Corn Plant In-Row Distance Analysis Based on Unmanned Aerial Vehicle Imagery and Row-Unit Dynamics

Abstract

Uniform spatial distribution of plants is crucial in arable crops. Seeding quality is affected by numerous parameters, including the working speed and vibrations of the seeder. Therefore, investigating effective and rapid methods to evaluate seeding quality and the parameters affecting the seeders’ performance is of high importance. With the latest advancements in unmanned aerial vehicle (UAV) technology, the potential for acquiring accurate agricultural data has significantly increased, making UAVs an ideal tool for scouting applications in agricultural systems. This study investigates the effectiveness of utilizing different plant recognition algorithms applied to UAV-derived images for evaluating seeder performance based on detected plant spacings. Additionally, it examines the impact of seeding unit vibrations on seeding quality by analyzing accelerometer data installed on the seeder. For the image analysis, three plant recognition approaches were tested: an unsupervised segmentation method based on the Visible Atmospherically Resistant Index (VARI), template matching (TM), and a deep learning model called Mask R-CNN. The Mask R-CNN model demonstrated the highest recognition reliability at 96.7%, excelling in detecting seeding errors such as misses and doubles, as well as in evaluating the quality of feed index and precision when compared to ground-truth data. Although the VARI-based unsupervised method and TM outperformed Mask R-CNN in recognizing double spacings, overall, the Mask R-CNN was the most promising. Vibration analysis indicated that the seeder’s working speed significantly affected seeding quality. These findings suggest areas for potential improvements in machine technology to improve sowing operations.

1. Introduction

With 202 million hectares [1], corn is one of the most widely grown cereal crops in various parts of the world. Corn production accounts for about half of all arable land in Serbia. According to the Food and Agricultural Organization [2], the total amount of corn grain produced in 2019 (7.3 Mt) nominates Serbia as a highly ranked world producer (19th place), and it has become a strategic export commodity.

Ensuring a uniform spatial distribution of plants is crucial in field agricultural production, especially for wide-row crops. Crops with robust plants necessitate a larger amount of open space for proper growth, highlighting the significance of evenly spacing the plants [3]. Furthermore, maize hybrid seed production heavily depends on the consistency of plant growth, which has a direct effect on subsequent operations, such as the elimination of off-types or the removal of tassels from the females [4]. Also, the success of weed control is strongly influenced by the quality of seeding, as the presence of empty areas resulting from seeding errors increases the likelihood of weed proliferation [5]. With the introduction of heavy-weight agriculture machinery, field conditions have become more difficult (soil is less homogenous and more compacted with a greater presence of plant residue), and high accuracy of seeding and uniform plant germination are far more complex to achieve [6].

The assessment of seeding quality for wide-row crops is conducted based on the guidelines outlined in ISO 7256/1 [7]. Sowing quality may be determined in the field either immediately after seeding or after plant germination. Both methods are time- and labor-demanding and include certain disadvantages in terms of limited sample size, seed in-furrow site disturbance during digging, reduction of plant population by pests, etc.

With the technological breakthrough of the last decade, UAV technology, in conjunction with image processing techniques, provides detailed insight into the field [8]. UAVs provide several benefits, including the ability to deploy swiftly, non-invasive observation with ultrahigh spatial resolution, and frequent data collection [9]. UAVs offer effective and repetitive measurements of relatively large fields [10]. Also, many efforts have been undertaken in the development of various algorithms for pattern recognition from aerial images with different expectations of weed mapping [11], canopy 3D mapping [12], plant density [13], plant row segmentation [14], etc. Plant counting from images captured in different growth stages has received certain attention in recent times since it is one of the most contributing factors to the grain yield of field crops [15]. Spatial plant density determination instead of pure average plant population has to be accounted for when yield variability is observed. Irregular plant density can indicate pest presence, local soil conditions (e.g., waterlogging or soil crusting), or seeder malfunction. Evaluating plant density is crucial, especially for winter crops in the northern hemisphere. These crops are prone to a decrease in population after the cold winter period. Therefore, in the spring, the nitrogen management strategy should be tailored to the actual plant density. This will help optimize tillage, plant growth, and nitrogen use efficiency [16,17]. The creation of the optimization model for efficient irrigation is related to local evapotranspiration potential, which is strongly related to plant population. Valente et al. [18] tested the plant counting accuracy under different spatial resolution setups. The results of the study showed that the methodology used allowed counting plants with an accuracy of 95% and a spatial resolution of 8 mm/pixel. Kitano et al. [19] attempted to develop computer vision techniques that enable automatic corn plant counting based on a deep learning approach, using images of several corn crops obtained with an unmanned aerial vehicle (UAV) equipped with a low-cost RGB camera. The authors concluded that the best results achieved for corn plant counting were obtained with plant densities of around 70,000 plants/hectare at the earliest growth stage (V4) and a flight height of 20 m. The accuracy of automatic plant detection from RGB images is unclear in the presence of weeds. They compromise the clarity of the plant’s distinctive features. A few studies have been carried out [20,21] with the aim of determining plant in-row distance variability by combining traditional methods for seeding quality evaluation. Zhang et al. [22] presented a UAV-based image-processing algorithm that was developed to calculate maize plant distances. They underlined that the combination of area and shape parameters is useful for distinguishing maize from other vegetation (weeds).

