2.1. Dataset Preparation and Wide-Angle Camera Distortion Correction

A custom dataset comprising 1,054 high-resolution images was collected from an industrial net production line. The images were originally captured at a resolution of \(1920 \times 1080\) pixels using a Sanwa Supply wide-lens webcam (USB connection, 150° ultra-wide-angle field of view, 2 megapixels, CMS-V53BK). During the image acquisition, the camera was fixed beneath the production machine at an approximate camera-to-net distance of 8 cm. The same camera position and imaging setup were used for both the dataset collection and production line testing. Although the images were resized to \(640 \times 640\) pixels for YOLOv11 inference, the knot size measurements were converted back to the original \(1920 \times 1080\) image scale. In the original image scale, individual knots were typically represented by approximately \(22 \times 12\) pixels, corresponding to an area of about 264 pixels\(^2\). Based on 146 sampled knots, the approximate knot size ranged from 13 pixels to 33 pixels in width and from 12 pixels to 30 pixels in height. This camera was selected because of its ability to capture large net sections with high spatial coverage, while maintaining sufficient image resolution. The captured images included multiple sections of the net observed under different orientations and perspectives, thereby increasing the dataset diversity while preserving adequate detail for accurate knot detection.

For model training, all images were resized to \(640 \times 640\) pixels to conform to the input requirements of YOLOv11, while balancing computational efficiency with sufficient feature representation. Resizing the original \(1920 \times 1080\) images to \(640 \times 640\) inevitably reduced the pixel representation of individual knots. However, the knots remained visible and detectable because their bounding boxes, when mapped back to the original image scale, were approximately \(22 \times 12\) pixels. The use of high-resolution source images also helped preserve sufficient knot texture and contrast after resizing. Cropping or tiling was considered as an alternative approach to preserve more local details for small knots. However, a full-frame \(640 \times 640\) input was selected in this study because it retained the global row-wise mesh arrangement required by the linking logic, avoided duplicate detections across tile boundaries, and simplified the inference process computationally. Cropping or tiling may be beneficial for future applications involving smaller knots, larger images, or more severe scale variations. To ensure accurate spatial measurements and preserve real-world distance relationships, all images captured with the 150° ultrawide-angle lens were preprocessed using a camera distortion correction procedure, as illustrated in Fig. 2.

The intrinsic camera parameters (\(f_x\), \(f_y\), \(c_x\), and \(c_y\)) and lens distortion coefficients (\(k_1\), \(k_2\), \(k_3\), \(p_1\), and \(p_2\)) were obtained using a standard camera calibration procedure based on a planar checkerboard pattern ¹⁹,²⁰. Multiple images of a known checkerboard (a \(6 \times 8\) grid with a square size of 20 mm) were captured at different orientations and positions under uniform illumination.

The checkerboard corner points were automatically detected using OpenCV’s findChessboardCorners() function, and the camera parameters were estimated using the calibrateCamera() function. This process minimized the reprojection error between the observed and projected corner points, yielding an optimized camera matrix and distortion coefficients that characterized the lens geometry. The resulting parameters were then applied to image rectification using cv2.undistort() prior to model training.

The distortion correction followed the standard pinhole camera model combined with the Brown–Conrady radial-tangential distortion formulation.

The intrinsic camera matrix \(K\) is defined as

The radial and tangential distortions are modeled as

The dataset reflects a broad range of real-world conditions, including varying lighting environments and zoomed-in and zoomed-out views ²¹. All images were meticulously annotated with bounding boxes using Roboflow, which provides a user-friendly annotation interface, consistent labeling formats, and integrated quality control tools.

This ensured precise and standardized ground-truth labels for supervised training, while also facilitating dataset versioning and direct export in formats compatible with YOLOv11. To promote robust generalization of unseen production scenarios, the dataset included realistic variations in knot orientation, mesh scale, deformation, and illumination. The dataset was divided into training, validation, and testing subsets using a 70%–15%–15% split, ensuring representative distributions of net configurations across all subsets.

