YOLOv8-A: Enhanced Lightweight Object Detection with Nonlinear Feature Fusion and Mathematical Optimization for Precision Small Target Detection in Industrial Silicon Melting Processes

Handcrafted feature extraction was a foundational approach for small-target detection in the early stages of computer vision. Zhao and Cheng (2011) employed edge detection algorithms to monitor crystal diameters during the Czochralski (CZ) process. While this approach was computationally efficient, it exhibited significant limitations, particularly in noisy and dynamic environments, leading to high rates of false positives (Zhao & Cheng, 2011)[18] Moreover, handcrafted methods struggled to adapt to the diverse lighting conditions and material properties commonly encountered in industrial production.

To address the shortcomings of pure edge detection, Zhao and Wang (2018) integrated machine learning techniques, utilizing least-squares support vector machines (LSSVM) to classify aperture images into distinct temperature patterns. This approach marked a step forward by automating the recognition of crystal fusion stages, but its reliance on handcrafted features limited its adaptability and generalizability across varying production settings (Zhao & Wang, 2018)[19]. These constraints underscored the need for more robust and adaptive techniques.

Deep learning frameworks, particularly convolutional neural networks (CNNs), have significantly enhanced object detection capabilities. Zhang et al. (2022) leveraged AlexNet to classify the melting stages of silicon crystals, achieving a notable increase in accuracy over traditional methods. However, the model’s computational demands made real-time deployment challenging in resource-constrained environments (Zhang et al., 2022)[17]. This limitation highlighted the trade-off between model complexity and operational efficiency in industrial applications.

The YOLO (You Only Look Once) framework revolutionized object detection by balancing real-time performance and accuracy. YOLOv5 introduced CSP networks, which optimized feature extraction and reduced computational redundancy, resulting in faster inference times (Jocher, 2020)[6]. YOLOv7 further advanced this framework by incorporating Trainable Bag of Freebies (TBoF), a set of augmentation techniques that improved detection accuracy without additional computational costs (Wang et al., 2022)[13]. Despite these advancements, challenges persisted in detecting small, overlapping targets under complex industrial conditions.

The DETR (DEtection TRansformer) model introduced a novel approach to object detection, reformulating the task as an object query problem. By eliminating region proposals and employing a Transformer-based architecture, DETR achieved end-to-end optimization and scalability (Carion et al., 2020)[1]. However, the model’s high computational requirements limited its deployment in edge devices, particularly in industrial scenarios where resource efficiency is critical.

To mitigate the computational burden of standard Transformer models, Yang et al. (2023) proposed lightweight adaptations that incorporated efficient multi-scale feature fusion. These enhancements improved small-target detection accuracy while reducing latency, making Transformers more applicable to industrial tasks (Yang et al., 2023)[16]. The integration of lightweight Transformers into existing frameworks presents an opportunity for combining precision with scalability.

In recent years, research has focused on developing lightweight architectures tailored for resource- constrained environments. Zhao et al. (2023) integrated GhostNet modules into YOLOv8, achieving substantial reductions in model size and computational complexity while maintaining high detection accuracy (Zhao et al., 2023)[21]. These innovations align with the increasing demand for real-time solutions in industrial applications.

Li et al. (2024) proposed incorporating dynamic upsampling mechanisms into YOLOv8 to enhance the precision of small-target detection. By optimizing feature resolution at multiple scales, this approach reduced computational demands and improved inference speed, providing a viable solution for industrial silicon melting processes (Li et al., 2024)[7].

Existing object detection models such as YOLOv5 and YOLOv7 face significant challenges in detecting small targets, particularly in complex industrial environments:

1) Feature Loss During Downsampling: Traditional convolution operations tend to lose critical small-target features, reducing detection accuracy. For example, YOLOv7 suffers up to a 12% mAP drop when detecting objects smaller than 32 ×32 pixels (Zhao et al., 2023)[20].