Nonetheless, the processing of UAV imagery for early crop growth stages remains challenging due to the crop size and complex backgrounds [23]. Traditional computer vision techniques for plant detection in UAV images rely on methods such as thresholding-based image segmentation applied to vegetation index masks, followed by template matching (TM) approaches [14,24]. Recent developments in deep learning have shown significant promise in accurately separating plants from the soil background in low-altitude UAV images [18,24,25]. Segmentation of different types of crops is successfully addressed using various deep-learning models: Segnet and VGG-UNet for corn and tobacco [25], U-Net for corn and purple rapeseed leaves [26], and LeNet for corn [27].

All cited studies were exclusively centered on the subject of plant identification and quantification, neglecting to delve into the underlying factors that may contribute to irregularities in plant spacing. As a result, we expanded our research from [28] by examining the dynamics of the seeding unit and its impact on the identified distances between plants. The established research objectives are as follows:

1. Develop a deep learning (ML) algorithm for accurate plant detection;

2. Analyze the seeder performance based on images captured by the unmanned aerial vehicle (UAV);

3. Examine the vibrational dynamics of the seeding unit and its impact on seeding accuracy through machine learning-estimated corn plant spacings.

2. Materials and Methods

2.1. Trial Field Setup

The field trial was performed in 2021 in the northern part of the Republic of Serbia (geographic location: 45°34′24.67″ N, 19°50′36.72″ E). To enhance the understanding of the experiment, the flowchart is presented in Figure 1. The trial field encompassed a 0.53 ha area that was traditionally cultivated using the wheat–maize–soybean crop rotation. The field was characterized as being flat with minimal variations in elevation or slope.

The experimental field was scanned using an EM-38 MK2 probe (Geonics Ltd., Mississauga, ON, Canada) to map soil electrical conductivity (EC) and soil variability for subsequent soil sampling planning. The results are presented in Table S1 and Figure S1. The corn seeds were sown using a 4-row precision seeder (Trail version, Precision planting LLC, Tremont, IL, USA) in 6 consecutive passes at a row spacing of 0.7 m. The planter was equipped with a hydraulic downforce system (DeltaForce^®) on each row unit and finger-pickup seed meters (Precision Planting, LLC., Tremont, IL, USA). An authorized team of professionals had the responsibility for all settings (Livona Doo, Belgrade, Serbia). The seed spacing was adjusted to 0.19 m based on the experts’ knowledge and the common practice applied for the specific soil types in the region. The experimental field was divided into six (6) plots, each of which included one pass with the seeder. The seeder travel speed was the factor evaluated in the trial. The working speed remained constant during the single pass in every plot. At each subsequent pass, the speed was increased by 1 km h⁻¹. The speed range considered for data collection was from 8 km h⁻¹ to 13 km h⁻¹. The proposed hypothesis was that the variability in plant spacing could be induced by the varying speed settings, despite the seeder’s sophisticated dosing and seed delivery mechanisms being engineered to mitigate this problem. When seeds are released from the seeding mechanism and allowed to fall freely, there is still a probability for a stochastic event to take place. The corn hybrid used in the research was the Pioneer 0217 AQ (Corteva Agriscience, Wilmington, DE, USA).

The characteristics of the seed form were determined by measuring the dimensions of 240 individual randomly selected seed samples.

