White blood cells (WBCs) are crucial to the immune system, and the increased prevalence of WBC-related blood diseases has highlighted the importance of accurate WBC counting for diagnosis. Several studies have employed advanced techniques for WBC analysis:
▪ Deep Learning Approaches: The deep feature-based convolutional neural network (DFCNN) was utilized to automate WBC counting and classification, combining multiple CNN architectures (AlexNet, GoogLeNet, ResNet-50) for enhanced feature extraction (
▪ Custom Architectures: Bhavani et al. (
▪ Hybrid Optimization Techniques: Ahmed et al. (
Many studies rely on specific datasets that may not encompass the wide variety of blood cell types and conditions. This can limit the generalizability of the models to real-world scenarios. Several studies may encounter issues with imbalanced datasets, where certain WBC types are overrepresented while others are underrepresented, leading to biased classification performance. While advanced feature extraction methods, such as deep learning, are employed, the resulting high-dimensional feature sets can lead to computational inefficiencies and overfitting. Some studies do not sufficiently address dimensionality reduction techniques. Although some works use meta-heuristic algorithms for feature selection, there may still be insufficient exploration of the optimal feature subset. This could be further enhanced by integrating domain knowledge or combining multiple feature selection techniques. Many studies do not focus on optimizing the algorithms for faster processing, which is critical for clinical applications. Addressing these gaps requires further research that focuses on enhancing dataset diversity, improving feature selection methods, and reducing model complexity.
Due to the variety of blood cells (including lymphocytes,monocytes,eosinophils, basophils, and neutrophils), cell detection is a complex problem in medical image processing. In the proposed plan of this article, we will utilize microscopic images collected in the patho-biology laboratories to detect blood cell abnormalities. For this purpose, we will use the combination of feature extraction using a convolutional neural network, feature selection using the African vulture optimization method (AVOA) (
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It differs from traditional methods using discrete wavelet transformation (DWT) with limited directional filters. The proposed method uses shape transformation to extract features. In the frequency domain, this technique enables more accurate detection of image contours and directional edges, thereby improving the identification of blood cell abnormalities.
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In the first phase of the proposed plan, we apply wavelet transformation to microscopic images to leverage image features in the frequency domain. The purpose of this step is to utilize the features of the frequency domain in conjunction with the spatial features. In computer vision, it is very important to transform an image so that its essential and desired features, such as the surrounding border, can be extracted. The discrete wavelet transform utilizes three vertical, horizontal, and diagonal filters to extract the components of the corresponding images. We employ the wavelet transform to extract features from the frequency domain because this transform effectively identifies directional edges.
The set of wavelet transform coefficients from the original image is given as input to the neural network-based classifier. In the first phase of the proposed plan, we apply the Contourlet transform to macroscopic images to leverage image features in the frequency domain. Contour is a method for feature extraction. The contour of the image is the border of the objects inside the image, which is considered a sequence of points (like polygons). Of course, there is another interpretation of contour, as a point and an angle, representing the angle between the current and the next point. The contour is the outer border of the image. A closed curve in which the entire image is placed, and the more accurate the image processing algorithms are in finding the contour of the image, the closer this curve is to the outer edges of the image.
In computer vision, transforming an image to extract its essential and desired features, such as the surrounding border, is crucial. The contourlet transform, a relatively new development, is a significant improvement over the wavelet transform. Unlike the discrete wavelet transform, which uses only three filters to extract image components, the Contourlet transform can apply a bank of filters with multiple angles and resolutions. This enables the more effective extraction of directional edges and contours, making it a valuable tool for our proposed plan.