The 100 randomly selected fishing net images described in Section 4.2 were collected separately during production line testing while the machine was running. These images were captured using the same camera setup as the training, validation, and testing datasets, but they were used as an additional practical evaluation set to assess the detection and linking performance under operating conditions. Sample images from the dataset, illustrating the variations in the imaging conditions, are shown in Fig. 3.

2.2. Model Selection and Training

The YOLOv11m (medium) variant was selected as the detection backbone to balance the detection accuracy and computational efficiency, making it suitable for deployment on production hardware. Larger variants such as YOLOv11L and YOLOv11XL generally achieve higher mean average precision (mAP); however, their increased parameter counts and computational demands significantly reduce the inference speed. This trade-off makes them less appropriate for continuous, high-throughput inspection tasks.

Given that the primary system requirement was reliable knot detection under triggered or intermittent high-accuracy inspection, YOLOv11m was selected as an effective compromise between precision and processing speed. The YOLOv11m model contains approximately 13.8 million parameters and requires 28 giga floating point operations per second (GFLOPs) per inference. Compared with the lightweight YOLOv11n variant, it offers higher detection precision while maintaining a practical inference speed for downstream tasks such as distance estimation and defect classification. This balance ensures a smooth integration into the inspection workflow with manageable graphics processing unit (GPU) requirements and acceptable latency.

Training was performed on a custom-annotated dataset using transfer learning from pretrained YOLOv11m weights. The model was trained for 200 epochs with a batch size of 16 and input resolution of \(640 \times 640\) pixels. Automatic mixed precision (AMP) was used to accelerate training and reduce GPU memory consumption. To improve generalization and robustness, a range of data augmentation techniques were applied, including random scaling, translation, brightness variation, horizontal flipping, mosaic augmentation (disabled after the first 10 epochs), copy–paste augmentation, and random erasing. These augmentations enhanced the robustness to variations in net geometry, orientation, and illumination conditions.

By leveraging the improved accuracy of the YOLOv11m variant and comprehensive data augmentation, the trained system achieved high-precision knot detection while maintaining acceptable latency for triggered inspection. This made the proposed approach well-suited for deployment in industrial-scale inspection environments without compromising detection reliability.

2.3. Assessment of the Detection Model

The trained knot detection model was assessed using established object detection metrics: precision (\(P\)), recall (\(R\)), and mean average precision (mAP). Evaluations were performed both at a fixed intersection-over-union (IoU) threshold of 0.5 and across a range of thresholds from 0.5 to 0.95. The precision measures the fraction of correct detections among all predictions, whereas the recall expresses the fraction of correctly identified knots relative to the total number of ground-truth instances. The formal definitions of these metrics are given in Eqs. (5) and (6), following ²².

In this study, \(c = 1\), because the model was trained specifically to identify knots in the fishing nets. During training, the loss components associated with the bounding box regression, classification, and objectness were tracked. As illustrated in Fig. 4, these loss values decreased steadily and converged after approximately 180 epochs, suggesting that the network successfully captured the relevant visual features for knot detection.

The curves shown in Figs. 5 and 6 correspond to validation set performance during YOLOv11 training and evaluation. They were generated using the validation subset defined in Section 2.1 and were separated from the additional 100-image production line evaluation described in Section 4.2. The progression of precision and recall values, shown in Fig. 5, indicated that both metrics stabilized after approximately 50 epochs. Their high values, approaching 100%, confirm the robustness of the model when applied to diverse net images.

Figure 6 shows the AP scores across the IoU thresholds. The model achieved nearly perfect detection, as indicated by the mAP50, as well as strong performance, as indicated by the mAP50–95 of 0.86, confirming robustness even under stricter evaluation criteria. The final trained detector achieved an overall accuracy of 0.983 and a recall of 0.979, indicating that 98.3% of the predictions were correct and 97.9% of all knots were successfully localized. These results highlight the effective balance between precision and recall, thereby reinforcing the suitability of the model for deployment on automated net inspection systems.