2.2. Evaluators of Plants In-Row Uniformity

To assess the accuracy of image-based plant spacings, the standard metrics commonly used for precise seeder accuracy evaluation were introduced. This approach provides an opportunity to assess the effectiveness of plant recognition models over different domains. Six well-established plant uniformity indicators, such as mean (Me), standard deviation (Std), quality of feed index (Qfi), Miss index (Mi), Multiple index (Mu), and precision (PS) were calculated according to ISO 7256/1 [7] (Table 1).

2.3. Measurement of Seeder Row Unit Vibration

Alongside the evaluation of the seeding and plant emergence efficiency, the seeding row unit vibration dynamics during the trial were observed and analyzed. Seeding unit vibrations are a contributing factor that increases the likelihood of seeding errors. The vibrations directly affect the relationship between the various seed-releasing momentums and the loosening of seeds on the seeding plate. The data acquisition process was carried out using the QuantumX MX440A (HBM, Inc., Darmstadt, Germany), a high-resolution universal measurement module. A portable, single-axis accelerometer system (B12/200, HBM) was used to record the vertical acceleration of the seeding row unit. The data acquisition frequency was 300 Hz. Time domain vibration analysis is provided to quantify the strength of a vibration profile, such as peak-to-peak and root mean square (RMS). The peak-to-peak value is significant because it represents the wave’s highest displacement, whereas the RMS value is the most meaningful measure of amplitude because it considers the wave’s entire time history and provides an amplitude value that is directly linked to the energy content. Moreover, the fast Fourier transform (FFT) provides a representation of vibration amplitude as a function of frequency, enabling an understanding of how the operating speed affects the excitation of vibrations in the seeder structure.

2.4. Methodology for Corn Plant Detection and Spacing Estimation Based on UAV Orthomosaic

In this study, 210 raw high-resolution RGB images of the experimental corn field were acquired, with 21 corn-sowed rows (part of the entire trial field of 0.53 acres). The aerial image dataset was acquired using a UAV (unmanned aerial vehicle) on 2 June 2021 (24 days after planting) while the plants were at the V4 vegetative growth stage. The UAV was a DJI Inspire 1 outfitted with a Zenmuse X3 camera (DJI, Shenzhen, Guangdong, China). The data were gathered at an altitude of 15 m above ground. This was highlighted in the studies of Pallottino [29] and Veramendi [30] as adequate for low-cost drones equipped with RGB cameras for plant phenotyping purposes. Given the characteristics of the equipment used in the study, this flight altitude setup ensured sufficient resolution for detecting corn plants at the V4 growth stage. In addition, to ensure the acquisition of high-quality data, the aerial images were collected under clear skies and at low wind-speed conditions with wind gusts < 2 m s⁻¹, thus eliminating the possibility of uneven illumination or blurriness within images. Maintaining a constant and low drone flight speed resulted in high-quality images with clear visible details of the imaged scene.

At the stage of four visible leaves (V4), corn plants are adequately developed and, thus, clearly visible from the nadir view. For the data acquisition, the UAV was set up to capture 75% frontal and 65% side lap, which led to generating high-quality orthomosaic (5795 × 27754) with a ground sampling distance (GSD) of 0.9 cm using Pix4DMapper (2024 Pix4D SA). A GIS software (ArcMap v10.5, ESRI, Redlands, CA, USA) was employed to accurately obtain GPS coordinates for each plant, which were manually annotated. Subsequently, the actual spacing between the plants was calculated, enabling accurate population estimates in each plot. In total, 16,720 plants were annotated within the orthomosaic, and the distances between each consecutive plant within a row were obtained. Further, the RGB orthomosaic was divided into patches of 240 × 240 pixels. A 20% overlap between adjacent patches was applied to ensure comprehensive coverage, resulting in a total of 810 patches further used for the plant detection and distance estimation. The workflow of UAV-derived image processing is represented in Figure 2.

In the following, we focus on three methods with different complexities and computational efficiencies for corn detection based on created orthomosaics. Comparing them reveals their advantages and disadvantages in terms of seeding procedure evaluation.

The first method for plant detection is an unsupervised segmentation approach based on the Visible Atmospherically Resistant Index (VARI) map [31]. By utilizing the visible range of the spectrum, the index serves as a quantitative measure of vegetation fraction and can be calculated using the following equation [32], where $r,g,b$ represent channels of created RGB patches:

(1)$VARI\left(x,y\right)={\displaystyle \frac{g\left(x,y\right)-r(x,y)}{g\left(x,y\right)+r\left(x,y\right)-b(x,y)}}$

The final positions of corn plants are identified as the centroids of connected components in the segmented mask, following binary thresholding of the map derived from Equation (1). Further obtained components whose bounding box is out of range (48–52 cm²) are filtered out since the average size of corn plants in the current growth stage is approximately 50 cm².

