Data provenance. The blood-smear images used to construct the dataset were provided by the Blood Transfusion Center (CTS) and the Regional Hospital Center (CHR) of Yamoussoukro, with an additional occasional contribution from the CTS of Abidjan. The authors thank Dr. D. Bosso (CTS Yamoussoukro), Dr. C. Houedanou (CHR Yamoussoukro), K. Hermann (CHR Yamoussoukro), Dr. B. Dembélé (CTS Abidjan), K. Eugène (CHR Yamoussoukro), and T. Abalé (CTS Abidjan) for their collaboration in the production of this work.

Figure 1. Flowchart of the blood-smear red-blood-cell classification process.

Ethical status. Data collection was carried out as part of a previous collaboration of the research group, with authorization from the CTS and CHR laboratories in Yamoussoukro to use blood-smear images for research purposes. This authorization was granted institutionally by the partner laboratories; it does not constitute formal approval by an independent ethics committee, and no record of individual patient consent was available to the authors of the present study. The images used contain no nominative or identifying information that would allow them to be traced back to an individual patient.

Acknowledged limitation—patient/smear traceability and selection criteria. The smear images were provided to the authors as an already assembled collection, without information on the number of distinct patients from whom the 470 smears originated or on the criteria used to select these smears from all examinations performed by the partner institutions.

Diagnostic reference and adjudication process. Assignment of each image patch to one of the five morphological classes followed a three-level hierarchical procedure: first, a literature review was used to establish the reference morphological criteria for each class; laboratory technicians then annotated the smear images according to these criteria; the annotations were subsequently confirmed or rejected by biological-analysis engineers; finally, hematology laboratory physicians adjudicated the remaining disputed cases. Cells for which disagreement or ambiguity persisted after this procedure were removed from the dataset rather than assigned a default label—this exclusion concerned only a marginal number of cells (approximately 20).

Annotator qualifications. The annotation team consisted of two laboratory physicians specialized in hematology, two biological-analysis engineers from the hematology department, and three laboratory technicians.

Classifier scope. The classifier developed in this study operates exclusively on pre-isolated single-cell image patches and recognizes only the five morphological classes included in the training data. A cell exhibiting a pathological morphology outside these five classes would, in the current version of the system, necessarily be incorrectly assigned to one of the five known classes; accordingly, the clinical-diagnostic claims made in this manuscript are restricted to this scope.

The raw image consists of 470 color BMP smear images with a resolution of 1024 × 768 pixels, acquired without Giemsa staining. Images were captured at 1000× total magnification using a 100× objective lens and a 10× eyepiece. Illumination was provided by a 6V-220W halogen lamp. Acquisition was performed with a Moticam2 2 MP color CMOS camera, and images were transferred to a computer via USB 3.0.

The improved cell-isolation algorithm of Alico et al. (2020) [29] was applied to generate the image patches composing the dataset. Figure 2 shows an example of a blood-smear image, and Figure 3 presents examples of image patches after cell isolation.

Red blood cell extraction was performed in MATLAB on an HP computer with an Intel i5-3230M CPU, 12 GB RAM, and a 477 GB SSD. Model training was conducted on an MSI workstation with a Core i7 processor and an NVIDIA GTX 1070 GPU.

Figure 2. Example blood-smear image obtained from the acquisition protocol.

Furthermore, the distribution of our dataset by morphological class is as follows: echinocytes (86 images), acanthocytes (92 images), elliptocytes (138 images), drepanocytes (106 images) and ovalocytes (138 images), for a total of 560 image patches. To ensure a balanced representation of each class during model evaluation, a 5-fold stratified cross-validation was applied, preserving the relative proportions of the five classes in each fold. This approach guarantees that the minority classes (echinocytes and acanthocytes) are systematically present in the training and validation subsets, see Table 1.

Figure 3. Red blood cells isolated from blood-smear images (Alico et al., 2020 [29]). (a): Echinocytes, (b): Acanthocytes, (c): Elliptocytes, (d): Drepanocytes, (e): Ovalocytes.

Table 1. Distribution of image patches by class and by cross-validation fold.

