Because the seedling tray image includes some non-detection areas such as the border of the seedling tray, it is necessary to locate the detection area. The vertical projection method (Chen et al., 2021) is used to solve this problem in this paper.

The vertical projection method is as follows: In the binary seedling tray image ( Figure 4 ), white oval dots represent seeds with a grayscale value of 0, while black areas represent non-seed parts such as seedling soil or the border of the seedling tray, with a grayscale value of 1. The cumulative grayscale values for each row and each column are computed in pixel units, following the methods described in Equations 1 and 2.

where W and H represent the number of rows and columns, respectively. In this paper, W = 4,032 and H = 2,268. w(i) represents the cumulative grayscale value of the ith row, h(j) represents the cumulative grayscale value of the jth column, and p(i,j) represents the grayscale value of the corresponding pixel at the ith row and jth column.

Based on the grayscale values of the binary image, a vertical projection curve ( Figure 5A ) was plotted with the number of horizontal pixels as abscissa and the cumulative grayscale value of each column as ordinate. Similarly, a horizontal projection curve ( Figure 5B ) was plotted with the number of vertical pixels as abscissa and the cumulative grayscale value of each row as ordinate. As shown in Figure 5 , there are four abrupt segments on both sides of the images of the vertical projection curve and the horizontal projection, namely, A₁B₁, C₁D₁, or A₂B₂, C₂D₂. In segments A₁B₁ and A₂B₂, the cumulative grayscale value suddenly increases from 0 to a larger value, owing to the appearance of the border of the seedling tray in the image, in which A₁ and A₂ represent the outer side of the seedling tray border, while B₁ and B₂ represent the inner side of the seedling tray border. Conversely, in segments C₁D₁ and C₂D₂, the cumulative grayscale value suddenly drops from a larger value to 0. The reason for this is that the border of the seedling tray in the image disappears. At this point, C₁ and C₂ represent the inside of the seedling tray border, while D₁ and D₂ represent the outside of the seedling tray border. This indicates that A₁B₁, C₁D₁, A₂B₂, and C₂D₂ respectively represent the positions of the four borders of the seedling tray. Taking the positions of the pixel numbers corresponding to B₁, C₁, B₂, and C₂ as the positions of the four edge lines of the detection area, then the detection area is located.

In general, in order to distinguish the description of pots in a pot tray, it is customary to refer to the unit area of blanket tray as the seed grid. A seed grid in a blanket tray is equivalent to one pot in the pot tray. In order to evaluate the sowing uniformity of blanket-seedling nursing, it is necessary to manually divide seed grids and mark them in seed images.

Without considering the deformation of seedling blocks, one seed grid is equal to the unit seedling-taken area during mechanical transplanting. A unit seedling-taken area of mechanical transplanting = horizontal seedling cutting quantity × longitudinal seedling cutting quantity. Therefore, the key to dividing seed grids is to determine the horizontal seedling cutting quantity and the longitudinal seedling cutting quantity. In theory, the number of seeds in the seed grid is the basis for estimating the number of seedlings per hill in the field during mechanical transplanting. Practical experience shows that the actual germination rate of hybrid rice seeds is from 75% to 85% (Li et al., 2019). To achieve high-yield cultivation of hybrid rice, theoretically, the number of seeds in one seed grid is relatively suitable at 2.7–2.9. At this time, the average number of seedlings per hill is 2–2.5. Therefore, the method for dividing seed grids in seed images is as follows:

In hybrid rice blanket-seedling nursing with strip sowing, an 18-row seeder is usually used for sowing. After sowing, the seeds in the seedling tray appear as 18 seed strips. Therefore, the seed image is evenly divided into 18 parts horizontally. At this time, the number of cutting times of horizontal seedling by seedling claw of the rice transplanter is 18, and the horizontal seedling cutting quantity is 15.6 mm (208 mm ÷ 18 = 15.6 mm). The number of cutting times of longitudinal seedling by seedling claw of the rice transplanter is determined by the longitudinal seedling cutting quantity. The longitudinal seedling cutting quantity is set by the longitudinal seedling feeding mechanism of the transplanter. Usually, the adjustment range for the longitudinal seedling feeding mechanism is from 8 to 18 mm. There are 11 gears available, with a 1-mm interval between each gear.