Template matching (TM) is used as a second method for corn plant detection that involves comparing a predefined image template (a small image patch representing the target object—in this case, a corn plant) with the target image using a similarity metric and convolution operation [33]. TM detection techniques have been utilized in some studies for corn detection and can be used to identify specific structures within the plants [34,35,36]. Detection is conducted by sliding the template image over the entire image and calculating the similarity between the template and the covered window on the image using the following formula, where $c\left(x,y\right)$ represents the template correlation image, $f\left(x-i,y-j\right)$ corresponds to the pixel values of the image window being analyzed, and $t\left(x, y\right)$ denotes the pixel values of the template image patch [37]:

(2)$c\left(x,y\right)={\displaystyle \sum _{i=1}^M}{\displaystyle \sum _{j=1}^N}t\left(i,j\right)·f(x-i, y-j)$

Template matching-based detection techniques have been utilized in some studies for corn detection and can be used to identify specific structures within the plants [35,36,37]. With the fast normalized cross-correlation [38] as the similarity metric, and by binarizing the obtained $c\left(x,y\right)$ from Equation (2), the plants were detected as centers of extracted connected components within the binary image. As in Grbović et al. [39], five templates were randomly selected from the ground truth, and, therefore, each patch image was processed five times before the final locations of detected plants were obtained.

The third method for corn plant detection we used is the deep learning-based model Mask R-CNN [40], specifically designed for instance segmentation and object detection tasks. Mask R-CNN is a two-stage architecture that extends the Faster R-CNN framework, being widely adopted and consistently showing a strong performance in agricultural studies [28,41,42,43,44,45]. This method incorporates an additional branch for generating object masks alongside bounding box predictions. In this study, we used the Mask R-CNN model with R50-FPN as the backbone deep learning network trained on Microsoft’s Common Objects in Context (COCO) dataset, a large-scale dataset consisting of 200k images [46]. The selected deep learning architecture, the Mask R-CNN R50-FPN model, was trained to classify two categories: corn plants and non-corn plant objects. The non-corn plant objects encompass various scene elements that are not the primary focus of detection, including weeds, rocks, and soil disturbances caused by machinery.

For a qualitative evaluation of the corn detecting and counting model, four standard metrics were used, which are presented in the following table (Table 2):

Plant spacing estimation from detected corn plants with the used methods requires the identification of rows. This was accomplished by connecting adjacent plants within the rows represented through the centroids of the nearest detected connected components. If the distance between the nearest connected components exceeded 75 cm (interrow space), the connection to the nearest remaining plant was skipped. Consequently, polylines were formed within the rows, linking nearby plants. These polylines were extended until they intersected with the nearest line. Connected polylines present the row lines and serve to ensure accurate plant detection. The row lines were intersected with the prior plant-detected positions, which filter out plants located within interrow spacing (Figure 3). We further analyzed created polylines to identify plant spacings.

3. Results

3.1. Plant Recognition Efficiency Comparison

The impact of threshold selection within VARI and TM methods for plant detection is significant. While lower threshold values may increase sensitivity and capture more detections, they can also introduce noise and false positives. Higher thresholds enhance specificity and reduce false positives but may risk missing some valid detections. In the context of the VARI-based method, a threshold of 0.6 is used to ensure that a broader range of potential plant detections is included, allowing for greater sensitivity. This is particularly useful in early growth stages when variations in plant health and density may not be as pronounced, and we want to capture as many relevant areas as possible without missing potential detections. Nevertheless, the higher threshold of 0.7 for the template correlation image indicates a more stringent requirement for similarity between the template and the image window. This higher threshold helps to minimize false positives by ensuring that only those areas with a strong correlation to the template are considered significant. In this case, prioritizing accuracy over inclusivity is essential, especially when precise identification of specific plant types or conditions is required, and represents one but crucial step in the density estimation and determination of the impact of the velocity of sowing. The overall metrics of qualitative evaluation were calculated for all methods and are presented in Table 3. For the third method, Mask R-CNN, a total of 21 images out of 810 were utilized for training, containing 588 masks for corn plants and 42 masks for non-corn objects. The training was conducted over 4000 epochs with a batch size of 2 images and a learning rate of 0.00025. After training, the model’s performance was assessed on a fully georeferenced orthomosaic, employing a threshold of 0.7 for plant detection.