The acquired images comprise several red blood cells at once, with different morphological and colorimetric shades, and these occupy on average a memory space of 2.305 MB. First, pre-processing was carried out, consisting of extracting each cell from its surroundings, without resizing the original image. The dataset obtained consists of individual red blood cells, called image patches, showing various morphologies, distributed among the five (05) classes retained. Next, in order to reduce the number of parameters of the models to be estimated, the image patches were resized to 224 × 224 × 3 pixels, in accordance with the input data requirements of the ResNet18 and MobileNetV2 models. Finally, each image was labeled according to its class for model training.

Automatic classification of pathological red blood cells is carried out using two deep convolutional neural architectures: ResNet18 and MobileNetV2. This choice is based on the relatively limited size of the database (560 images distributed across five morphological classes), the need to obtain good generalization capacity, and the use of transfer learning from models pre-trained on ImageNet.

Indeed, ResNet18 (Residual Network with 18 weighted layers), proposed by He et al. (2016), introduces the concept of residual connections, allowing deep networks to learn residual functions rather than complete transformations. This innovation facilitates gradient propagation and limits the performance degradation observed as network depth increases. With approximately 11.7 million parameters, ResNet18 offers an attractive trade-off between representation capacity, computational cost and the risk of overfitting on a limited database. The overall architecture of ResNet18 used in this study is shown in Figure 4.

Figure 4. ResNet18 architecture.

As for MobileNetV2, it was developed by Sandler et al. (2018) and designed to offer excellent computational efficiency while maintaining good classification performance. Its architecture relies on inverted residual blocks combined with linear bottlenecks and depthwise separable convolutions, which considerably reduces the number of parameters and the cost of operations. With approximately 3.5 million parameters, MobileNetV2 constitutes a compact architecture, favoring reduced training and inference times. The corresponding MobileNetV2 architecture is illustrated in Figure 5.

The choice of these two architectures is motivated by their complementarity: ResNet18 favors a deep representation of morphological features thanks to its residual connections, while MobileNetV2 relies on an efficient representation based on a lightweight architecture. Since few studies have jointly evaluated these two architectures on the simultaneous classification of the five erythrocyte morphologies considered here, this comparison appears relevant. Before training, all images are resized to 224 × 224 × 3 pixels; the features extracted by the convolutional layers are passed to a classification layer whose outputs are converted into probabilities by the Softmax function.

Figure 5. MobileNetV2 architecture.

The limited availability of large annotated databases constitutes one of the main difficulties of automatic classification of pathological red blood cells. Since our database comprises only 560 images patches distributed across five classes, training from a random initialization would expose the deep architectures to a high risk of overfitting. We therefore resort to transfer learning, which consists of reusing the representations learned by a deep network on a large-scale source task (ImageNet, approximately 1.28 million images distributed across 1000 categories) for a target task with few examples.

The adopted process comprises five steps: 1) loading the ResNet18 and MobileNetV2 weights pre-trained on ImageNet; 2) replacing the final classifier (1000 categories) with a new five-neuron layer corresponding to the five morphological classes studied; 3) feature extraction, where the pre-trained convolutional layers are frozen and only the new classification layers are trained; 4) fine-tuning, where part of the last blocks is progressively unfrozen to adapt the deep representations to erythrocyte morphologies; 5) final classification via the Softmax function. This principle is applied identically to both architectures, with the only difference being the nature of the blocks unfrozen during fine-tuning (residual blocks for ResNet18, inverted residual blocks for MobileNetV2).

Optimization of the training hyperparameters—learning rate, number of epochs and mini-batch size—is carried out by grid search. The values tested are the batch size (12, 16, 24, 28, 32) and the learning rate (10⁻⁴, 3.10⁻⁴, 5.10⁻⁴, 10⁻³), i.e. 20 combinations per architecture-optimizer pair. The number of epochs is not fixed manually: the 5-fold stratified cross-validation incorporates an early-stopping mechanism, which halts training as soon as validation performance stops improving, thus limiting overfitting. For k = 5, each configuration in the table produces 5 training runs, i.e. 100 training runs per architecture-optimizer pair (5 × 20), and 400 training runs in total across the four configurations studied (ResNet18/MobileNetV2 × SGDM/Adam).