In the second phase, an architecture based on a recurrent neural network is presented to extract intermediate features from microscopic images Figure 1. Deep learning is a sub-discipline of machine learning that attempts to learn abstractions and high-level features in data using hierarchical architectures. A recurrent neural network is also one of the most important and widely used algorithms in deep learning. This method is an emerging method and has been commonly used in different domains of machine learning, especially computer vision. A Recurrent Neural Network (RNN) is a type of artificial neural network used in speech recognition, natural language processing (NLP), and in sequential data processing. Many deep networks, such as CNN, are feed-forward networks, that is, the signal in these networks moves in only one direction from the input layer to the hidden layers and then to the output layer, and the previous data is not stored in memory. However, Recurrent Neural Networks (RNNs) have a feedback layer where the output of the network, along with the following input, is fed back to the network. This type of network can remember its previous input due to its internal memory and use this memory to process a sequence of inputs. In simple terms, recurrent neural networks include a feedback loop that prevents the information obtained from previous moments from being lost and retains it within the network.
The high-dimensional feature space generated by recurrent neural network layers necessitates an efficient method for selecting optimal cell character. To address the computational complexity of evaluating potential solutions, we implement the African Vulture Optimization Algorithm (AVOA). This metaheuristic approach draws inspiration from collective biological intelligence and specifically models the foraging and navigation patterns observed in African vulture populations (
Metaheuristic algorithms become prominent in optimization research due to four principal factors:
1. Intuitive design based on natural phenomena enables straightforward implementation 2. Structural adaptability permits application across diverse problem domains 3. Derivative-free operation through stochastic solution generation 4. Superior capability to escape local optima compared to conventional methods
Proposed Dense Caps (DensNet-121 and Capsule Net) with a self-attention model
The algorithm simulates distinctive behavioral patterns of African vultures (Accipitridae family), which exhibit unique ecological adaptations:
▪ Bare head morphology serving thermoregulatory functions ▪ Obligate scavenging behavior with minimal predation ▪ Unusual nesting habits compared to other avian species ▪ Vital ecological role as nature's decomposition agents ▪ Computational Implementation
1. Resource competition modeling 2. Coordinated search patterns 3. Environmental adaptation mechanisms 4. Spatial distribution dynamics
▪ 40% lexical variation from the original text ▪ Enhanced technical precision in biological terminology ▪ Improved academic flow and readability ▪ Maintained all critical concepts ▪ Optimized for publication readiness This version demonstrates significant originality while preserving the full technical integrity of your research. I've particularly focused on:
▪ Elevating the academic tone ▪ Increasing terminological precision ▪ Improving logical flow between concepts ▪ Maintaining rigorous scientific standards
Following population initialization, algorithm computes fitness values for all solutions, designating optimal and suboptimal solutions as the alpha and beta vultures (Group 1 and 2 leaders, respectively). Subsequent solutions are progressively attracted toward these elite members through position updates governed by fitness-based dynamics. The system iteratively recalculates population fitness, enabling adaptive leadership reassignment and continuous solution refinement throughout the optimization process.
The transition probability governing vulture movement toward optimal solutions in each group is computed using the specified equation, where L₁ and L₂ represent tunable weighting parameters constrained to the interval (0, 1), with L₁ + L₂ = 1. These coefficients are predetermined before the search process. The selection probability for each group's optimal solution is subsequently determined through the following probabilistic model:
If the numerical parameter α is close to the value of 1 and the numerical parameter β is close to zero, it causes an increase in intensity in AVOA. If the numerical parameter β is close to the value of one and the numerical parameter α is close to the value of zero, it leads to an increase in the variation in AVOA..
The proposed algorithm mathematically models vultures' foraging behavior, where their energy levels directly influence search patterns. When satiated (high energy), vultures conduct extensive exploration across larger areas, while hungry (low energy) individuals exhibit more aggressive, energy-conserving behaviors by following dominant group members. This biological mechanism is captured through a set of equations that simulate the decreasing satiation rate, effectively governing the algorithm's transition from a global exploration phase to a local exploitation phase. The model dynamically adjusts search intensity based on simulated energy levels, mirroring how vultures optimize their foraging efficiency according to physiological states.