Slightly lower results are obtained in [47], but those plants are detected in the presence of weeds. An unsupervised method based on VARI and semi-supervised TM with threshold t values of 0.6 and 0.7, respectively, demonstrated lower performance in corn plant detection compared to a supervised Mask R-CNN method in terms of all evaluation metrics shown in Table 3. Although VARI has a lower precision score than TM, its recall is higher compared to TM recall, indicating that VARI detected significantly more relevant instances (corn plants), which are represented through the F1 score. The best-performing method, Mask R-CNN, has very high (>0.95) and balanced scores for precision and recall, resulting in an F1 score of 0.98, showing superior detection of corn plants. Overall, while VARI and TM have their strengths, particularly in precision, Mask R-CNN provides the most robust and balanced performance across all metrics. Even a novel object detection algorithm, such as Yolov8, performs similarly for plant detection tasks [28]. To provide more insight into model performance, the number of true positives (TPs), false positives (FPs), true negatives (TNs), and false negatives (FNs) were calculated and are presented in Table 4 as additional performance metrics.

Mask R-CNN had the highest number of true positives (16,156), indicating it correctly identifies the most actual instances, and the lowest number of false positives (135), suggesting it rarely misidentifies an instance that is not actually present. On the other side, it has the highest number of true negatives (916), suggesting it correctly identifies negative instances more frequently, and the lowest number of false negatives (500), indicating it misses fewer positive instances. VARI shows a moderate number of true positives (9611), meaning it correctly identifies a significant but smaller number of instances compared to Mask R-CNN, but has the highest number of false positives (1505) and the lowest number of true negatives (74), suggesting it has the highest rate of inaccuracy. TM has the lowest number of true positives (9265), indicating it correctly identifies the lowest number of actual instances among the three methods. The number of false positives (900) indicates it makes some incorrect positive identifications, and the highest number of false negatives suggests that it misses a significant number of positive instances, which could impact its overall effectiveness. A visual representation of detection results for all three methods on the test patch is given in Figure 4.

Unsatisfactory results with VARI-based and TM methods are caused by falsely detecting weeds and grassland as corn plants. This misclassification undermines the reliability and usefulness of the VARI index, as it fails to provide an accurate representation of the distribution and density of the corn plants. Secondly, the unsupervised segmentation of the VARI-based method heavily relied on the greenness of plants and faced difficulties in accurately detecting smaller plants within the field. Consequently, the challenge of establishing an appropriate threshold that would enable the precise detection of plants of all sizes proved to be a complex and demanding task, even if high-resolution RGB images were provided. On the other hand, the main drawback of the template matching approach is the high computational complexity, especially in scenarios where a comprehensive analysis of a large number of plants is required, such as in this study. The Mask R-CNN model is trained using two classes: corn plant and non-corn plant objects, which encompass various elements such as weed plants, rocks, and machinery marks in the soil.

This comparison offers insights into how varying levels of algorithm complexity affect precision and, based on the obtained results, still underscores the importance of accurate human labels that are necessary for supervised algorithms, such as deep neural networks. In addition, this comparison highlights the trade-off between algorithm complexity and achieving optimal performance. While simpler methods like this VARI-based one may be easier to implement, they may not yield the same level of precision as more complex approaches like Mask R-CNN in specific tasks such as plant detection, where the accuracy of plants is a crucial part of the estimation of the plant density. Finding the right balance between complexity and performance is crucial in the development of effective plant detection algorithms intended for edge computing, ensuring real-time results.

3.2. In-Row Plant Uniformity Estimators in the Context of Plant Detection

In Figure 5, the estimated distribution of plant spacings inferred from considered methods for plant detection is illustrated. The distributions of estimated plant spacings extracted from TM and VARI-based plant detection methods indicate a wide range of distances, with a relatively high proportion of spacings outside the expected distance range. In the case of Mask R-CNN plant detections, the estimated distribution of extracted spacings among plants is the most similar to the actual values indicated by the ground truth (GT).