To overcome these limitations, YOLOv8-A introduces:

1) GSConv Module: A lightweight convolution module combining GhostNet-inspired feature generation and ShuffleNet channel shuffling for efficient feature extraction(Han et al., 2020)[4].

Figure 3 provides an overview of the YOLOv8-A architecture.

Figure 3.

Improved YOLOv8-A Structural Design

Standard convolutional layers in CNNs are computationally expensive and prone to feature redundancy, which limits their scalability for lightweight models. Depthwise Separable Convolutions (DSC) partially address this issue but struggle to capture inter-channel dependencies, which are critical for high-accuracy small-object detection.

To address these challenges, the GSConv module integrates:

1) ·Ghost Feature Maps: These maps are lightweight approximations of standard convolution outputs, reducing computation without compromising accuracy (Han et al., 2020)[4].

Figure 4 illustrates the internal structure of the GSConv module, highlighting how the Ghost feature generation and ShuffleNet mechanisms operate.

Figure 4.

Structural of GSConv

Where Y is the output feature map,W_SC and W_DSC are weights for standard and depthwise separable convolutions, respectively, N is the number of ghost feature maps generated.The ghost feature generation process is further defined as: (2) Fghost =Fconv +∑i=1kWi·Gi $${{\rm{F}}_{{\rm{ghost}}\,}} = {{\rm{F}}_{{\rm{conv}}\,}} + \mathop \sum \limits_{{\rm{i = 1}}}^{\rm{k}} {{\rm{W}}_{\rm{i}}} \cdot {{\rm{G}}_{\rm{i}}}$$

Where:

F_conv is the standard convolution output.

The primary innovation of GSConv lies in its ability to reduce model parameters by over 21.5% while retaining critical small-object features. By incorporating GhostNet principles and channel shuffling, GSConv significantly lowers computational redundancy without compromising detection performance.

This improvement is particularly beneficial for real-time applications on resource-constrained devices, making YOLOv8-A suitable for deployment in edge devices.

Figure 5 provides a visualization of feature maps before and after GSConv integration, showcasing its effectiveness in retaining small-object details.

Figure 5.

Visualization of Feature Maps

Comparison of feature maps before and after GSConv integration, highlighting improved retention of small-target details.This improvement is particularly beneficial for real-time applications on resource-constrained devices, making YOLOv8-A suitable for deployment in edge devices.

Conventional upsampling mechanisms, such as bilinear interpolation and nearest-neighbor interpolation, utilize fixed grids for sampling. While computationally efficient, these methods distort geometric relationships in the feature map, especially for small objects.DySample replaces fixed grids with dynamic sampling grids, adapting to the spatial structure of feature maps.This approach significantly improves the geometric consistency of upsampled features, ensuring better alignment with ground-truth targets(Wang et al., 2023)[14].

Figure 6 illustrates the dynamic upsampling process employed by DySample, preserving geometric consistency across scales.

Figure 6.

Dynamic Up-sampling Based on Sampling Points

The DySample mechanism computes dynamic offsets O for each position in the feature map to create an adaptive sampling grid G′:

DySample generates offsets O dynamically for each feature map:

Where:

1) G: Fixed grid (e.g., bilinear or uniform sampling grid).

The upsampled feature map X′ is then computed using a grid sample operation, which performs bilinear interpolation based on the dynamically adjusted grid G′. The formula for X′is: (4) SX(i,j)=∑k,lX(k,l)⋅bilinear(G'(i,j),(k,l))

Herr:

1) i, j:These are the spatial coordinates in the upsampled feature map X, representing the output pixel positions where values are computed. Each position (i,j) aggregates contributions from the input feature map based on the adjusted sampling grid.

As illustrated in Figure 6, the sampling point generator predicts the offsets O by learning spatial relationships in the input feature map X. This is achieved using a trainable module (e.g., linear layers or convolutional neural networks), which extracts contextual information and minimizes geometric distortions. The process can be expressed as:

To further refine the upsampled feature map, DySample integrates a pixel shuffle operation after grid sampling. This operation rearranges and redistributes spatial information across channels, enhancing the spatial resolution of the upsampled features. The final output is computed as:

Figure 7 shows the structure of the sampling point generator in DySample. The generator predicts the optimal sampling offsets based on the input feature map to minimize geometric distortion.

