Edge–Region Collaborative Segmentation of Potato Leaf Disease Images Using Beluga Whale Optimization Algorithm with Danger Sensing Mechanism

Abstract

Precise detection of potato diseases is critical for food security, yet traditional image segmentation methods struggle with challenges including uneven illumination, background noise, and the gradual color transitions of lesions under complex field conditions. Therefore, a collaborative segmentation framework of Otsu and Sobel edge detection based on the beluga whale optimization algorithm with a danger sensing mechanism (DSBWO) is proposed. The method introduces an S-shaped control parameter, a danger sensing mechanism, a dynamic foraging strategy, and an improved whale fall model to enhance global search ability, prevent premature convergence, and improve solution quality. DSBWO demonstrates superior optimization performance on the CEC2017 benchmark, with faster convergence and higher accuracy than other algorithms. Experiments on the Berkeley Segmentation Dataset and potato early/late blight images show that DSBWO achieves excellent segmentation performance across multiple evaluation metrics. Specifically, it reaches a maximum IoU of 0.8797, outperforming JSBWO (0.8482) and PSOSHO (0.8503), while maintaining competitive PSNR and SSIM values. Even under different Gaussian noise levels, DSBWO maintains stable segmentation accuracy and low CPU time, confirming its robustness. These findings suggest that DSBWO provides a reliable and efficient solution for automatic crop disease monitoring and can be extended to other smart agriculture applications.

1. Introduction

The potato (Solanum tuberosum L.), the fourth most important staple crop globally, serves as a primary food source for over one billion people, with its yield stability and disease resistance playing a pivotal role in ensuring food security [1,2]. However, potatoes are susceptible to infection by various pathogens including fungi, bacteria, and viruses throughout their growth cycle, with late blight [3], early blight [4,5], and black scurf [6] being the most devastating diseases. According to data from the Food and Agriculture Organization (FAO), worldwide potato yield losses due to these diseases reach 20–40% annually, resulting in direct economic losses exceeding USD 10 billion, which severely threatens the livelihoods of smallholder farmers and destabilizes regional food supply chains [7,8]. Therefore, early and accurate disease detection has become paramount for enhancing agricultural productivity and implementing effective crop health management strategies.

The implementation of precision agriculture relies on efficient and non-destructive disease detection technologies. Currently, image processing technology has been widely applied in agricultural disease detection, particularly through image segmentation and feature extraction to locate lesions [9,10,11,12]. However, traditional lesion detection methods, such as manual visual assessment, suffer from strong subjectivity and low efficiency, which means they cannot meet the demands of large-scale field data collection and analysis. In recent years, the integration of computer vision and spectral imaging technologies has provided new solutions for plant phenotypic analysis. Image-based disease detection technology enables non-destructive and high-throughput early diagnosis by extracting the morphological, textural, and spectral features of leaf lesions [13].

As a critical preprocessing step for feature extraction and classification, the accuracy of image segmentation directly determines the final detection performance. Current segmentation methods primarily include threshold-based segmentation [14,15], edge detection [16], and region growing [17]. Among them, the threshold segmentation method is more suitable for resource-constrained agricultural embedded systems due to its advantages of requiring no training data and having low computing cost [18,19]. The classical Otsu algorithm exhibits high efficiency in lesion segmentation under conditions of uniform illumination by maximizing the between-class variance to determine the optimal threshold [20,21]. It still has a few major drawbacks, though: (1) Although edge detection algorithms can accurately identify lesion contours, they do not incorporate internal region information, making comprehensive segmentation difficult to achieve; (2) single-dimensional grayscale histogram analysis is not sufficiently adaptable to complex scenarios with non-uniform lighting, soil residue, and leaf overlap interference, which may result in over-segmentation (pseudo-lesion noise) or edge loss [22].

To address the shortcomings of the Otsu method, researchers have proposed various improvement strategies. For instance, by integrating Otsu threshold segmentation with metaheuristic algorithms like particle swarm optimization and genetic algorithms, the precision of threshold optimization can be enhanced [23,24,25,26]. These enhanced techniques still have a lot of shortcomings, though. First, they struggle to find globally optimal threshold combinations because they are first prone to premature convergence, in which the search process becomes stuck close to local optima too soon and does not adequately explore the whole solution space. Second, these methods are not flexible enough to accommodate the non-linear changes in brightness that are typical of disease lesions on infected leaves. They have a greater missed detection rate for early-stage disease spots because they are unable to dynamically modify thresholds based on the actual characteristics of lesions [27,28]. Consequently, advancing lesion segmentation accuracy, robustness, and environmental adaptability persists as a critical research frontier.