In the following, our analysis will be focused on establishing an association between the identified plant spacings rather than solely relying on corn plant detection. The number of misses N_miss and doubles N_multiple provides relatively trustworthy indications of the method’s performance, and further research was carried out. The GT of the manually labeled plants revealed a total of 16,698 plants in the surveyed location. The VARI-based and TM methods accurately recognized 9611 and 9256 plants, respectively (Figure 6a). In the observed area, the Mask R-CNN method achieved the highest number of recognized plants (16,156), indicating that only 3.3% of plants remained unidentified. These findings suggest that the Mask R-CNN method could be used to predict the quantity of maize plants in various planting density scenarios. Another query that requires an answer is the structural correspondence between the GT plant spacings and the plant spacings estimated according to the detected plants by the considered methods. Figure 6b indicates that the Mask R-CNN exhibited inferior relative accuracy in identifying doubles, recognizing only 11, in contrast to VARI’s 63 and TM’s 76. Because VARI and TM produced poor results in terms of plant detection, the consequence is a significantly higher number of missed spacings, with the majority of them being irrelevant. When the 3569 and 4089 missing plants that are yielded via VARI-based and TM are taken into consideration, the missed spacings that are derived from the Mask R-CNN (1602) technique are rather close to the GT (1347). Understanding missed spacing, which can be either a single miss or multiple misses, represents an additional level of plant detection quality analysis. Taking a look at Figure 6, it is evident that the Mask R-CNN (8.45%) algorithm achieved results that were comparable to those of the GT algorithm (7.54%) in terms of the relative share of single missed spacings. The VARI-based algorithm demonstrates a significantly higher relative quantity of single missed spacings (18.87%), and the TM algorithm provided the greatest discrepancy from GT parameters (23.59%). An identical outcome was observed concerning the double missed spacings, wherein the GT spacings recorded a mere 0.64%. The percentage of double missed spacings by the Mask R-CNN was 1.2%, whereas it was significantly higher for the TM (9.78%) and marginally lower for the VARI-based (7.10%). It can be inferred that the ratio of achieved outcomes for various detection techniques remains consistent across all levels of spacing errors.

Figure 7 can provide insights into specific attributes of the tested models.

QFi illustrates (Figure 7) the precision with which the models perceive the population of maize plants. The predicted percentages of 90.10% for Mask R-CNN, 67.33% for the VARI-based method, and 59.03% for TM show that Mask R-CNN is better at estimating the plant population within the expected spacing range than the other two methods. The Mask R-CNN model has the smallest variability in plant spacing (15.96%), the TM model has the highest variability (20.82%), and the VARI (19.66%) model has spacing variability that is closest to the GT (18.88%).

3.3. The Interaction Between Seeding Unit Vibration and Plant Distribution Faults as a Function of Working Speed

An analysis of seeding row unit vibration was performed to assess and quantify its effect on seeding quality. Additionally, the Mask R-CNN data and vibration parameters were analyzed in relation to working speed to validate the reliability of the machine learning method for specific applications. As seen in Figure 8, the results suggest that varying seeding velocities influence the frequency of gaps in the plant population, reducing the plant population, which supports the results obtained by Quanwei et al. [48] and Badua et al. [49]. There has been a slight drop in the number of identified plants as the working speed increased.

From Figure 9, it is clear that the vibration amplitude of the seeding row unit gradually increased as the working speed of the seeder reached 13 km/h. When the working speed was increased from 8 to 10 km h⁻¹, the RMS (root mean square) parameter indicated an increase in vibration energy. However, further speed increases did not significantly affect the vibration’s energy. The interaction between the seeder structure and the soil layer resulted in distinct vibration characteristics at a particular working speed. When the speed reached 10 km h⁻¹, additional frequencies that could be excited dampened the main vibration components that speed could enhance. Looking forward at Figure 10, the major frequencies, as well as vibration amplitude, can be noted for specific working speeds.

The most prominent features are the spectral densities within the frequency range of 0 to 7 Hz. Two more frequencies have noticeable amplitudes (12–15 Hz for 13 and 11 km h⁻¹ and 28–30 Hz for 13 km h⁻¹). The highest vibration energy was detected at a speed of 13 km h⁻¹, followed by vibration at 12 km h⁻¹. Working speeds of 9 and 11 km h⁻¹ produced similar vibration amplitudes as well as 8 and 10 km h⁻¹.