In conclusion, the YOLOv11m-based detector demonstrated high reliability in identifying knots under different conditions of overlap and deformation. Its high detection accuracy and efficiency render it suitable for integration into real-world industrial inspection pipelines.

3.1. Knot Position and Centroid Extraction

Once the YOLOv11 model detects a knot, it is localized by a bounding box, which is defined as

These centroids provide a precise spatial representation of the knot positions within the image. Formally, the set of all the knot centroids is denoted as

3.2. Linking Logic and Distance Measurement Using KNN Regression Model

The KNN regression model was selected because the pixel-to-distance relationship after wide-angle correction was not strictly linear across the image plane. Although camera undistortion reduced the dominant radial distortion, residual nonlinear effects could still persist because of the ultrawide lens, local perspective variation, centroid localization error, and small changes in the knot shape. A global linear regression model represents the entire calibration range using a single slope and intercept, which may be insufficient in the presence of local variations. In contrast, KNN regression is a nonparametric local estimation method. For each measured pixel distance, the prediction is calculated from nearby calibration samples, rather than from a single global function. This makes the KNN regression model suitable for the proposed calibration task because the calibration samples cover the expected measurement range of the net, allowing local interpolation within the operating range. However, the KNN regression model is not intended for reliable extrapolation outside the calibrated range, and additional calibration points are required if the camera position, mesh size, or measurement region changes significantly.

The proposed linking logic was designed for regular knotted nets with a diamond-shaped mesh topology. In this topology, knots were arranged in staggered rows, and each knot was expected to connect diagonally to at most two neighboring knots in the next row. Therefore, this method assumed a repeated diamond mesh pattern, a fixed camera position, and a known target mesh eye size for calibration and quality assessment.

In practice, the row and column relationships are determined from the detected knot centroids. After knot detection, each bounding box was converted into a centroid coordinate \((c_{x}, c_{y})\). The expected mesh spacing in the pixels was estimated from the calibration model and target mesh size. The image height was then divided into row regions according to this expected spacing, whereas the image width was divided into column regions. Each detected centroid was assigned to a row and column index based on its pixel location.

For the centroid located in row \(r\) and column \(c\), the next row is defined as row \(r+1\). The same column refers to column \(c\) in the next row, while the adjacent columns refer to columns \(c-1\) and \(c+1\), when they exist. Therefore, the candidate knots for linking were searched only in row \(r+1\) and within columns \(c-1\), \(c\), and \(c+1\). This restricted search prevented long-range or physically implausible connections.

The linking logic connected knots sequentially from the top row to the bottom row to reconstruct the diamond-shaped mesh structure.

To illustrate this concept, one knot was selected as the reference knot and labeled \(K_0\), as shown in Fig. 8. Linking was performed only between two consecutive rows to avoid physically implausible long-range connections. For the reference knot \(K_0\), the candidate knots were searched exclusively in the immediately following row \((r+1)\) and restricted to the same column and its adjacent columns. This constrained search region ensured that only local and physically valid neighbors were considered.

The candidate knots were then divided into two groups according to their horizontal positions relative to \(K_0\). The knots located to the left of \(K_0\) formed the left candidate set \(C_L\), and the knots located to the right formed the right candidate set \(C_R\). The nearest knot was selected from each candidate set to form the diagonal connections. The closest knot in \(C_L\) was labeled \(P_L\), and the closest knot in \(C_R\) was labeled \(P_R\), where the closeness was determined by the smallest horizontal displacement. If no candidate existed on one side, the corresponding connection was omitted. For each reference knot, the Euclidean distance to all candidate knots in the permitted neighboring cells was calculated. The candidates were sorted by distance, and up to two closest candidates were selected as links. This corresponded to the physical structure of a diamond-shaped knotted mesh in which each knot was connected diagonally to at most two knots in the next row. If no valid candidate was found on one side, that link was omitted rather than replaced by a distant knot.

