Evaluation of droplet deposition parameters based on the Genetic-Otsu algorithm

Spraying platform

The UAV employed in this study is the 3WQFTX-101S intelligent electric multi-rotor plant protection UAV manufactured by Henan Anyang Quanfeng Aviation Plant Protection Technology Co., Ltd., utilized as the spraying platform (Fig. 1). Table 1 shows the key performance parameters of this multi-rotor plant protection UAV, featuring a spraying system comprising four XR TEEJET 110015VS pressure nozzles with spray angles of 110°.

Experimental design

The experiment took place at the Anyang Institute of Technology in Anyang City, Henan Province. A vacant area measuring 30 m × 10 m was designated as the spraying zone. Throughout the experiments employing the spraying platform, the WSP (76 mm × 26 mm) was placed symmetrically along both sides of the UAV flight path, with five sampling points on each side, amounting to a total of 10 sampling points. The spacing between WSPs on one side in the vertical flight direction was 0.4 m. The flight path and sampling point configuration are depicted in Fig. 2. Three different flight speeds were utilized for the spraying experiments to gather sample data at various coverage. The spray test was repeated three times with the same WSP layout under the same speed conditions to ensure test accuracy. Table 2 presents the main parameter settings of the UAV platform during field application.

Sample collection and processing

After the UAV completed the spraying operation for 10 min, the WSP samples were sealed and dried using labeled kraft paper envelopes. Subsequently, all the WSPs were scanned using an HP SCANJET G4050 high-definition image scanner to obtain sample images at a resolution of 96 DPI. Finally, the collected 90 WSP images were categorized based on the droplet pixel area (PA) into dense droplets group (40,000 < PA < 90,000), medium droplets group (12,000 < PA ≤ 40,000), and sparse droplets group (PA ≤ 12,000). Figure 3 displays the WSP sample images of these three droplet groups, which will be used for the subsequent analysis of droplet coverage and density.

Evaluation metrics for droplet deposition effectiveness

Droplet coverage and density are critical metrics for evaluating deposition uniformity and are essential for accurately assessing spray quality (Lv et al., 2019). Droplet coverage represents the ratio of the total area covered by all droplet particles deposited on the target surface to the total area of the target surface. The formula for evaluating droplet coverage is as follows:

(1) $$\begin{array}{c}C={\displaystyle \frac{{\mathrm{A}}_{\mathrm{S}}}{{\mathrm{A}}_{\mathrm{P}}}\times 100\mathrm{\%}}\end{array}$$where C is the droplet coverage; A_S is the total area of droplets; and Ap is the area of WSP.

Droplet density refers to the number of droplets deposited on a unit area of the target surface. The evaluation index formula is as follows:

(2) $$\begin{array}{c}D={\displaystyle \frac{\mathrm{N}}{\mathrm{A}}\times 100\mathrm{\%}}\end{array}$$where D is the droplet density; N is the number of droplet particles on the target; and A is the area of WSP.

Fixed threshold segmentation methods

The fixed threshold method is a widely adopted image processing technique utilized in the fields of image segmentation, contour extraction, and feature extraction (Qi et al., 2022). This method operates by setting a fixed threshold and analyzing the gray-level distribution characteristics of the image. The algorithm scans each pixel value in the image, comparing it with the pre-defined threshold. Pixels exceeding the threshold are set to the maximum gray level value, while pixels below the threshold are set to the minimum gray level value, resulting in image binarization. The basic idea is as follows:

(3) $$\begin{array}{c}G(x,y)=\{\begin{array}{c}{255}_{,}f\left(x,y\right)\ge T\\ 0_{,}f\left(x,y\right)<T\end{array}\end{array}$$where T is the fixed threshold, f(x, y) is the pixel point gray value.

WPS is a highly sensitive professional test paper that exhibits a color reaction upon contact with water, creating a distinct color contrast between the paper and the droplets (Fox et al., 2003). Based on this color contrast, the threshold was set as a constant value of 0.60, corresponding to a value of 153 within the 8-bit range [0,255] (Brandoli et al., 2021).