Figure 7.

Sampling Point Generator in DySample

In summary,DySample introduces a dynamic sampling mechanism that overcomes the limitations of traditional upsampling methods like bilinear or nearest-neighbor interpolation by replacing fixed grids with adaptive, spatially aware grids. By dynamically generating offsets based on input feature maps, DySample ensures geometric consistency during upsampling, especially for small objects, while maintaining alignment with ground truth. The mechanism combines grid sampling, bilinear interpolation, and pixel shuffle to achieve refined, high-resolution feature maps with minimal geometric distortion. This approach has been shown to improve precision and reduce errors in tasks such as small-object detection, making it particularly suitable for applications requiring high accuracy, such as industrial inspections.

Multi-scale feature fusion is critical for detecting objects of varying sizes, but traditional methods like PANet use unidirectional connections, limiting the flow of information between shallow and deep features(Tan et al., 2020)[12].BiFPN enhances this process through:

1) Bidirectional Pathways: Allowing efficient information flow between deep and shallow layers.

Figure 7 illustrates the design of the BiFPN neck feature network, showing how bidirectional connections improve the fusion of multi-scale features, thereby enhancing small-target detection accuracy.

Figure 8.

Neck Feature Network Design

The feature fusion process in BiFPN is expressed as: (6) Fi=∑jwj· Fj∑jwj+ϵ

Where:

1) F_i: The output feature at level i in the BiFPN.

BiFPN introduces an innovative approach to multi-scale feature fusion by leveraging bidirectional pathways and learnable weighted connections, ensuring efficient information exchange between shallow and deep layers. This design improves the integration of multi-scale features, especially for small-target detection, by incorporating a high-resolution P2 layer. The adaptive weighting mechanism dynamically prioritizes the most relevant input features while maintaining numerical stability through normalization. As a result, BiFPN achieves significant improvements in detection accuracy, contributing to a 3.5% increase in mean Average Precision (mAP) and a 4.7% boost in recall for small-object detection. These advancements make BiFPN a robust and scalable solution for diverse detection tasks, particularly in scenarios with challenging multi-scale requirements.

The dataset consists of 12,000 high-resolution images (640 × 640 pixels), captured using a Basler acA2500-14um industrial camera. This camera was chosen for its high accuracy and sensitivity in detecting small defects, which is essential in silicon crystal growth processes where even the smallest anomalies can compromise the final product’s quality. The images were acquired under controlled lighting conditions and at varying angles to simulate the challenges faced during actual industrial inspection processes. The lighting intensity and noise levels were adjusted to replicate real-world conditions where variations in light and sensor noise can occur. This helps ensure the robustness of the trained model in different environmental conditions.

Figure 9.

Automated Defect Detection Platform for Crystal Processing and Melting Stages.

Figure 9 illustrates the automated defect detection platform used for data collection during the crystal processing and melting stages. This setup enabled the systematic acquisition of defect images, which were later categorized into three defect types for analysis.

The dataset is categorized into three main defect types commonly observed in silicon wafer production:

1) Single Aperture Defects: Small, circular features that are typically caused by impurities or uneven material melting. These defects are difficult to detect due to their small size and similarity to normal surface features.

Each defect type contains 4,000 samples, ensuring balanced representation across all categories. These samples are divided into training, validation, and test sets in a 7:2:1 ratio, respectively, to ensure the model is trained effectively while also being rigorously validated.

To improve model generalization and reduce overfitting, data augmentation techniques were extensively used. Data augmentation techniques, such as random rotation, brightness adjustment, and flipping, were applied to enhance generalization, following best practices in small-target detection (Wang et al., 2023)[14].The augmentation methods include:

1) Random rotations (up to 20°), to account for different orientations of defects in the images.