The beluga whale optimization algorithm (BWO) [29], proposed by Changting Zhong in 2022, is a swarm intelligence optimization algorithm inspired by the swimming, foraging, and whale fall behaviors of beluga whales. Experimental studies have demonstrated that BWO exhibits certain advantages in solving optimization problems. Nevertheless, practical applications frequently encounter complex and diverse challenges where the standard BWO method proves insufficient. Although existing improved BWO methods [30,31] have enhanced the ability to escape from local optima to some extent, they still suffer from issues such as a large number of parameters requiring complex configuration, long computation time, and low convergence efficiency.

Therefore, to enhance the solution accuracy and convergence speed of BWO, a beluga whale optimization algorithm with a danger sensing mechanism (DSBWO) is proposed. By incorporating improved control parameters B_f, a danger sensing mechanism, a dynamic foraging mechanism, and whale fall behavior, the convergence speed of the algorithm is accelerated, preventing it from becoming stuck in local optima. Subsequently, a collaborative strategy integrating DSBWO with Otsu and Sobel edge gradient constraints is implemented. This strategy optimizes the optimal threshold in parallel in the color space, effectively refining the contour of potato lesion edges and improving segmentation accuracy. The suggested approach, which has excellent adaptability in agricultural image processing, dramatically improves the accuracy of early-stage potato disease diagnosis, according to experimental results.

The main contributions of this study are:

(1)

The introduction of DSBWO’s image edge–region collaborative optimization strategy, which enhances the quality of threshold segmentation.

(2)

The application of CEC 2017 testing functions and other segmentation experiments to evaluate the performance of DSBWO and compare it with other optimization algorithms.

(3)

The innovative integration of Otsu–Sobel edge detection, significantly improving the accuracy and segmentation quality of lesion localization.

(4)

The verification of the improved algorithm’s effectiveness in potato leaf segmentation, offering a novel solution for the early diagnosis of agricultural diseases.

The organizational structure of this paper is as follows: Section 2 provides a detailed description of the proposed DSBWO method and threshold segmentation strategy. Section 3 presents the settings of the comparison algorithms, parameter configurations, and evaluation metrics. Section 4 displays the experimental results and offers a comparative analysis of the algorithm’s performance on various benchmark tests and image segmentation tasks. Finally, Section 5 summarizes the research conclusions and outlines directions for future work.

2. Materials and Methods

To address the issues of slow convergence speed and low solution accuracy in traditional BWO, DSBWO is proposed to solve these problems. It is applied to optimize Otsu and Sobel to accurately locate the lesion contours in potato disease images, providing a high-precision solution for disease detection in complex field environments. The following content introduces the components of DSBWO and the thresholding methods.

2.1. Beluga Whale Optimization Algorithm with Danger Sensing Mechanism

2.1.1. Control Parameters Based on S-Shaped Function

By analyzing the standard BWO [29], we can know that as the algorithm iterates, the control parameter B_f decreases with the number of iterations, thereby controlling whether the beluga whale in the population will perform swimming behavior (exploitation phase) or foraging behavior (exploration phase). Therefore, B_f dramatically impacts BWO’s performance. Equation (1) is the calculation formula for B_f in BWO. Equation (1) shows that at the beginning of algorithm iteration, the number t is small and the probability of B_f > 0.5 is higher, enabling the algorithm to conduct exploration behavior. As the number of computations increases, t gradually increases, B_f decreases, and the algorithm enters the development stage with stronger exploitation capability and faster convergence. To observe the trend of B_f value changes during algorithm iteration more intuitively, we calculated B_f according to Equation (1) and drew its change curve after 1000 iterations, as shown in Figure 1.

$$B_f=B_0\left(1-{\displaystyle \frac{\mathrm{t}}{2T_{\max }}}\right)$$

(1)

In Figure 1, the algorithm varies randomly in the range [0, 1] during the iteration process of the algorithm B_f. This situation is closely related to the initial value of B₀, which is a random number in the range [0, 1], and therefore, there will be a situation that randomly enters the exploration and exploitation stages during the iteration process of the algorithm. Moreover, there is a greater chance of B_f being less than 0.5 in the final iteration stage, which permits the algorithm to advance to the exploitation phase. In this way, it is easy to encounter problems such as slow algorithm convergence speed and low solution accuracy. In response to the above situation, control parameters based on the S-shaped function are proposed.