In order to achieve the target of precise transplanting of one to three seedlings per hill, the number of seed grids per tray is related to the sowing density. The higher the sowing density, the more the seed grids there will be. According to the thousand-grain weight and sowing density of hybrid rice seeds, the number and the division method of seed grids under different sowing densities are calculated as shown in Table 1 .

In Table 1 , the thousand-grain weight of hybrid rice taifengyou 208 is 24.75 g. When the sowing density is 50 g/tray, theoretically, there are approximately 2,020 seeds per tray. If the number of seed grids per tray is set to 738 grids (18 rows × 41 columns = 738 grids), then the average number of seeds per grid is 2.74, which meets the agronomic requirements. Similarly, when the sowing density is 60 g/tray and 70 g/tray, the seed grids per tray is 864 grids (18 rows × 48 columns) and 1,044 grids (18 rows × 58 columns), respectively. Theoretically, the number of seeds per grid is approximately 2.81 and 2.71, respectively.

The full name of ODConv is Omni Dimensional Dynamic Convolution, also known as Full Dimensional Dynamic Convolution. This method was first introduced in the article by Li et al. (2022). The motivation for introducing this module in this article is as follows:

In YOLOv8n, the standard Conv is adopted by the C2f module, which essentially uses the same static convolution kernel to learn from the input samples in each convolution layer. At this point, the extraction of sample feature information is insufficient. To address this, researchers have studied dynamic convolutions, such as DyConv (Chen et al., 2020) and CondConv (Yang et al., 2019). The essence of dynamic convolution is to introduce an attention mechanism that learns a linear combination of n convolutional kernels with attention as weights. For example, the DyConv is defined as:

where x ∈ R h × w × c i n and y ∈ R h × w × c o u t represent the input feature and output feature respectively. h and w represent the height and width of the channels, respectively. c_in and c_out represent the number of input channels and output channels, respectively. W_i represents the ith convolutional kernel. α_wi is an attention scalar that weights W_i , where i = 1,…, n, and * represents the convolution operation. Research has shown that dynamic convolution can effectively improve the accuracy of lightweight convolutional neural networks while ensuring efficient inference (Yang et al., 2019; Chen et al., 2020; Li et al., 2022).

However, dynamic convolution only improves the convolution operation in terms of the number of convolutional kernels, neglecting the spatial kernel size dimension, input channel dimension, and output channel dimension. This reduces the ability of the convolution operation to extract information about sample characteristics. To address this limitation, Li et al. (2022) proposed ODConv based on multi-dimensional attention mechanisms and parallel strategies, defined as:

x represents the input features, while y represents the output features. W_i represents the ith convolutional kernel. α_wi , α_fi , α_ci , and α_si are four attention scalars, respectively, representing the weights of the convolutional kernel W_i (i = 1, …, n) in the dimensions of kernel quantity, output channels, input channels, and spatial kernel size. The structure is shown in Figure 7 , where ⨀ represents the multiplication operator across different dimensions in the kernel space, and * represents the convolution operation.

In brief, in ODConv, α_si assigns different attention to the filters (convolution parameters) at each spatial location (k × k in total, where k is the kernel size). α_ci assigns different attention to each input channel (C_in ). α_fi assigns different attention to each output channel (C_out ). α_wi assigns different attention to each convolutional kernel. These four types of attention are complementary and are multiplied with the convolutional kernel W_i in a sequential order of position, channel, filter, and kernel. This provides performance guarantees for capturing rich temporal and spatial cues. In summary, compared to mainstream dynamic convolutions like DyConv and CondConv, ODConv enhances feature learning capabilities and improves the accuracy of convolutional neural networks by obtaining complementary attention for the convolutional kernels along all dimensions of the kernel space in each convolutional layer. Additionally, ODConv outperforms other attention modules in adjusting output features or convolutional weights.