Two optimizers are compared. Stochastic gradient descent with momentum (SGDM) introduces an inertia term that dampens gradient-descent oscillations and accelerates convergence (Figure 6). The Adam optimizer (Adaptive Moment Estimation) computes an adaptive learning-rate step for each parameter from exponential moving averages of the first and second moments of the gradient, with bias correction.

Figure 6. Damping of stochastic-gradient-descent oscillations by the momentum method (SGDM).

Formulation of the Adam optimizer (first- and second-order moments, bias correction)

Adam [26], is a method that computes a learning-rate step described as adaptive for each parameter. During training, in addition to storing an exponentially decaying average of the squares of the previous gradients as with RMSprop, the algorithm also keeps the exponentially decaying average of the previous gradients according to the equations:

It should be noted that m t updates the exponential moving average of the gradient and is referred to as the first-order (“1”) moment estimate. As for v t , it updates the exponential moving average of the squared gradients and is referred to as the second-order (“2”) moment estimate. According to the authors, m t and v t are initialized as vectors of “0” and are biased towards this point during the initial steps, particularly when the decay coefficients ( β 1 , β 2 ) are small (close to “1”). They propose a bias correction for the estimates using the following relations:

Then comes the parameter update ( θ ):

η , the learning rate, β 1 and β 2 , damping coefficients (typically close to “1”, for example, 0.9 and 0.999), ε , a small constant added to avoid division by zero.

For the parameters β 1 , β 2 and ε , the authors propose default values of 0.9, 0.999, and 10 − 8 .

The advantages provided by Adam, make it the most widely used optimizer in neural network training.

3.6.1. Multi-Objective Vector

Each hyperparameter configuration x = (Epoch, Learning Rate, Batch Size) is evaluated using seven criteria representing both classification performance and model complexity:

f(x) = (1 − F1, 1 − MCC, 1 − AUC, GapAcc, GapLoss, Params_norm, Latency_norm) (6)

1 − F1: error associated with the F1-score (macro average over the five classes);1 − MCC: error associated with the Matthews correlation coefficient;1 − AUC: error associated with the area under the ROC curve (macro, one-vs-rest average);GapAcc: gap between training and validation accuracy;GapLoss: gap between training and validation loss;Params_norm: number of model parameters, normalized by the maximum observed;Latency_norm: inference latency, normalized by the maximum observed.

As all components are formulated as minimization criteria, the problem is written as: minimize f(x).

3.6.2. Pareto Front and TOPSIS Method

In multi-criteria optimization, a configuration A dominates a configuration B (A ≤ B) if f_i(A) ≤ f_i(B) for all criteria i, and if there exists at least one criterion j such that f_j(A) < f_j(B). The non-dominated solutions constitute the Pareto Front, which reduces the search space to the optimal trade-offs only.

The Pareto Front identifies optimal solutions but does not allow them to be ranked. The TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method ranks these solutions using two fictitious references: an ideal solution (best values observed for each criterion) and an anti-ideal solution (worst values observed). For each configuration, the Euclidean distance D⁺ to the ideal solution and D⁻ to the anti-ideal solution are computed, then the closeness coefficient Ci = D⁻/(D⁺ + D⁻), with 0 ≤ Ci ≤ 1. The closer Ci is to 1, the more the configuration is simultaneously close to the ideal and far from the anti-ideal. The Pareto Front thus acts as a qualitative filter, and TOPSIS as a geometric quantifier used to designate the best configuration within each search block.

Classification performance is evaluated from the multi-class confusion matrix, aggregated over the 5 cross-validation folds, using the following metrics:

F1-score (macro):

F1 = 2 × (Precision × Recall)/(Precision + Recall) (7)

It is averaged over the five classes (computed from the cumulative confusion matrix of the 5 folds). Assesses the precision/recall balance, giving equal weight to each class, even minority ones.

MCC (Matthews Correlation Coefficient):

Measures the model’s overall consistency, robust to class imbalance.