The S-shaped function [32], commonly used in mathematics, is summarized in Equation (2):

$$f(x)={\displaystyle \frac{1}{1+e^{-x}}}$$

(2)

It is evident from an analysis of Equation (2) that the S-shaped function is increasing monotonically.

$$B_f={\displaystyle \frac{2}{1+e^{4\frac{t}{T_{max}}}}}$$

(3)

As shown in Figure 2, the control parameter B_f is decreasing non-linearly, and in the early stage of the iteration, B_f decays relatively gently from 1 to 0.5, at which time the algorithm performs exploration behavior, and the beluga whales in the population search for the best solution throughout the search space. When the algorithm is in the middle of the computation, B_f < 0.5, this is when the beluga population enters the exploitation phase. This approach prevents the beluga whales from wasting their global optimization capability and allows the beluga to have more time for effective local optimization to better enhance the exploitation capability of the beluga population and greatly increase its optimization efficiency.

2.1.2. Danger Sensing Mechanism

Sharks are not the only predators of the docile beluga. Polar bears also pose a threat, as they use their forepaws to pummel and drag them onto the ice for consumption. The position update method of BWO in the exploration stage of the algorithm depends on the current individual and random individuals in the population, without considering whether there is a threat in the surrounding environment. The individual movement mode during the exploration phase of the algorithm has a significant impact on the convergence speed of BWO and affects its performance. Therefore, to improve the precision of BWO, a danger sensing mechanism can be added in the exploration stage. Beluga whales pay attention to whether there are dangerous situations around them when searching for food through their auditory and visual senses. The specific formula for the danger sensing mechanism is shown in Equation (4):

$$X(t+1)=X_a(t)+l\times \left(X_b(t)-X_i(t)\right)$$

(4)

$$X_i(t+1)=\left\{\begin{array}{ll}{X}_i^P(t)+\left(X_r^j(t)-X_i^P(t)\right)\left(1+r_1\right)\sin \left(2\pi r_2\right)\hfill & j=2NP\hfill \\ X_i^P(t)+\left(X_r^j(t)-X_i^P(t)\right)\left(1+r_1\right)\cos \left(2\pi r_2\right)\hfill & j=2NP+1\hfill \end{array}\right.$$

(5)

where $X_i^P(t)$ denotes the position of the i-th beluga whale in dimension P, and P (j = 1, 2, ..., D) denotes the random number selected from the dimension. X_a(t) and X_b(t) are two randomly selected individuals at the t-th iteration. r₁ and r₂ are random operators in the range (0, 1). l is the dynamic perception coefficient: when the beluga whale senses danger and needs to escape, the individual starts to adjust its position. Beluga move further and further out of the danger zone with each iteration, and the perceived risk decreases. The formula for l is shown in Equation (6).

$$l=r_1\times (1-{\displaystyle \frac{t}{T_{\max }}})$$

(6)

Therefore, the following is the mathematical model of the danger sensing mechanism:

$$X_i(t+1)=\left\{\begin{array}{ll}\begin{array}{ll}{X}_i^P(t)+\left(X_r^j(t)-X_i^P(t)\right)\left(1+r_1\right)\sin \left(2\pi r_2\right)\hfill & j=2NP\hfill \\ X_i^P(t)+\left(X_r^j(t)-X_i^P(t)\right)\left(1+r_1\right)\cos \left(2\pi r_2\right)\hfill & j=2NP+1\hfill \end{array}\hfill & r_2>ST\hfill \\ X_{\mathrm{a}}(t)+l\times \left(X_b(t)-X_i(t)\right)\hfill & \mathit{otherwise} \hfill \end{array}\right.$$

(7)

where ST = 0.3 × r₃.

When r₂ > ST, this indicates that the positions of the beluga whale and its food are in a safe zone, and the position is updated according to Equation (5). Otherwise, it is updated using Equation (4). The danger sensing mechanism emphasizes that the algorithm has a strong ability to explore in the search space during the exploration phase. On the other hand, it ensures that the beluga whales are hunting prey in a safe location and that the algorithm obtains the best solution. The danger sensing mechanism improves the convergence speed of the algorithm, enriches the diversity of individual position updates, and enhances the algorithm’s search capability.