Considering that the Backbone network and Neck network of the YOLOv8n model mainly rely on the C2f module for connection, the main function of the C2f module is to input the multi-scale feature maps extracted by the Backbone network into the Neck network. To this end, the ODConv module is introduced into the C2f module that connects to the Neck network, which will fully exploit the target feature information across different dimensions. This allows richer image features to be transferred from the Backbone network to the Neck network, thereby enhancing the model’s ability to recognize small and partially occluded targets. Subsequent experiments will show that not only is the model’s performance significantly improved, but also the computational complexity is reduced during the training process.

The seedling soil used for hybrid rice seedling nursing is usually a mixture of peat, vermiculite, coconut coir, clay, specialized fertilizer, and yellow soil. Owing to the different colors and shapes of the components in the seedling soil, a complex background is formed in the seed images of hybrid rice, which interferes with the identification of the number of seeds in a unit seed grid image. In addition, the unit seed grid image is generated by cutting the seed image, and some seeds are cut into incomplete seeds, which also poses some difficulties for accurate seed counting. To improve the model’s focus on seeds, this paper introduces the ECA attention mechanism (Wang et al., 2020) into the Neck network of the model (the introduced location is shown in Figure 6 ). This mechanism enables the network to prioritize the semantic information in the feature map, thereby enhancing the network’s ability to extract deep semantic feature information of detection targets. Thus, the model can better obtain the feature information of seed images while suppressing background information such as seedling soil.

In neural networks, attention mechanisms are typically classified into spatial attention mechanisms and channel attention mechanisms. The channel attention mechanism assigns different weights to the channels of feature maps, allowing the model to have different degrees of attention to different channels of the feature map, thereby capturing local important feature information, suppressing interference feature information, and improving recognition accuracy. ECA is a type of channel attention mechanism that has been improved from the traditional Squeeze and Excitation Networks (SE) attention mechanism. The main improvements include (1) removing the fully connected layers in the SE attention mechanism module; (2) using a one-dimensional convolution to learn features after global average pooling (GAP); and (3) proposing a non-dimensional reduction local cross-channel interaction strategy, effectively avoiding the impact of dimensionality reduction on the learning effect of channel attention. Its module structure is shown in Figure 8 .

In Figure 8 , x represents the input features with dimensions H×W ×C. After global average pooling (GAP), x is compressed into a feature vector of size 1×1×C. A one-dimensional convolution operation is performed on the feature vector, where the kernel size k is adaptively determined. The weights of each channel are computed through a Sigmoid activation function, denoted as σ in Figure 8 . Multiply the weighted feature vector with the input features x to get the output features x ˜ , and in Figure 8 , ⊗ denotes the multiplication.

YOLOv8n’s loss function consists of two parts: classification loss and regression loss. The classification loss is computed using BCE Loss, while the regression loss is computed using CIoU Loss. The formula for calculating CIoU Loss is as follows:

where w, h, and (x, y) represent the width, height, and center coordinates of the predicted bounding box, respectively; w_gt , h_gt , and (x_gt , y_gt ) represent the width, height, and center coordinates of the ground truth bounding box, respectively; W_g and H_g represent the width and height of the smallest enclosing rectangle that contains both the ground truth and predicted bounding boxes; W_i and H_i denote the width and height of the intersection area between the ground truth and predicted bounding boxes. α is a weighting function used to balance the parameters, and v is a parameter used to measure the consistency of the length–width ratio, as shown in Figure 9 .