These augmentation techniques led to a 30% increase in dataset variability, which greatly enhanced the robustness of the trained model.

The experiments were conducted using a high-performance computational setup designed to handle large-scale datasets and deep learning models:

1) CPU: Intel Xeon Gold 5320 @ 2.20 GHz

This setup ensured optimal model training and inference performance, particularly for large models like YOLOv8-A, which require substantial GPU memory and computational power.

The YOLOv8-A model was trained using the following optimized parameters. These settings were carefully chosen based on the characteristics of the dataset and the goal of minimizing both overfitting and underfitting,as shown in Table 1.

These parameters ensure that the model was trained efficiently, converging faster while maintaining high generalization ability. The use of AdamW as the optimizer has been shown to outperform standard optimizers like SGD in deep learning tasks, especially in scenarios with complex models and small datasets (Loshchilov & Hutter, 2017)[25].Training parameters, such as batch size and epochs, were carefully tuned to balance overfitting and underfitting (Li et al., 2024)[7].

A critical component of the training process was the use of learning rate decay via a cosine annealing scheduler. This technique gradually reduces the learning rate throughout the training process, allowing the model to converge more smoothly and avoid overfitting at later stages. The use of cosine annealing has been proven to significantly improve training efficiency by adapting the learning rate based on the optimization trajectory (Loshchilov & Hutter, 2017)[25].

Early stopping was employed to halt the training process if no improvement in validation accuracy was observed after 50 epochs. This prevents unnecessary computation and ensures the model does not overfit to the training data. The combined use of learning rate decay and early stopping ensures that YOLOv8-A is trained to converge at an optimal point, balancing between underfitting and overfitting.

Precision (P) and Recall (R) are two fundamental metrics in object detection, especially in industrial defect detection, where the costs of false positives (FP) and false negatives (FN) can be significant.

These two metrics are often presented together in a Precision-Recall Curve, which plots Precision against Recall at different thresholds. Figure 10 below shows the Precision-Recall curves for YOLOv8-A and other models, highlighting the improvements achieved by the proposed model in detecting small targets.

Figure 10.

Precision-Recall curves comparing YOLOv8-A with Faster R-CNN, YOLOv3,YOLOv5, and YOLOv8m,demonstrating YOLOv8-A’s superior precision and recall in small target detection

The Mean Average Precision (mAP) is the most commonly used metric for evaluating object detection models. It takes into account both precision and recall across various Intersection over Union (IoU) thresholds, which measure the overlap between the predicted bounding box and the ground truth.

Figure 11.

Comparison of mAP@0.5 and mAP@0.5:0.95 across different models

Intersection over Union (IoU) is a metric that measures the overlap between the predicted bounding box and the ground truth. It is used to determine whether a detection is valid and is essential in evaluating localization accuracy.

In this study, evaluations were conducted at two IoU thresholds:

1) IoU@0.5: A threshold of 50% overlap is commonly used to classify predictions as correct.

This metric is crucial for ensuring that predicted bounding boxes align accurately with actual object locations, particularly for small targets in industrial applications, where precise localization is vital.

In addition to detection accuracy, computational efficiency is an essential consideration for real-time industrial applications. FPS (Frames Per Second) measures the inference speed of the model, which is critical when the model is deployed in time-sensitive environments like manufacturing or quality control.

Table 2 compares the FPS and inference time of YOLOv8-A with other state-of-the-art models. YOLOv8-A achieves real-time performance with 28 ms per frame on edge devices, such as the NVIDIA Jetson Nano.

The GSConv module plays a pivotal role in improving feature retention for small targets. It helps in reducing the computational cost while maintaining high performance. The addition of GSConv increased mAP@0.5 by 1.0% over YOLOv8m. Mathematically, GSConv can be described as: (12) GSConv Output = Conv2D ( Input Features )· Sparse Matrix

where the sparse matrix significantly reduces redundant computations while retaining critical features for small target detection.