AUC: area under the ROC curve

where TPR = TP/(TP + FN) and FPR = FP/(FP + TN).

Computed from the cumulative confusion matrix of the 5 folds. Indicates the model’s ability to correctly separate classes, independently of the chosen threshold.

GapAcc = |Accuracy_training – Accuracy_validation| (10)

Overfitting indicator based on accuracy.

GapLoss = |Loss_training – Loss_validation| (11)

overfitting indicator based on the loss function.

Params_norm = Nb_model_parameters/Nb_max_parameters (12)

Number of model parameters normalized with respect to a fixed reference ceiling of 12 × 10⁶, selected as a safety margin above the parameter count of the largest architecture evaluated in this study (ResNet18, ≈11.18 million parameters after adaptation to a five-class output layer).

Latency_norm = Model_latency/Max_latency (13)

Inference time normalized relative to the slowest configuration tested.

The selection of the optimal configurations combines the Pareto Front, which retains the non-dominated solutions, and the TOPSIS method, which ranks them according to their proximity to the ideal solution, in order to identify the best trade-off between accuracy, generalization capacity and computational cost.

The experiments are conducted on the 560 image patches described in Section 3.1, using a 5-fold stratified cross-validation applied independently to each of the four architecture-optimizer configurations (ResNet18/MobileNetV2 × SGDM/Adam). For each configuration, a grid search of 20 combinations (5 batch sizes × 4 learning rates) is evaluated, i.e. 100 training runs per configuration and 400 training runs in total. The number of epochs is determined automatically by early stopping. Each combination is summarized by the seven-component multi-objective vector defined in Section 3.5, then filtered by the Pareto Front and ranked by TOPSIS in order to identify, for each learning-rate value, the best (epoch, batch size) combination, before a final selection among the four retained candidates.

4.2.1. Hyperparameter Optimization via Grid Search

Tables 2-5 present, for each of the four configurations, the best (epoch, batch size) combination retained by the Pareto Front + TOPSIS for each of the four learning-rate values tested, along with the associated metrics. For the sake of readability, the 20 raw training runs per configuration (100 per architecture-optimizer pair in total) are not fully reproduced here; they are available as supplementary material.

4.2.2. Comparison of the Optimal Configurations

Table 6 gathers, for the four configurations ultimately retained following the TOPSIS selection, the values converted into directly interpretable metrics as well as the complexity and generalization indicators.

Table 2. ResNet18 + SGDM—best configuration for each learning-rate value (Pareto Front + TOPSIS). Selected configuration: Epoch = 25, LR = 10⁻⁴, BS = 24.

Table 3. ResNet18 + Adam—best configuration for each learning-rate value. Selected configuration: Epoch = 14, LR = 10⁻⁴, BS = 32.

Table 4. MobileNetV2 + SGDM—best configuration for each learning-rate value. Selected configuration: Epoch = 40, LR = 10⁻⁴, BS = 28.

Table 5. MobileNetV2 + Adam—best configuration for each learning-rate value. Selected configuration: Epoch = 16, LR = 3.10⁻⁴, BS = 32.

Table 6. Comparison of the four optimal configurations (architecture × optimizer).

4.2.3. Cumulative Confusion Matrices (5 Folds)

In order to document the nature of the residual errors between morphologically close classes, the cumulative confusion matrix over the 5 cross-validation folds is presented below for each of the four optimal configurations retained (Table 6). Each matrix aggregates the validation predictions of the 5 folds; the percentages at the bottom of each column indicate the precision per predicted class (proportion of image patches correctly classified among those predicted in that class), the classes being coded ACH (Acanthocytes), DRE (Drepanocytes), ECH (Echinocytes), ELL (Elliptocytes) and OVA (Ovalocytes).

Figure 7. Cumulative confusion matrix over 5 folds: ResNet18 + SGDM (Epoch = 25, LR = 10⁻⁴, BS = 24).

Figure 8. Cumulative confusion matrix over 5 folds: ResNet18 + Adam (Epoch = 14, LR = 10⁻⁴, BS = 32).