To assess the impact of the vibration of the seeding row unit on the quality of sowing parameters, as well as to evaluate the compatibility of established relationships for different methods of detecting corn plant spacing, a correlation analysis was conducted. By showing seeding parameters for specific data types (e.g., GT and Mask R-CNN) computed for a specific speed and, consequently, vibrational energy, this may indirectly reflect the discrepancy between actual and estimated spacings. The results of this analysis are presented in Figure 11. The relationship between vibration power (RMS), amplitude (peak-to-peak), and aspects of seeding quality exhibited similar characteristics. However, the amplitude showed a somewhat better correlation with seeding quality compared to vibration energy. Zhai et al. [50] observed that variations in field conditions affect the nature of the vibration of seeding row units, making it challenging to anticipate potential disturbances in sowing quality caused by vibrations. Nevertheless, the employed detection methods exhibited varying degrees of association with vibrations despite their comparable nature. In fact, the GT spacing of plants was used as a standard to measure correlations. In some cases, however, a stronger correlation was seen when comparing the output data from Mask R-CNN detection. Research demonstrated that vibrations had a beneficial impact on the rise in the proportion of failures in sowing (Mi), aligning with the findings of Wang et al. [51]. The impact of vibrations on the occurrence of failures in sowing is determined to be 50% based on GT data. Undoubtedly, the abrupt rise in the speed of the seeding row units raises the likelihood of sudden seed discharge from the sowing plate, particularly when managing larger seeds, resulting in a failure. Based on the provided information and the GT data, the vibration amplitudes were more significant for missed spacing occurrence than the vibration energy. In contrast, the presence of multiple plants was inversely correlated with vibration, which can be explained by the fact that vibration reduces the likelihood of retaining a greater number of seeds on the seeding plate.

The correlation between the percentage of misses and multiples with vibrations leads to a significant impact on QFi, which is an inverse derivative of the same analysis. QFi has a high association with the amplitude and power of vibration, reaching up to 77% in the case of GT data. Comparing two distinct DNN algorithms using a bench-based seeding quality trial configuration, Pareek et al. [52] discovered comparable results regarding QFi. Significant correlations were established between the average variation in plant spacing and vibrations, with explanations reaching as high as 65%. This suggests that even with the testing of a modern seeding system that integrates advanced techniques for seed manipulation and singulation, we have not completely eliminated extrinsic factors like vibration. Future research should focus on mitigating the adverse effects of vibrations during sowing. One potential solution is to employ a specialized suspension system to connect the sowing apparatus and the seeder’s main frame. This suspension system, acting as a buffer, can effectively dampen vibrations and prevent their amplification due to resonance frequencies.

4. Conclusions

Based on the results presented in previous sections, the following conclusions can be delineated:

1. UAV photography has been demonstrated to be an effective method for the rapid assessment of corn populations at the V4 growth stage. In future research, trials should be conducted at various developmental stages of corn and at different population densities to provide a comprehensive understanding of the algorithm’s capabilities and limitations.

2. Mask R-CNN had superior performance, correctly identifying 96.5% of all plants. It outperformed the VARI-based unsupervised classification method, which achieved a recognition rate of 57.5%, and TM, which achieved a recognition rate of 55.4%. By developing a user-friendly mobile or PC application, potential users can practically utilize the Mask R-CNN algorithm for rapid evaluation of maize plant counts, automating the processing of images captured by phone (or drone) cameras. Nonetheless, the model can be susceptible to overfitting, particularly when trained on smaller datasets, and its computational demands can pose challenges for real-time deployment.

3. Additionally, employing techniques such as data augmentation and transfer learning may further boost accuracy and robustness. By addressing these factors, we aim to advance the capabilities of plant detection methods and contribute to the broader field of precision agriculture. The working speed of the seeder directly affects the vibration characteristics of the seeder unit. As the speed increases, the vibration energy also increases. Most seeding quality evaluators exhibit significant positive associations with both vibration amplitude and energy, aside from a negative correlation between the occurrence of multiples and vibrations. To reduce the detrimental effects of vibration on seeding performance, the seeder’s design might be improved by incorporating a counter accelerator or a specialized dampening suspension system for the seeding unit. This would effectively eliminate the negative impact. The results of the vibration analysis of the current study can serve as a starting point for the development of a warning system for real-time adjustments of a seeder’s travel speed, maximizing the seeding accuracy.