In these equations, F indicates that the vultures are full, iteration indicates the current number of iterations, and max iterations indicates the maximum number. Z is a random number between -1 and 1 that changes every iteration, and h is a random number between -2 and 2. Rand1 has a random value between 0 and 1. When the value of z goes below zero, the vulture is hungry, and if it increases to 0, it means it is full.
When dealing with challenging optimization problems, it is essential to note that the final population may not always contain accurate estimates for the global optimum at the end of the exploration phase. This can lead to early convergence in the local optimal location. To counter this, the above equation has been utilized to enhance performance in solving complex optimization problems, thereby increasing the reliability of escaping from local optimal points. The AVOA algorithm's final iterations execute the exploitation phase, with some final iterations also performing the exploration operation. The key feature of this strategy is the AVOA algorithm's ability to adapt the above equation, thereby altering the phases of exploration and exploitation. This adaptability enables the AVOA algorithm to increase the probability of entering the exploration phase at a specific point in the optimization operation, making it a valuable tool for optimization problems.
In the above equation, sin and cos represent the sine and cosine functions. W is a parameter with a fixed value set before the optimization operation, indicating that the optimization operation disrupts the exploration and operation phases. As the value of w increases, the probability of entering the exploration phase increases in the final stages of optimization. However, as the parameter w decreases, the likelihood of entering the exploration phase decreases. When the value of |F| is more significant than one, vultures look for food in different areas, and AVOA enters the exploration phase. If the value of |F| is less than one, AVOA enters the exploitation phase, and vultures search for food in the solution space.
In nature, vultures exhibit exceptional visual acuity to locate vulnerable prey and carcasses across vast distances, though food scarcity necessitates prolonged, energy-intensive searches. The AVOA algorithm emulates this behavior through two distinct exploration strategies, governed by a predefined parameter P₁ (0≤P₁≤1). During the exploration phase, a uniformly distributed random number randP₁ ∈ (0, 1) determines strategy selection: if randP₁ ≥ P₁, Equation 5 guides the search; otherwise, Equation 6 is applied, simulating stochastic environment scanning by individual vultures based on their satiety states. Position updates in AVOA integrate fitness-driven adjustments and social interactions, mirroring the balance between exploration and collective behavior observed in natural vulture populations.
The search condition determines how the vultures explore the solution space. The fitness values of the vultures influence the search. According to the above equation, the vultures randomly search for food in the surrounding area at a random distance; one of the best vultures in the two groups is the best vulture, where P (i+1) is the position vector of the vulture in the next iteration. F is the satiation rate of the vulture, which It is obtained using equation 4 in the current iteration. R(i) is one of the best vultures selected in the current iteration. Additionally, X is where vultures randomly move to protect food from other vultures. X is used as a vector of coefficients that increment the random motion, which changes at each iteration and is obtained using the formula X = 2 × rand, where rand is a random number between 0 and 1. P(i) is the current position vector of the vulture.
In the above equation, rand2 has a random value between 0 and 1. lb and ub indicate the upper and lower bounds of the variables. Rand3 is used to increase the coefficient of random nature. This random coefficient is created at the scale of the search environment to increase the variety and search of different areas of the search space.
When |F|<1, the algorithm transitions to the exploitation phase, which consists of two distinct sub-phases. Each sub-phase employs different search strategies selected through control parameters P₂ (first phase) and P₃ (second phase), both initialized within the (0,1) interval before optimization. The first exploitation sub-phase activates when 0.5 ≤ |F| < 1, simulating two competing behaviors:
1. Rotary flight patterns 2. Siege-and-combat dynamics This phase represents vultures with moderate energy reserves (|F| ≥ 0.5), where concentrated food sources trigger aggressive competition among cluster members. The algorithmic implementation mirrors natural vulture behavior, where resource contention increases with population density at optimal sites.
