (10).

(10)

The average of the IU of erythrocytes and nonerythrocytes given in (11) is used as the mean value for each category of MIU.

(11)

Table 2 demonstrates the quantitative and qualitative findings from the same dataset, and (Fig 12) is the graphical representation (box plots) for the MIoU, DSC, and MPA. The outcomes demonstrate that this method for WBC segmentation is more efficient than the other available techniques.

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Table 2. Quantitative results of three algorithms.

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Fig 12. The box-plots of three measure segmentation accuracy.

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Several practical approaches can be considered to ensure the successful integration of the semantic segmentation system for white blood cell (WBC) smear images with existing hospital databases, digital pathology platforms, and automated microscopy equipment. These integration methods should aim to minimize disruption to current workflows and optimize clinical processes. Below are proposed ways to achieve this integration:

5. Conclusion

This work proposes semantic segmentation of white blood cells based on UNet++, a DensNet-based technique, and the MW algorithm to address the issues of WBC clustering and overlapping With the integration of ODE (Orderly Differential Equation). The DensNet-based UNet++ network is specifically built to extract image features using an encoder concept. The skip connections in the proposed technique close the semantic gap between surface and deep feature maps. The features from the encoder are concatenated with the input from the corresponding skip connection in the decoder part. The ODE is embedded after convolution to calculate small values to reduce errors and prevent the model from propagating big values as errors. The experimental results demonstrate that compared to the MW method and the UNet++ algorithm separately, the UNet++ and WM, in combination with the integration of ODE, are efficient in segmentizing WBC. The proposed technique achieves segmentation accuracy of on DSM, on MPA, and on MIU, which are quite high than the existing techniques given in the experimentation section. Furthermore, the proposed technique efficiently segmentized the immature, blasted, and overlapping WBCs. Even though the results of the proposed technique are encouraging, they can be enhanced using some other deep learning technique. The limitation of the proposed technique in its current state is that it is computationally complex. The next step is to make the system lightweight for use in low-resource devices, i.e., smartphones. The proposed technique can be used for decision-making in the digital laboratory. Soon, research will also be conducted to develop a technique suitable for Mobile Digital laboratories.

Acknowledgments

The authors would like to acknowledge the support of Prince Sultan University for paying the Article Processing Charges of this publication. This article is derived from a research grant funded by the Research, Development, and Innovation Authority (RDIA)-Kingdom of Saudi Arabia-with grant number (13292-psu-2023-PSNU-R-3-1-EF-).