2.1.3. Dynamic Foraging Mechanism

BWO generates novel solutions through the foraging stage, so if the updating method is not excellent enough, the resulting new solutions will hardly improve the quality of the solutions. During algorithm iteration, the position update of the algorithm population relies on the optimal individual. Although this can quickly converge upon the current optimal individual, it is more likely to cause BWO to fall into local optima, resulting in lower solution accuracy. It is evident from the development phase equation that members of the population will cluster around the best solution, X_best, through iteration. In addition, r₃ is a random value range in the interval [0, 1]. Relying only on parameter r₃ will not assist the population in escaping the local optimum when X_best is not the global optimal solution.

A dynamic foraging mechanism, designed to balance the algorithm’s global and local search capabilities, improves solution quality. The mechanism consists of two population position updating formulas; one is an updating method that further exploits the current optimal solution. Another approach is to randomly select a beluga individual, and based on this, refer to the position of the optimal individual and introduce a binary step size to prevent the algorithm from becoming trapped in a local optimum. The mathematical model of the dynamic foraging mechanism can be found in Equation (8).

$$X_i(t+1)=\left\{\begin{array}{ll}{X}_{\mathit{best}}(t)+A_1\left(X_a(t)-X_i(t)\right)\hfill & r_3<r_4\hfill \\ X_a(t)+A_1(X_{best}(t)-{\mathrm{X}}_{\mathrm{i}}\left(t\right)+(1-A_1)\times U\times (X_b(t)-X_c(t))\hfill & \mathit{otherwise} \hfill \end{array}\right.$$

(8)

$$A_1=2r_4\times \left(1-{\displaystyle \frac{t}{T_{\mathit{max}}}}\right)$$

(9)

where X_a(t), X_b(t), and X_c(t) are three randomly selected individuals in the population with an iteration count of t. r₄ is a random value within the range [0, 1]. U is a binary vector used to determine when to apply a step size to avoid moving individuals towards the same position in the population. U is assigned according to Equation (10):

$$U=\left\{\begin{array}{ll}1\hfill & r_4<r_5\hfill \\ 0\hfill & \mathit{otherwise} \hfill \end{array}\right.$$

(10)

where r₄ and r₅ are two vectors that represent random values in the interval [0, 1].

In Equation (10), the two position updating methods are performed randomly, and when r₄ < r₅, individuals in the population are more inclined to exploit the excellent individuals further, gradually approaching the excellent individuals as the algorithm iterates, increasing the likelihood of discovering the globally optimal solution. On the contrary, individuals seek optimal positions, mitigating the risk of local optima entrapment, and concurrently exploring the search space by tracking other individuals’ solutions. By avoiding missing possible optimal solutions and pausing at local optimal solutions, this approach ensures a balance between global search and local exploitation while also encouraging algorithm exploration and exploitation.

2.1.4. Improved Whale Fall Strategy

When the balance factor B_f is less than the whale fall probability W_f, the algorithm enters the whale fall phase. When a whale fall occurs, the beluga whale has already lost its optimization ability, so it is believed that the beluga whale that has experienced a whale fall will leave the population. However, to ensure that the population does not change, young beluga whales will be added to the optimization queue. This paper proposes a simple and feasible whale fall idea. The main idea of the improved whale fall strategy is that individuals with poor optimization-seeking ability in the population gradually leave the population as the number of iterations increases. Furthermore, beluga positioned in the middle gradually converge towards the best beluga to ensure their own safety. Finally, a disturbing factor vc is added on this basis, and vc decreases with the iteration of the algorithm, which helps to improve the convergence accuracy of the algorithm. The specific update strategy is:

$$W_f=0.01-0.05\times {\displaystyle \frac{t}{T_{\max }}}$$

(11)

$${\mathrm{X}}_{\mathrm{i}}(t+1)=vb\times X_{best}(t)-r_6\times X_{mid}(t)-vc\times X_{worst}(t)$$

(12)

where vb is a random number in the range [−1, 1]. r₆ is a random number in the range [0, 1]. X_mid(t) and X_worst(t) represent the individuals in the middle and worst position of the population sorted by fitness value, respectively.

vc is the disturbing factor controlling the occurrence of whale falls where beluga whales will leave the population, and the formula for vc is given in Equation (13).

$$vc=1-{\displaystyle \frac{t}{T_{\max }}}$$

(13)

where t is the current number of iterations and T_max is the maximum number of iterations.