Although the CIoU loss function considers overlapping area, distance, and aspect ratio, CIoU employs a monotonic focusing mechanism. This means that the bounding box regression loss uses fixed weights to balance the losses of position and scale. Because of the influence of geometric factors such as distance and aspect ratio, this can increase the penalty on low-quality samples and reduce the generalization performance of the YOLOv8n model. Specifically, when the aspect ratio of the predicted box and the ground truth box are linearly related, the penalty term of CIoU degrades to zero. In this case, whether the anchor boxes are of high quality or low quality, it can be detrimental to the regression loss (Tong et al., 2023).

Owing to the artificial cutting of some seeds in the unit seed grid image, there are some low-quality anchor boxes. Therefore, this paper chooses the dynamic non-monotonic focusing mechanism of the WIoU loss function to replace the original CIoU loss function. Essentially, the WIoU loss function adaptively adjusts the weights of regression loss based on the importance of the targets by introducing an attention mechanism. This helps to better balance the losses of position and scale, thereby balancing low-quality and high-quality samples to improve the accuracy of object detection. There are currently three versions of WIoU: WIoUv1, WIoUv2, and WIoUv3, among which WIoUv2 and WIoUv3 are enhanced versions of WIoUv1 (Tong et al., 2023). WIoUv3 is used in this paper, which is defined as follows:

where r represents the non-monotonic focusing coefficient, β represents the outlier degree, and α and δ represent hyperparameters, which are set to 1.9 and 3, respectively. L IoU ¯ denotes the moving average, and L ˜ IoU indicates an operation that separates from the computation graph, making it a constant without gradients. When R WIoU ∈ [ 1 , e ) , it increases the L _IoU of medium-quality anchor boxes, and when L IoU ∈ [ 0 , 1 ] , it reduces the R _WIoU of high-quality anchor boxes.

WIoUv3 uses the outlier degree β instead of the overlap area IoU to evaluate the quality of the anchor box. Since the moving average is dynamic, the standard for classifying anchor box quality is also dynamic. The non-monotonic focusing coefficient r is constructed from the outlier degree and hyperparameters. It can reduce the gradient gain of the loss function on high-quality samples and decrease the harmful gradients generated by low-quality anchor boxes, allowing WIoUv3 to focus on medium-quality anchor boxes.

After dividing the seed images into unit seed grid images, the seeds located on the boundaries of the seed grids may encounter the problem of misjudging the ownership of the seed grid.

Overall, there are four situations regarding the positional relationship between seeds and seed grids (as shown in Figure 10 ): (a) Seeds do not intersect with the boundaries of seed grids, and seeds completely fall within a certain seed grid; (b) the seed intersects with one seed grid boundary and falls into two adjacent seed grids; (c) the seeds intersect with the boundaries of two seed grids, and the seeds fall into three adjacent seed grids; (d) the seeds intersect with the boundaries of the four seed grids, and the seeds fall within the adjacent four seed grids.

At present, there is no good way to determine which seed grid a seed belongs to when there is a cross between the seed and the seed grid. In this paper, an area-based approach is employed to determine the ownership of seeds within seed grids. Specifically, the seed grid with the largest proportion of the area of the seed in the adjacent four seed grids is considered as the seed’s belonging grid. The specific method is as follows: According to the OEW-YOLOv8n model provided in the following text, the seed recognition box covers the area size within four adjacent seed grids for discrimination, and the seed grid with the largest coverage area is the seed grid where the seed belongs.

The key to evaluating the uniformity of seed images using uniform qualification rate is to calculate the number of qualified seed grid images for each seed image. According to the national standard of the People’s Republic of China “Rice Transplanter-Test Method” (GB/T 6243-2017), the uniformity qualification rate is calculated as follows: the uniformity qualification rate = (number of qualified small seedling blocks/total number of seedling blocks tested) × 100%. Because of the agronomic requirement of planting one to three seedlings per hill in hybrid rice cultivation, this article uses the qualification rate of one to three seeds per grid as the evaluation indicator of sowing uniformity. The qualification rate of one to three seeds per grid is calculated as: The qualification rate of one to three seeds per grid = (number of grids with one to three seeds per grid ÷ total number of seed grids per tray) × 100%.