Consequently, each knot established up to two diagonal links to the next row: a left link to the \(P_L\) and a right link to the \(P_R\). The same linking procedure was then applied to \(P_L\) and \(P_R\) as new reference knots in subsequent rows. Repeating this process row by row naturally produced the characteristic X-shaped and diamond-shaped mesh topologies observed in fishing nets.

For other net structures such as rectangular, square, hexagonal, or irregular mesh patterns, the knot detection stage can still be used if the knots are visually similar to those in the training data. However, the row-indexing strategy, neighbor-search region, expected number of links per knot, and quality threshold definition should be modified according to the corresponding mesh topology. In addition, the pixel-to-distance calibration should be repeated whenever the camera position, net type, or target mesh size changes.

For each valid connection, the Euclidean distance is computed in pixel units and is defined as

The fishing net evaluated in this study was designed with the target mesh eye size \(\mu\), specified by the manufacturer as 100% (normalized measurement). This value represents the target reference against which all measured knot distances were evaluated. To avoid the disclosure of absolute dimensional specifications and enable a scale-independent evaluation, all the measured distances were normalized with respect to the target mesh size. The accurate conversion of pixel distances to real-world metric measurements is essential for quantitative quality assessment. Although a preliminary wide-angle correction was applied (Section 2.1), residual nonlinearities may persist in the rectified image plane because of the 150° ultrawide lens. The KNN regression model was selected as the candidate calibration model because it demonstrated strong performance in mapping pixel-based measurements to real-world targets in related visual inspection and net mesh size measurement tasks using YOLO-derived outputs ²⁴,²⁵. To address this issue, two regression approaches were evaluated using a calibration dataset comprising 45 distance measurements, as shown in Fig. 9.

Linear regression (LR) assumes global linear mapping, whereas KNN regression directly predicts the real-world distances based on local neighborhoods in the calibration data. The linear regression model is represented as

The dataset was divided into training and testing sets (80% and 20%, respectively) using stratified sampling to ensure representative coverage across the entire distance range. Hyperparameter optimization for the KNN regression model was performed for \(k = 1\)–10, and the model performance was evaluated on the held-out testing set using the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination \(R^2\) metrics. As shown in Fig. 10, the optimal value was \(k = 4\), which yielded the smallest prediction error. Using the testing set, the KNN regression model with \(k = 4\) achieved an MAE of 2.31%, RMSE of 2.45%, and \(R^2\) of 0.995, significantly outperforming the linear regression model (\(\textrm{MAE} = 3.94{\%}\), \(\textrm{RMSE} = 4.53{\%}\), and \(R^{2} = 0.983\)). These results indicated the presence of mild nonlinearities in the pixel-to-distance relationship, which the KNN regression model captured more effectively than the global linear regression model.

Figure 11 compares the predicted and actual distances for both regression models. The linear regression model exhibited systematic overestimation and underestimation, particularly at larger pixel distances, whereas the KNN regression model with \(k = 4\) closely followed the nonlinear calibration curve and significantly reduced the prediction error.

Table 1 summarizes the numerical prediction results obtained for the representative test samples. The linear regression model showed consistent systematic bias across the calibration range, whereas the KNN regression model maintained substantially lower absolute errors, with all deviations confined to within \(\pm\)3.53%.

Each measured distance was evaluated against quality thresholds defined by \(\mu \pm \varepsilon\), where \(\mu\) denotes the expected mesh eye size and \(\varepsilon\) represents the user-defined tolerance. Connections were classified as acceptable, overtensioned, or undertensioned and were visualized using green, red, and orange lines, respectively. By enforcing directional, row-wise linking with constrained spatial neighborhoods, the proposed method preserved the mesh topology while enabling a reliable and interpretable quality assessment.