2.1.5. The Flowchart of DSBWO

Population initialization in DSBWO is carried out according to Equation (14). The pseudocode of DSBWO is shown in Algorithm 1. DSBWO also includes control parameters based on the S-shaped function, a danger sensing mechanism, a dynamic foraging mechanism, and an improved whale landing strategy.

$$X=LB+rand(NP,D)\times (UB-LB)$$

(14)

where NP is the population size, and D is the population dimension. UB and LB are the upper and lower limits of variables, respectively. rand is a random number generated in the range [0, 1].

Algorithm 1: DSBWO

Input: N, D ST, vb,Tmax, UB, LB; Output: the best solution Xbest;

1. The initial population X is generated according to Equation (14). 2. Evaluate the population and find the optimal individual Xbest. 3. t = 1;

4. while (t < Tmax) 5. for i = 1: N 6.  Calculate the Bf according to Equation (1). 7.   if Bf > 0.5% Exploration phase 8.    Update the position of the i-th using danger sensing mechanism in Equation (7). 9.   Else  %Exploitation phase 10.    Update the position of the i-th using dynamic foraging mechanism in Equation (8). 11.   End if 12. Calculate and rank the fitness values of beluga whales in the population. 13. Find the beluga whales in the best Xbest, middle Xmid, and worst Xworst positions. 14. Calculate the Wf according to Equation (11). 15.   if Bf ≤ Wf % Whale fall phase 16.    Update X according Equation (12). 17.   End if 18. End for 19.  t = t + 1. 20. End while

2.1.6. Complexity Analysis

The computational complexity of DSBWO involves the initialization of the population along with other proposed strategies. The computational complexity during the population initialization phase is O (NP × D). The computational complexity of the danger perception mechanism stage is O (NP × T_max). The computational complexity of the dynamic foraging mechanism stage is O (NP × T_max). The computational complexity of the improved whale fall phase is affected by the W_f and B_f, which can be approximated as O (0.1 NP × T_max). Therefore, the total computational complexity of DSBWO is O (0.1 NP × (1 + D + 0.1 T_max)).

2.2. Thresholding Methods

This section introduces two threshold segmentation methods: Otsu’s method and the Sobel edge detection algorithm, with details as follows:

Otsu’s method, also known as the Maximum Inter-class Variance Method, was proposed by Japanese scholar Otsu in 1978 [14]. This method takes an image as input and divides its pixels into target regions and background regions based on the grayscale histogram. By maximizing the difference between the target and background, the optimal threshold is determined [33,34]. Its principle is as follows: assuming the maximum grayscale level of the image is L, the method first calculates the frequency of each grayscale value. Then, pixels are classified into target and background groups based on a candidate threshold TH. The probabilities and average grayscale values of these two groups are computed, and the inter-class variance σ₂ is derived. The threshold that maximizes σ₂ is selected as the optimal threshold.

The Sobel edge detection algorithm, proposed by Irwin Sobel and Gary Feldman, is a discrete differential edge detection algorithm. It calculates the approximate brightness gradient of an image, identifies points in specific regions where the gradient exceeds a certain value, and marks these points as edge points [35,36]. A unique feature of the Sobel algorithm is its consideration of the influence of neighboring pixels on the current pixel: the closer the neighboring points, the greater their impact, while distant neighbors have minimal influence. Based on this principle, the algorithm employs horizontal and vertical gradient templates to compute the grayscale-weighted difference between a pixel and its upper, lower, left, and right neighbors [37,38]. Additionally, the Sobel algorithm integrates Gaussian smoothing and differentiation, which not only smooths the image to reduce noise interference but also enhances robustness against noise, enabling the more precise extraction of edge information.