Figure 9. Cumulative confusion matrix over 5 folds: MobileNetV2 + SGDM (Epoch = 40, LR = 10⁻⁴, BS = 28).

Figure 10. Cumulative confusion matrix over 5 folds: MobileNetV2 + Adam (Epoch = 16, LR = 3.10⁻⁴, BS = 32).

Table 7. Precision per predicted class (%), read at the bottom of the cumulative confusion matrices (Figures 7-10).

Reading Figures 7-10 and Table 7 confirms the hypotheses formulated in Section 2: the Ovalocytes (OVA) class systematically shows the lowest precision of the five classes, regardless of configuration (88.1% to 94.4%), which is consistent with the morphological proximity between elliptocytes and ovalocytes already reported in the literature. This effect is most pronounced for MobileNetV2 + SGDM (88.1%), a configuration for which the Ovalocytes class visibly concentrates the most prediction errors among the four configurations studied. Conversely, the Acanthocytes (ACH) and Drepanocytes (DRE) classes achieve a precision above 96.7% in all configurations, and up to 100% for Acanthocytes with MobileNetV2 + Adam, indicating that these morphologies are the most easily discriminated by both architectures. These observations qualify the ranking obtained on the global metrics (Table 6): two configurations displaying an almost identical global F1 (ResNet18 + Adam and MobileNetV2 + Adam, F1 ≈ 0.966) may nevertheless show different per-class error profiles, a criterion to take into account depending on the targeted clinical use (for example, if reliable detection of ovalocytes is a priority).

4.2.4. Learning Curves (Representative Fold)

Figures 11-14 illustrate, for a representative fold among the five cross-validation folds, the evolution of accuracy and the loss function during training for each of the four optimal configurations. These curves make it possible to qualitatively verify the stability of convergence and the absence of divergence between the training and validation curves, complementing the GapAcc and GapLoss indicators reported in Tables 2-6.

Figure 11. Learning curves (representative fold): ResNet18 + SGDM.

Figure 12. Learning curves (representative fold): ResNet18 + Adam.

Figure 13. Learning curves (representative fold): MobileNetV2 + SGDM.

Figure 14. Learning curves (representative fold): MobileNetV2 + Adam.

In line with the GapLoss values reported in Table 6, the curves of the configurations trained with Adam (Figure 12 and Figure 14) reach a high validation accuracy in a smaller number of epochs, at the cost of a slightly more pronounced training/validation gap on the loss function than for the SGDM configurations (Figure 11 and Figure 13), whose convergence is more gradual but results in a smaller final gap.

The performance obtained in this study (F1 between 0.951 and 0.968, MCC between 0.938 and 0.961, AUC above 0.995 for all four configurations) lies in the upper range of recent work using residual or lightweight architectures for deep-learning-based classification of erythrocyte morphologies [3][4]. Unlike several earlier studies that evaluate ResNet18 and MobileNetV2 separately or on a reduced number of classes, this work proposes a joint and systematic comparison of the two architectures on five pathological morphologies simultaneously, combined with multi-objective hyperparameter optimization—an approach still uncommon in the literature dedicated to digital hematology [3][4]. This direct comparison, although carried out on a modest-sized dataset as is often the case in this field, makes it possible to document an accuracy/complexity trade-off that is rarely quantified as explicitly in existing work.

Recent peer-reviewed studies further help position this contribution within the broader landscape of multiclass red-blood-cell morphology classification. Dhar et al. [30] proposed a hyperparameter-optimized KNN classifier for poikilocytosis classification, whereas Dhar et al. [31] developed a hybrid CNN-SVM approach for the same task; both studies, evaluated on datasets of comparable size, reported competitive classification performance without explicitly addressing the trade-off among predictive accuracy, generalization, model complexity, and inference latency. At a larger scale, Routt et al. [4] achieved approximately 98% accuracy using an ensemble of four CNNs for a seven-class red-blood-cell morphology classification task on a substantially larger dataset. Compared with these studies, the present work introduces an explicit multi-objective selection framework (Pareto Front and TOPSIS) that jointly balances classification performance, generalization indicators, model complexity, and inference latency—a dimension not addressed in [30][31] or [4].