4.1. Knot Detection

For evaluation, an \(\textrm{IoU} = 0.5\) was used as the main detection-matching threshold because it is a standard criterion for object-detection evaluation, following the PASCAL VOC evaluation protocol ²⁶. In addition, mAP50–95 has been reported to provide a stricter assessment of the localization performance across multiple IoU thresholds, following the MS COCO evaluation protocol ²⁷. The proposed YOLOv11-based detection framework demonstrated high accuracy in identifying knots within the fishing net images. For each detected knot, the model outputted a bounding box, parameterized by its top-left and bottom-right coordinates, as defined in Eq. (9). These bounding boxes provided not only the location but also the scale of each detected knot, ensuring robust detection even under varying lighting and background conditions.

From each bounding box, the centroid was calculated using Eq. (10) and served as a compact and representative feature of the spatial position of the knot. These centroids were particularly important because they formed the basis for distance calculations between knots, enabling the quantitative evaluation of mesh uniformity. Therefore, accurate centroid localization was a crucial step in the transition from object detection to geometric analysis of the net structure.

Figure 12 shows the sample outputs from the detection pipeline. The bounding boxes (green rectangles) delineate the detected knots and the corresponding centroids are marked by red points. This combination of bounding box detection and centroid extraction created a reliable representation of knot locations across the image, facilitating further processing stages, such as distance measurement, mesh consistency evaluation, and defect identification.

4.2. Detection Accuracy

To evaluate the knot detection performance, the proposed YOLOv11 model was tested on 100 randomly selected fishing net images. The ground-truth knot count (gt_count), detected knot count (det_count), and matched knot count (matched_count) were recorded for each image. The detection accuracy, computed as the ratio of matched predictions to ground-truth knots, ranged from 90.60% to 97.30%, with a mean value of 94.87%. These results show that the detector consistently localized most knots despite variations in lighting, contrast, mesh deformation, and partial occlusion. The results are summarized in Table 2.

Figure 13 shows the per-image accuracy distribution. The values clustered tightly at approximately 95%, demonstrating stable performance across diverse environmental and imaging conditions. Although the detector did not achieve a perfect score of 100%, this did not hinder the subsequent measurement stages. The linking logic relied on pairs of correctly detected knots and not on the exhaustive detection of every knot in the frame. Missed detection typically occurred near the image boundaries or in low-contrast zones that had a minimal contribution to the core measurement region. Thus, the mesh structure could still be reliably reconstructed.

Furthermore, the YOLOv11 model achieved strong localization quality (\(\textrm{mAP50} = 0.99\) and \(\textrm{mAP50–95} = 0.86\)), indicating that nearly all detected knots had accurate bounding boxes. The small number of unmatched cases typically arose from annotation ambiguity or borderline detections, rather than systematic model failures. Because the downstream pipeline used the centroid positions of the correctly detected knots, the effect of these minor discrepancies on the real-world distance estimation was negligible. Overall, the achieved mean accuracy of 94.87% was sufficient to support the measurements of the proposed inspection system. The robustness of the detection stage provided a strong foundation for linking logic and geometric reconstruction, as described in the following section.

4.3. Linking Logic and Distance Measurement

Figure 14 shows the output of the proposed linking algorithm applied to the detected knot centroids. The reconstructed X-pattern accurately represented the geometric structure of the fishing net, demonstrating that the system could reliably group knots into aligned rows and form consistent diagonal and vertical connections. This behavior remained stable even in the presence of mild occlusion, irregular illumination, or small detection gaps. To quantitatively evaluate the robustness of this linking stage, a link success analysis was performed on 100 randomly selected evaluation images. The expected number of links was computed from the ground-truth annotations, whereas the predicted links were obtained from the linking logic based on the detected knots. The link success rate is defined as

More importantly, the linking logic did not generate crossed, duplicated, or structurally inconsistent connections, even when knot detections were missing. Instead, it only omitted links for which insufficient evidence was available. Consequently, the reconstructed mesh remained geometrically valid and suitable for the subsequent pixel-to-millimeter conversion and quality assessment. This robustness ensured that the overall inspection pipeline functioned reliably under real-world production conditions, even when the detection stage was not flawless.