The results of the ablation experiment are shown in Table 3 .

Based on Table 3 , it is evident that after replacing the Conv module in the YOLOv8n network with the ODConv module in Experiment 1, the Params and model size slightly increased, but the FLOPs decreased. The precision (P), recall (R), and mAP of the model increased by 2.8%, 3.1%, and 1.3%, respectively. The RMSE decreased by 12%. Experiments 2 and 3 showed that adding ECA attention mechanism or replacing CIoU loss function with the WIoUv3 loss function did not significantly change the Parms, FLOPs, and model size. The precision of the model increased by 1.9% and 1.5%, the recall increased by 2% and 2.2%, and the mAP increased by 0.6% and 0.4%, respectively. The RMSE decreased by 4% and 2%. These experiments demonstrate that both the ECA attention mechanism and the WIoUv3 loss function can enhance the model’s detection accuracy. Experiment 4 is an experiment adding the ECA attention mechanism on Experiment 1. The Params and FLOPs remained nearly unchanged, while the model size slightly increased. The precision, recall, and mAP further improved, with the mAP increasing from 97.4% to 98.1%, an increment of 0.7%. The RMSE decreased by 23.7%. Experiment 5: Building on Experiment 1 by replacing the CIoU loss function with the WIoUv3 loss function, there was no significant change in the Params, FLOPs, and model size. However, precision, recall, and mAP improved by 0.1%, 0.9%, and 0.3%, respectively. The RMSE decreased by 7%. Experiment 6: Building on Experiment 2 by replacing the CIoU loss function with the WIoUv3 loss function, the Params, FLOPs, and model size remained largely unchanged, with improvements observed in precision, recall, and mAP. The RMSE decreased by 2%. Experiment 7: Building on Experiment 4 by replacing the CIoU loss function with the WIoUv3 loss function, the Params, FLOPs, and model size remained largely unchanged. Precision, recall, and mAP improved by 0.6%, 0.4%, and 0.5%, respectively. The RMSE decreased by 10%.

In summary, using the ODConv module to replace the original Conv module slightly increases the Params and model size, but reduces the FLOPs by 0.2 G and improves the mAP by 1.3%. Adding the ECA attention mechanism does not significantly change the model’s complexity, yet it raises the model’s mAP by approximately 0.6%. Replacing the CIoU loss function with the WIoUv3 loss function also does not alter the model’s complexity, but the precision improves by 0.4%. Implementing all three strategies simultaneously results in an increase of 0.34 M in Params, 0.71 MB in model size, a reduction of 0.2 G in FLOPs, and improvements in precision, recall, and mAP by 4.5%, 4.8%, and 2.5%, respectively. This indicates that all three improvement strategies enhance the model’s detection accuracy and have a cumulative effect, with the ODConv having the most significant impact. The slight increase in Params and model size is primarily due to the introduction of the ODConv module.

To examine the impact of different strategies on the convergence speed of the model, Figure 11 shows the curve of mAP of different models in the ablation experiment as the number of model iterations changes.

From Figure 11 , it can be found that after approximately 25 iterations, the fluctuations in the mAP curve begin to diminish, and after approximately 150 iterations, the mAP curve tends to stabilize. This indicates that all models exhibit good convergence speed. Among them, Experiment 7 performs the best, while Experiment 0 performs the worst. This demonstrates that all three improvement strategies enhance convergence speed, and employing all three strategies simultaneously can achieve relatively faster convergence speeds and higher convergence values.

In this study, the bounding box regression loss function has a significant impact on the accurate identification of the number of seeds in a unit seed grid. In existing deep learning models, common regression loss functions include CIoU, EIoU, SIoU, and WIoU. The loss function of the YOLOv8n model is CIoU. In order to investigate the influence of different regression loss functions on the performance of the OEW-YOLOv8n model, the convergence of OEW-YOLOv8n under different loss functions was compared and analyzed. The experimental results are illustrated in Figure 12 .