Otsu threshold segmentation methods

The Otsu thresholding method, known as the maximum between-class variance method, is a widely employed image binarization segmentation algorithm (Xu et al., 2011). The core principle of the Otsu algorithm is to compute the intra-class variance and inter-class variance of the image at various thresholds to identify the optimal threshold that maximizes the inter-class variance. Initially, the algorithm classifies each pixel in the image based on its grayscale value. Subsequently, it calculates the probabilities of pixels being categorized as foreground and background separately, along with the cumulative mean of the target grayscale level. The algorithm then determines the optimal threshold value by maximizing the inter-class variance between the foreground and background. Assuming a threshold value of k, the expression for the cumulative mean m of the gray level K is:

(4) $$\begin{array}{c}{P}_1=\sum _{i=0}^{k}pi,P_2=\sum _{i=k+1}^{255}pi,m=\sum _{i=0}^{k}ipi\end{array}$$where p_i is the probability of the grayscale value and being i, P₁ is the probability of a pixel being assigned to the background region, P₂ is the probability of being assigned to the target region.

(5) $$\begin{array}{c}{\sigma }^2\left(k\right)=\underset{0\le k\le 255}{max}{\displaystyle \frac{{\left(m_G\ast P_1-m\right)}^2}{P1\ast P2}}\end{array}$$where m_G represents the average grayscale value of the entire image, σ² (k) is the maximum inter-class variance, and K is the optimal threshold value.

Threshold segmentation method based on the Genetic-Otsu algorithm

The genetic algorithm is a stochastic global search optimization method inspired by natural selection and genetic processes in biological systems (Mirjalili, 2019). Commencing with an initial population, the genetic algorithm utilizes a combination of random selection, crossover, and mutation operations to iteratively generate a population of individuals that exhibit improved adaptation to the prevailing environment. This evolutionary process enables the population to navigate towards more advantageous regions within the search space, gradually converging towards a subset of individuals that are optimally aligned with the environmental conditions.

The genetic algorithm is adept at globally searching for optimal solutions, irrespective of the mathematical characteristics of the problem. It is especially effective for tackling complex, multi-parameter, and nonlinear problems. The application of the Genetic-Otsu algorithm in extracting droplets from WSP is exemplified in Fig. 4.

Morphological processing

Morphological processing stands out as a highly utilized technique in the realm of image processing. Its basic idea is to use a special structuring element to measure or extract the corresponding shapes or features in the input image, to further analyze the image and recognize objects (Chanda, 2008). This method is commonly used in the preprocessing and postprocessing of images and is an effective image enhancement technique. It comprises essential operations such as erosion, dilation, opening, and closing.

Erosion operation is a process that “shrinks” the foreground area in an image, which can be used to eliminate edges and noise, making the image edges smoother. Dilation is a process that “expands” the foreground area in an image, making the image structure more complete. The opening operation begins with erosion followed by dilation, aiming to reduce noise and refine image edges. This process helps in smoothing irregularities and improving image quality. Conversely, the closing operation starts with dilation followed by erosion. This operation fills holes in the image and improves image segmentation. By closing small breaks in the image structure, this operation enhances the continuity and completeness of image features (Zhang, 2009).

In this study, the droplets on the WSP were extracted, and it was observed that there were many holes inside the droplet contours after threshold segmentation. This could affect the accuracy of droplet parameter calculation. To address this issue, a morphological closing operation was applied to optimize the segmented image, resulting in more complete and accurate droplet contours. Figure 5 compares the effects of droplet contours before and after threshold segmentation and morphological closing operation.

Data processing and analysis

In this study, Adobe Photoshop 2024 software was used to manually measure 90 WSP samples. For each sample, three researchers performed pixel-level contour extraction. By averaging the results of the three extractions, we calculated the actual values of droplet coverage and density.