Author Contributions

Conceptualization, M.M.K.; methodology, M.M.K. and Ž.G.; software, M.M.K., R.W. and A.S.; validation, M.P. and A.C.T.; formal analysis, B.I. and A.S.; investigation, R.W., B.I. and M.P.; resources, A.C.T.; data curation, Ž.G., B.I. and A.C.T.; writing—original draft, M.M.K. and Ž.G.; writing—review and editing, M.M.K. and A.C.T.; visualization, M.P.; supervision, M.M.K.; funding acquisition, Ž.G. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The data presented in this study are available on request from the corresponding author (data are part of an ongoing study).

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Tables

Figure 1. The illustration of the in-field activities and data processing procedures.

Figure 2. The pipeline of the UAV orthomosaic creation followed by its patch-based division procedure.

Figure 3. The proposed procedure for the identification of rows and plants within them.

Figure 4. The efficiency of corn plant detection techniques is demonstrated on a portion of the patch.

Figure 5. Distribution of plant spacing determined by the plant detection method. The distribution of GT spacings illustrates the disparity in plant detection accuracy among the chosen methods.

Figure 6. Comparative effectiveness of various plant detection techniques using GT data as reference values: (a) absolute values included and the proportion of mis-spaced plants in the overall population (b).

Figure 7. Plant spacing uniformity indicators with relative metrics.

Figure 8. The expected number of plants compared to the number of detected plants for each row along a selected route. The blue line indicates the estimated plant numbers as calculated by the Mask R-CNN model, whereas the red line depicts the theoretical plant numbers.

Figure 9. The expected number of plants vs. the number of detected plants per row level.

Figure 10. Spectral densities of the seeding row unit vibrations excited by the working speed.

Figure 11. The relationship between vibration parameters of the seeding row unit and seeding quality parameters for the ground-truth data (orange dots) and for the Mask R-CNN data (blue dots): RMS compared to Miss index (a), Multiple index (c), quality of feed index (e), and standard deviation (g) and peak-to-peak compared to the Miss index (b), Multiple index (d), quality of feed index (f), and standard deviation (h).

Table 1

The derived parameters together with their corresponding equations.

Me (m)	Std (m)	Mi (%)	Mu (%)	QFi (%)	PS (%)
${\displaystyle \sum _{i=1}^{Ntotal}}{\displaystyle \frac{x_i}{N}}$	$\sqrt{{\displaystyle \frac{{\sum }_{i=1}^N\left(x_i-\overline{x}\right)}{N-1}}}$	${\displaystyle \frac{N_{miss}}{N}}\times 100$	${\displaystyle \frac{N_{multiple}}{N}}\times 100$	${\displaystyle \frac{n}{N}}\times 100$	${\displaystyle \frac{Std’}{n}}\times 100$

Note: N is the total number of observations; xi is the distance between consecutive plants in the same row; and N_miss is the number of spacings greater than 1.5 × α. N_multiple is the number of spacings less than 0.5 × α; n is the number of spacings in the expected range [>0.5 × α or <1.5 × α], while α is the predefined seeder plant distance by the farmer; and $Std’$ is the average plant-to-plant distance deviation if considering an expected range [>0.5 × α or <1.5 × α].

Table 2

Evaluation metrics for model performance.

Metrics	Equation
Accuracy	${\displaystyle \frac{TP+TN}{TP+TN+FP+FN}}$
Recall	${\displaystyle \frac{TP}{TP+FN}}$
Precision	${\displaystyle \frac{TP}{TP+FP}}$
F1 score	${\displaystyle \frac{2·(Recall·Precision)}{Recall+Precision}}$

Note: TP is a true positive and correctly detected plant; TN is a true negative, a non-plant accurately detected as the ‘other’ class; FP represents the ‘other’ class detected as a plant; and FN is a missed plant.

Table 3

Evaluation of plant detection methods.

Metrics	VARI (t = 0.6)	TM (t = 0.7)	Mask R-CNN
Accuracy	0.61	0.52	0.96
Recall	0.66	0.55	0.97
Precision	0.88	0.91	0.99
F1 Score	0.76	0.69	0.98

Table 4

Performance metrics (true and false positives and negatives) for all three detection methods.

Metrics	VARI	TM	Mask R-CNN
TP	9611	9265	16,156
FP	1505	900	135
TN	74	78	916
FN	4951	7580	500

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/app142210693/s1, Table S1: Soil physical properties; Figure S1: Maps of the soil properties.

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