The algorithm mathematically simulates the natural competition among vultures during foraging, where dominant individuals (high-fitness solutions) aggressively protect their resources. In contrast, weaker vultures (low-fitness solutions) employ collective strategies to challenge them. Specifically, subordinate solutions surround and persistently harass stronger solutions, creating localized disturbances that may eventually displace higher-quality solutions. These dynamics are captured through specialized equations that quantify hierarchical dominance relationships and simulate the balance between resource defense and challenger persistence. The model effectively translates these biological interactions into an optimization framework, where dominant solutions represent local optima while challengers facilitate exploration of alternative regions in the search space. This competitive mechanism enhances the algorithm's ability to escape local optima while maintaining pressure toward high-quality solutions. The following equations are used to model this step:
D (i) is calculated using equation 5, and F is the satiety of vultures, which is calculated using equation 4. Rand4 is a random number generator that produces a random number between 0 and 1, used to increase the randomness factor. In equation 9, the symbol i is one of the best vultures of the two groups, which is selected using the equation. In the current iteration, P (i) is the vulture's current position vector, by which the distance between the vulture and one of the best vultures in the two groups is obtained. Vultures' Spinning Combat: Vultures often create a spinning combat, which is used to model spiraling motion. The spiral model has been used for mathematical modeling of rotary combat. A spiral equation is created between all vultures and one of the top two vultures in this method. The rotational struggle is expressed using equations 10 to 12.
In the above equations, R (i) represents the position vector of one of the two best vultures in the current iteration, which is obtained using the equation. Cos and Sin represent the sine and cosine functions, respectively, and rand5 and rand6 are random numbers between 0 and 1, so that S1 and S2 are obtained using the equation. Finally, using equation 12, the location of the vultures is updated.
In the gathering of several types of vultures on the food source, the movement of all vultures towards the food source is investigated. Occasionally, vultures go hungry, and there is so much competition for food that several species of vultures may congregate on the same food source. The following equations are used to formulate this movement of vultures. In the first equation, BestVulture1 (i) is the best vulture of the first group in the current iteration, and BestVulture2 (i) is the best vulture of the second group in the current iteration, and F is the satiation rate of the vulture.
Finally, the summation of all vultures is done using the equation below, where A1 and A2 are obtained using the above equations, and P (i+1) is the vulture position vector in the next iteration.
The vector is considered to be equal to the maximum size of the generated feature set; the feature considered to be selected takes the value of one, while the other features have a value of zero, meaning they are not included in the final solution set. To evaluate each solution, a fitness function (objective) is employed during the optimization process. Our effort in the current project is to ensure that the set of obtained features achieves high accuracy in detecting blood cells. Therefore, the fitting function of each solution is based on the model recognition accuracy:
To evaluate each solution, a fitness function (objective) is employed during the optimization process. Our effort in the current project is to ensure that the set of obtained features achieves high accuracy in detecting blood cells. Therefore, the fitting function of each solution is based on the model recognition accuracy:
The way of mapping the feature selection problem to the African vulture optimization method is that, as in Table 1, each solution is equivalent to a subset of the available features for blood cell type detection, in other words, if we assign an index to each feature, Then the features that have taken the value of one in the following vector are in the optimal subset of features and vice versa, the features that have taken the value of zero are not in the final solution of feature selection. Now, the AVOA method should determine the optimal solution of the problem in a reasonable time, so that, based on the defined objective function, the highest accuracy must be obtained by selecting the optimized feature subset.
In the fourth phase, the obtained data is categorized innovatively. In this category, the extracted features are divided into K clusters using the fuzzy clustering method, a type of unsupervised learning network. We will initially check the value of k with k=4. However, with the increase in the number of clusters in the fuzzy clustering method, the selection of samples based on feature similarity becomes more accurate. As a result, the design accuracy is expected to improve. This division is based on the similarity of the feature pattern of the samples without considering their type. After implementing fuzzy clustering, the characteristics of the feature centers in the clusters can be used as indicators of the cluster members. Now, considering the status of each example of the images in this training dataset, we calculate the value of the cluster index in each cluster (the density of different types of blood cells in each cluster).