Based on the manual measurement data, the accuracy error of the three methods is calculated. In order to fully manifest the disparities among the data, Tukey’s method was employed to assess the differences among treatments in a one-way analysis of variance, with a significance level set at 0.05.

Additionally, OriginLab 2021 software was employed to plot the data, thereby enhancing the visualization of data distribution and trends.

Evaluation results of droplet coverage

Droplet coverage is one of the important indicators for evaluating the effectiveness of drone spraying. It reflects the uniformity and effectiveness of droplets on the target. Accurate detection of droplet coverage is crucial for optimizing drone parameters and improving pesticide utilization efficiency.

Figure 6 illustrates the relative errors in droplet coverage calculated by three threshold segmentation algorithms across three different droplet groups, compared to manual measurement results. The results indicate that, across the three groups, the Genetic-Otsu threshold method proposed in this study has lower segmentation errors and better extraction performance compared to the fixed threshold method and the Otsu threshold method. Specifically, in the sparse droplets group, the extraction performance of the three methods is comparable, and there is no significant difference in the relative error of droplet coverage results.

In the medium droplets group, the Genetic-Otsu threshold method proposed in this study yields significantly lower relative errors in droplet coverage compared to the fixed threshold method and the Otsu threshold method, with an average error of only 0.9% compared to manually calculated results. The average relative errors in droplet coverage obtained by the fixed threshold method and the Otsu threshold method do not show significant differences, with the Otsu threshold method slightly outperforming the fixed threshold method.

In the dense droplets group, the extraction performance of the fixed threshold method is poor, showing a significant difference in relative error compared to the Otsu threshold method and the Genetic-Otsu threshold method, with a relative error of 4.7%. Conversely, both the Genetic-Otsu threshold method and the conventional Otsu threshold method exhibit high segmentation accuracy in dense droplet groups, with no significant discernible difference between the two methods. The proposed algorithm in this study has a lower relative error compared to the Otsu threshold method, with only a 1.2% relative error.

Evaluation results of droplet density

Droplet density is an important evaluation indicator for the effectiveness of drone spraying and a key factor in determining the effectiveness of pesticide control. Figure 7 shows the relative errors in droplet density calculated by three threshold segmentation algorithms across three different droplet groups, compared to manual measurement results. The results indicate that across the three droplet groups, the Genetic-Otsu threshold method proposed in this study demonstrates outstanding extraction performance and outperforms both the fixed and traditional Otsu threshold methods in calculating droplet density.

In the sparse droplets group, the relative error of droplet density obtained using the fixed threshold method is significantly higher than that of the Otsu threshold method and the Genetic-Otsu threshold method, with an error of up to 19.7%. The results of the Otsu threshold method and the Genetic-Otsu threshold method are comparable, with no significant difference. In the medium and the dense droplet groups, there are significant differences in the relative errors of droplet density among the three methods. The Genetic-Otsu threshold method has the lowest average error in droplet density, followed by the Otsu threshold method, while the average relative error of the fixed threshold method is above 10%, indicating poorer performance.

Visualization of droplet extraction performance

Figure 8 illustrates the extraction results of three droplet extraction algorithms in three droplet groups. The results indicate that, across the three droplet groups, the fixed threshold method and the traditional Otsu threshold method both struggle to extract small-sized droplets. In contrast, across the three droplet groups, the Genetic-Otsu method proposed in this study shows effective extraction of small droplets and demonstrates superior extraction performance.

As illustrates in Fig. 9, with the increase in droplet density, both the fixed threshold method and the Otsu threshold method are prone to identifying the contours of multiple independent droplets that are adjacent but not in direct contact as a same droplet, leading to higher calculation errors in droplet deposition parameters. In contrast, the Genetic-Otsu threshold method proposed in this study exhibits excellent droplet extraction performance in all three droplet groups. This algorithm not only can effectively extract small-sized droplets but also can differentiate the multiple independent contours of adjacent droplets, thereby enabling accurate calculation of droplet deposition parameters.