4.4. Real-World Distance Estimation

This methodology allowed the automated and quantitative measurement of fishing net mesh size, bridging the gap between image-based detection and actual net geometry. By leveraging the previously established linking logic, the system ensured that the measurements were derived from valid knot pairs, maintaining structural consistency while providing accurate real-world distance estimates.

An important factor influencing the measurement accuracy was the image rectification applied to compensate for the 150° ultrawide-angle lens. Although the undistortion step corrected most of the radial deformation, small residual nonlinearities persisted across the rectified image plane, particularly toward the periphery, where the stretching and compression effects were more pronounced. These residual distortions directly affected pixel-to-millimeter mapping, where equal pixel distances in different regions of an image did not always correspond to equal real-world distances. This necessitated the use of a data-driven regression model, particularly KNN regression, which adapted locally to the calibration data and compensated for the remaining nonlinear behavior more effectively than a global linear model.

To validate the reliability of the regression-based pixel-to-millimeter conversion, a comprehensive analysis was performed using 100 random samples collected within the expected ideal range. The KNN regression model generated the corresponding predicted measurements for each sample.

Figure 15 shows the three key diagnostic plots used to assess the model behavior. Fig. 15(a) shows the distribution of actual versus predicted mesh distances. Dense clustering along the one-to-one reference line indicated a strong agreement between the true and estimated values. Fig. 15(b) shows the prediction error distribution, which was sharply centered at zero, confirming the absence of systematic overestimation or underestimation. Finally, the residual distribution in Fig. 15(c) exhibited a scattered residual concentrating around zero, demonstrating stable model behavior and consistent generalization across the full range of measurements.

In addition to these regression diagnostics, Fig. 16 provides a qualitative visualization of the final mesh measurement pipeline. The detected knot pairs were connected by color-coded lines, indicating the mesh size quality relative to the nominal specification. The reference mesh eye size of the evaluated fishing nets was considered to be 100%. In this study, the \(\pm\)5% tolerance band was selected arbitrarily for demonstration purposes and does not represent an industry standard or manufacturer-specified acceptance criterion. In practical deployment, the threshold should be replaced by the manufacturer’s specifications or an applicable quality control standard. The threshold was used only to illustrate how the proposed system could classify and visualize the mesh size deviations once a tolerance value was specified.

The KNN regression model showed a maximum observed prediction error of \(\pm\)3.53% for the test samples. Because this error was relatively close to the demonstration threshold of \(\pm\)5%, measurements near the decision boundary may be misclassified if evaluated from a single measurement alone. Therefore, the color-coded classification should be interpreted as a proof-of-concept visualization, rather than as a finalized industrial pass or fail rule.

In practice, borderline measurements should be performed using repeated measurements, a wider warning zone, or confirmation from neighboring mesh measurements.

Green lines represent measurements that fall within this tolerance range and therefore correspond to meshes that satisfy the nominal production requirement.

Orange lines indicate slightly undersized meshes, where the measured distance is less than 5% of the target mesh size, signaling localized compression or reduced tension. Red lines highlight oversized or overtensioned meshes in which the measured spacing exceeds 5% of the target mesh. These deviations may arise from manufacturing inconsistencies, uneven stretching, or local distortions during handling.

It is worth noting that for the purpose of demonstrating the sensitivity of the proposed inspection system, the net machine settings were intentionally left in a mildly nonoptimal configuration during this test. This setup introduced controlled variability in the mesh spacing, enabling the system to reveal a higher occurrence of orange and red classifications in the visualization. Consequently, Fig. 16 highlights the ability of the system to detect subtle deviations that may not be easily observed through manual inspection. The visualization illustrates not only the geometric reconstruction of the mesh but also the spatial distribution of quality deviations across the net. By encoding the measurement errors directly on the image, the system enabled the rapid identification of tension imbalances, gradual drift in mesh spacing, and localized defects that may require corrective action during production.