As shown in Figure 12 , when the bounding box regression loss function adopts EIoU, the convergence speed of the model is the slowest, and the final loss value after convergence is the highest. When using the CIoU loss function, its convergence speed and final loss value are almost equivalent to EIoU (shown in the graph as the red and gray lines overlapping). The convergence speed of using SIoU is slightly higher than that of EIoU and CIoU, and the final loss value after convergence is slightly lower than EIoU and CIoU. When WIoU is adopted, the convergence speed of the model is the fastest, converging approximately after 25 iterations. Although there are some fluctuations in the final loss value after convergence, which may be related to the use of non-monotonic focusing mechanism, the final loss value after convergence is significantly lower than those of the other three loss functions. The ablation experiment in Section 3.3.1 also showed that the use of WIoU resulted in some improvement in mAP. Therefore, this paper adopts WIoU to replace the CIoU loss function.

To evaluate the performance of the OEW-YOLOv8n model, comparative experiments were conducted with advanced object detection networks such as Faster-RCNN, SSD, YOLOv4, YOLOv5s, YOLOv7-tiny, and YOLOv10s. The dataset used in these experiments is the seed grid images used in this study. The experimental results are shown in Table 4 .

According to Table 4 , the Params, FLOPs, model size, and RMSE of the OEW-YOLOv8n model are all smaller than those of the other five models. Compared to Faster-RCNN, SSD, YOLOv4, YOLOv5s, YOLOv7-tiny, and YOLOv10s, the Params of the OEW-YOLOv8n model is reduced by 133.33 M, 20.26 M, 60.59 M, 3.48 M, 2.67 M, and 3.84 M, respectively. The FLOPs are reduced by 191.3 G, 265.2 G, 51.9 G, 7.9 G, 5.2 G, and 13.6 G, respectively, and the model size is reduced by 103.92 MB, 85.94 MB, 243.41 MB, 6.89 MB, 5.19 MB, and 7.85 MB, respectively. These indicate that the complexity of the model has significantly decreased. Conversely, the mAP of the OEW-YOLOv8n model is higher than that of the other five models, with improvements of 5.2%, 7.8%, 4.9%, 2.8%, 2.9%, and 3.3% over Faster-RCNN, SSD, YOLOv4, YOLOv5s, YOLOv7-tiny, and YOLOv10s, respectively. The RMSE is reduced by 0.331, 0.464, 0.321, 0.245, 0.275, and 0.298, respectively. Overall, the two-stage network model Faster-RCNN has high model complexity and low recognition accuracy. The one-stage network models such as SSD, YOLOv4, YOLOv5s, YOLOv7-tiny, and YOLOv10s have a relatively lower model complexity and a higher recognition accuracy.

To analyze the reasons for the differences in detection performance among different object detection models, Figure 13 shows the detection results of a representative seed grid under different sowing densities and sowing methods. In the experiment, to increase the number of seeds and reduce the segmentation of seeds during seed grid division and test the generalization ability of the model, a seed image was divided into 144 seed grids according to a specification of 9 times by 16 times in the experiment.

From Figure 13 , it can be seen that the SSD model performs the worst, with a large number of missed detections. For example, in cell B3, there are 13 seeds in the image (with 11 actual effective seeds), but the SSD model only identifies 8 seeds, missing 5 seeds, resulting in a 38.46% miss rate. In the SSD model, the missed seeds are mainly defective seeds at the edges of the image or seeds that are obscured. While Faster-RCNN, YOLOv4, YOLOv5s, YOLOv7-tiny, and YOLOv10s can identify defective seeds at the image edges, they also exhibit missed detections and have poor recognition accuracy for seeds obscured by seedling soil. The OEW-YOLOv8n model performs very well overall, capable of identifying both defective seeds at the image edges and obscured seeds, with almost no missed detections.

In summary, compared to the existing advanced networks, the improved OEW-YOLOv8n model performs better in detecting the number of seeds per unit seed grid.