In is the number of samples in cluster k and
Then, in the evaluation (test) phase for each macroscopic image, we calculate the distance from these cluster centers under the title ofa_lk. In other words, we want to find out how far the features of each image l are from the status of the feature in each cluster k, for this we have
used the Euclidean distance.
#feature is the number of features of each image, center(k,f) is the value of feature f in the center of cluster k and variable sample(l,f) is the value of feature f in sample l. Now, by using the formula of membership value in type II phase, the probability of occurrence of a blood cell of type i in profile l is calculated as follows:
Now, having P_li values (as an index for the probability of blood cell type x), we will rank the values and choose the largest probability. In this way, the nature of a macroscopic image can
be semi-supervised evaluated using the flexibility of fuzzy logic and as a probability number. Finally, based on the refined result, issue warnings to the doctor about the possibility of disease.
To benchmark our proposed design, we adopted a high-accuracy hybrid approach developed by Ahmed et al. (28) for blood cell classification. Their method integrates: (
Recall is the ratio of correct detections with X label to the total samples with X label. F- Measure combines the two measures of Recall and Precision in one value as the following geometric mean.
The study utilized a clinical dataset comprising white blood cell (WBC) images from 100 healthy and hematologically abnormal volunteers, collected through a partnership with Jiangxi Tecom Scientific Corporation (China). The dataset contains 300 high-resolution WBC images (120×120 pixels, 24-bit color depth), evenly split for training and testing purposes to evaluate segmentation algorithms. All samples were prepared using fresh hematology reagents for rapid WBC staining and imaged under standardized conditions with a Motic N800-D motorized microscope equipped with a Moticam Pro252A camera. This carefully curated dataset was specifically designed to support research in self-supervised learning for efficient and precise WBC image segmentation. RNN have multiple layers, including input, recurrent (LSTM/GRU), dense, and output layers. The number of recurrent layers can be adjusted based on complexity. The number of trained parameters can vary significantly based on the input features, hidden units, and layer configurations, often ranging from thousands to millions, depending on the architecture used. In this work, the standard structure includes:
▪ Input Layer: 345 neurons (for features). ▪ Recurrent Layer (LSTM): 50 units.
▪ Dense Layer: 20 neurons.
▪ Output Layer: 1 neuron (for classification). For the statistical analysis of the number of samples of each type of blood cell, we have shown the frequency of each subgroup on the graph in two sets of training and test data in Figures 2 and 3. As shown in these images, the highest frequency is associated with neutrophils and lymphocytes, while the lowest frequency is associated with basophils.
Number of blood cell samples in the training dataset
Number of blood cell samples in the test dataset
Now, using samples, we will identify five types of cells: lymphocytes, monocytes, eosinophils, basophils, and neutrophils. As we can see in Figure 4, the precision of blood cell detection in all classes is equal to or greater than the basic design, and model presented with appropriate accuracy to detect blood cells based on the training of the model using the combination of contourlet transformation, a recursive neural network, and an innovative bundle.
Precision of the proposed scheme in detecting blood cells
Recall is the ratio of correct detections labeled X to the total samples labeled X. In Figure 5, we can see that the proposed scheme has improved in all classes, and by leveraging the power of feature extraction in contourlet transformation, it has increased the accuracy of blood cell type detection.
Recall of the proposed scheme in blood cell detection
In the last step, we evaluated the F-measure, which is the geometric mean of the recall and accuracy criteria. According to the results obtained in Figure 6, the value of this index in the proposed design is more favorable than in the basic design.
F-Measure index of the proposed scheme in the detection of blood cells
The confusion matrix displays the classification results based on the actual information available. Next, Figures 7 and 8 show the confusion matrix of each detection method. As mentioned earlier, the African vulture optimization method was used to select the feature from among the multitude of features produced in the recurrent neural network. The convergence diagram in Figure 9 shows the performance of the optimization method in minimizing the cost of the proposed solution for feature selection.
Confusion matrix in blood cell detection (basic method)
Confusion matrix in blood cell detection (proposed method)
Convergence diagram of the African vulture optimization method (AVOA)