The four optimal configurations achieve an F1 above 0.95 and an MCC above 0.93, with an AUC systematically above 0.995 (Table 6). This level of performance, obtained on a database limited to 560 image patches distributed across five morphological classes, confirms the value of transfer learning: the generic representations inherited from ImageNet, combined with partial fine-tuning, are sufficient to effectively discriminate morphologies that are nonetheless visually close (echinocytes/acanthocytes, elliptocytes/ovalocytes), despite the small size of the dataset. The AUC varies very little between configurations (0.9954 to 0.9975), which indicates that it saturates quickly and loses its discriminating power for distinguishing between hyperparameters: it is essentially the pair (1 − F1, 1 − MCC), more sensitive to errors on minority classes, that drives the TOPSIS selection—consistent with the attention paid to preserving minority classes (echinocytes, acanthocytes) through stratified cross-validation (Section 3.1).

For the same Adam optimizer, ResNet18 and MobileNetV2 achieve an almost identical F1 (0.9659 versus 0.9659) and a very close MCC (0.9574 versus 0.9570). The deeper architecture of ResNet18 therefore does not provide a measurable discriminative advantage here over the lighter architecture of MobileNetV2, which confirms a posteriori the complementarity hypothesis formulated in Section 3.3: on a five-class problem with a limited dataset, the additional depth of ResNet18 does not bring a decisive representational gain. On the other hand, the gap is clear in terms of model complexity: the Params_norm parameter goes from 0.932 (ResNet18) to 0.187 (MobileNetV2), a direct reflection of the roughly 3.3 ratio between the ~11.7 million parameters of ResNet18 and the ~3.5 million of MobileNetV2. A more unexpected result concerns the normalized latency: it is systematically higher for MobileNetV2 (0.32 - 0.33) than for ResNet18 (0.177 - 0.179), whereas this architecture is designed for fast inference. This counter-intuitive result is likely explained by the fact that the depthwise separable convolutions of MobileNetV2, although less costly in terms of parameters and theoretical operations, are often less well optimized than classical dense convolutions by the libraries and hardware used (MATLAB implementation, GTX 1070 GPU), which do not necessarily benefit from the specialized kernels available on more recent frameworks. The theoretical gain in lightness therefore does not automatically translate into a measured gain in inference time, which constitutes a limitation to be documented more precisely in future work, through a framework-independent latency measurement.

The Adam optimizer consistently converges in a markedly lower number of epochs than SGDM, for an equivalent architecture: 14 epochs versus 25 for ResNet18 (a reduction of about 44%), and 16 epochs versus 40 for MobileNetV2 (a reduction of about 60%). This acceleration of convergence is consistent with Adam’s adaptive properties (Section 3.5), which individually adjust the learning-rate step per parameter, unlike SGDM, whose inertia improves the stability of the descent without necessarily accelerating its speed. This speed, however, has an observable counterpart on GapLoss, the overfitting indicator: for ResNet18, Adam shows a GapLoss of 0.0907 versus 0.0405 for SGDM, more than double; for MobileNetV2, the gap goes in the same direction although less pronounced (0.0623 versus 0.0458). Adam thus appears to converge more quickly towards an optimum that generalizes slightly less well than the one reached more gradually by SGDM, even though the early-stopping mechanism limits this risk by halting training as soon as validation stops improving. This trade-off between convergence speed and generalization qualifies the common belief that Adam is strictly superior to SGDM.

Examination of Tables 2-5 shows that the value LR = 10⁻⁴ recurs frequently among the configurations selected by TOPSIS (three of the four optimal configurations), confirming its position as a robust convergence value. Higher learning rates (5.10⁻⁴, 10⁻³) tend to reduce the number of epochs required but generally degrade F1 and MCC, reflecting the learning instability inherent to high learning rates. The optimal batch size varies more depending on the architecture and the optimizer (12 to 32 depending on the case), without as clear a trend as for the learning rate, which suggests a secondary sensitivity of this parameter within the tested range.