The DySample module addresses geometric distortions in the image, which are crucial for accurate small target detection. By refining the feature quality, DySample improved recall by 2.1% and mAP by 1.0%. It dynamically adjusts the sampling rate based on the target’s scale, ensuring higher precision for smaller targets(Yang et al., 2023)[27].

The BiFPN module improves multi-scale feature fusion, crucial for detecting small targets across different resolutions. The addition of BiFPN increased mAP@0.5 by 2.2%, showcasing its effectiveness in enhancing detection at multiple scales.

Figure 12 illustrates the progression of mAP@0.5 for YOLOv8-A, YOLOv8m, and Faster R-CNN during the training process over 20 epochs. YOLOv8-A shows a faster convergence rate compared to the other models, reaching higher final mAP@0.5 values (0.982). This result highlights YOLOv8- A’s ability to optimize detection performance more efficiently, which is critical for real-time industrial applications.

Figure 12.

mAP@0.5 Progression Across Training Epochs

Figure 13 demonstrates the relationship between Inference Time (in milliseconds) and mAP@0.5 for different models. YOLOv8-A achieves the best trade-off, combining the highest mAP@0.5 (0.982) with the lowest inference time (3.7 ms). Faster R-CNN, while having acceptable mAP@0.5 (0.768), suffers from significantly higher inference times (16.8 ms), making it unsuitable for real-time applications. YOLOv8-A’s performance showcases its lightweight architecture and suitability for edge-device deployment.

Figure 13.

Inference Time vs. mAP@0.5

Figure 14 presents the training loss curves, highlighting faster convergence of YOLOv8-A compared to baseline models, demonstrating the efficiency of its architecture.

Figure 14.

Training loss curves showing faster convergence for YOLOv8-A compared to baseline models.

Figure 15 shows a radar chart comparing YOLOv8-A with other models (YOLOv5, YOLOv7, DETR) across multiple dimensions: mAP, Precision, Recall, Inference Time, and Parameter Count. The chart highlights YOLOv8-A’s superiority in achieving high accuracy with low computational overhead.

Figure 15.

Radar chart comparing YOLOv8-A with YOLOv5, YOLOv7, and DETR across multiple performance metrics.

To evaluate the effectiveness of the proposed YOLOv8-A model, a comprehensive visual comparison of detection results was conducted on the aperture protrusion dataset, which captures defects during the silicon melting process. The results are illustrated in Figure 11, showcasing the comparative performance of YOLOv8m and YOLOv8-A.

The improved performance is attributed to the integration of GSConv, DySample, and BiFPN modules, which enhance feature extraction and small-object detection capabilities. The accuracy of YOLOv8-A has been validated in industrial deployment phases, meeting stringent requirements by minimizing the false detection rate and ensuring consistent reliability [(Liu et al., 2023)]^[10]

Figure 16.

Comparison of detection results for YOLOv8-A and YOLOv8m on aperture protrusion images .

YOLOv8-A is highly adaptable to a wide range of industrial applications, including:

1) Defect detection in photovoltaic cells

Its lightweight architecture and real-time inference capabilities make it suitable for automated quality control in high-throughput industrial environments.

We also evaluated the deployment of YOLOv8-A on edge devices, particularly the NVIDIA Jetson Nano and Xavier. Benchmarking results are shown in Table 5.

Real-world deployment tests confirmed YOLOv8-A’s practical viability on edge devices, achieving low latency and high throughput on NVIDIA Jetson platforms (Liu et al., 2023)[12]. This makes the model ideal for defect detection in silicon wafers and photovoltaic cells.These results demonstrate YOLOv8-A’s suitability for edge deployment, where both power consumption and inference speed are critical for real-time industrial applications.

The experimental results demonstrate that YOLOv8-A outperforms existing state-of-the-art models in terms of accuracy, speed, and parameter efficiency. Its superior performance in small-target detection and low computational complexity make it highly suitable for real-time industrial applications, particularly in silicon melting processes.