3. Experimental Setup

In this section, the proposed DSBWO algorithm is compared with several recently developed meta-heuristic algorithms across multiple aspects. The CEC 2017 functions were employed to comprehensively evaluate the optimization performance of the algorithms on a wide range of problem types [39]. Additionally, the Berkeley Segmentation Dataset was used to perform multi-level threshold segmentation on images with varying characteristics, assessing each algorithm’s segmentation accuracy [40]. To further evaluate the overall performance of the DSBWO collaborative segmentation framework, we conducted experiments on potato leaf images affected by early and late blight. DSBWO was rigorously tested on 28 functions from the CEC 2017 suite to validate its optimization capability in complex environments. Subsequently, segmentation experiments were conducted using Otsu’s method as the objective function, with performance evaluated across 10 images featuring different textures and edge complexities, to assess DSBWO’s effectiveness in practical image processing tasks. Finally, Gaussian noise with varying intensity levels was added to the images to test and evaluate the noise robustness of the proposed method.

The potato leaf dataset was sourced from a publicly available repository: https://www.kaggle.com/datasets/hafiznouman786/potato-plant-diseases-data, accessed on 18 March, 2025. The dataset includes early disease, late disease, and healthy leaves, with a total of 2152 images. The resolution of each image in the group is (256 × 256) pixels. Figure 3 shows the original images and histograms of the different potato leaves, where IM_E1 and IM_E2 are images of potatoes affected by early blight, and IM_L1 and IM_L2 are images of potatoes affected by late blight. The experimental parameters remained consistent with the previous image segmentation series. Optimal results in the obtained data are highlighted in bold for clarity. All algorithms were developed in MATLAB 2019b, and computations were performed on an AMD Ryzen 9 3900 12-core processor (3.09 GHz) with 31.9 GB RAM.

3.1. Experimental Preparation

We compared DSBWO with six meta-heuristic algorithms: the chaos-based improved Harris hawk algorithm (NCHHO) [41], adaptively balanced grey wolf optimization algorithm (ABGWO) [42], jellyfish-based beluga whale optimization algorithm (JSBWO) [30], red-tailed hawk algorithm (RTH) [43], particle swarm and sea horse optimization algorithm (PSOSHO) [44], and modified grasshopper optimization algorithm (MGOA) [45]. Details of the algorithms involved in the comparison are given in

Table 1. Parameter setting of comparison algorithm.

Algorithm	References	Parameters
NCHHO	[41]	E0 = [0, 1].
ABGWO	[42]	A = [−2, 2], C = [0, 2];
JSBWO	[30]	φ = [0, 1], γ = 1, α = 3, β r = [0, 1].
RTH	[43]	s = 0.01, β = 1.5, A = 15, R0 = 0.5.
PSOSHO	[44]	s = 0.01, p = 0.5, u = 0.5, v = 0.5.
MGOA	[45]	Cmin = 0.0001, Cmax = 1, l = 1.5, β = 0.4.
DSBWO	-	ST = [0, 0.3], vb = [−1, 1].

.

To further strengthen the systematic and logical structure of the literature review, a brief analysis of the representative strengths and weaknesses of these algorithms is provided. Firstly, NCHHO enhances population diversity by introducing chaotic mapping, which provides certain advantages in overcoming premature convergence. However, this method exhibits weak stability on high-dimensionally complex functions. ABGWO improves the balance between global and local search capabilities by introducing dynamic adjustment factors, but it relies heavily on the initial population distribution and has relatively slow convergence speed. JSBWO, which integrates jellyfish searching behavior with BWO, strengthens the ability to escape from local optima. But the model is complex, and there is a certain trade-off in terms of solution time and convergence efficiency. By mimicking the multi-stage predatory method of hawks in nature, RTH improves the exploration of the solution space and presents a richer individual update method. The algorithm’s capacity for global convergence could be enhanced, nevertheless, as it has not yet been substantially modified for issues like image processing. PSOSHO speeds up searches by combining two traditional methods. But because of the addition of several weighting variables, there is a chance of premature convergence, and its stability is readily affected by parameter changes. MGOA emphasizes jumping exploration ability in its design, achieving good performance in solution accuracy, but its performance tends to fluctuate in complex objective function problems.

Due to the stochastic nature of optimization algorithms, the following experimental settings were adopted to ensure fair performance comparisons and obtain statistically reliable results. In the numerical experiments based on CEC 2017 functions, the parameters were configured as follows: population size N = 40, dimensionality D = 30, 30 independent runs per experiment, maximum runtime per run T_max = 30 s, penalty factor M = 10⁸. The mean (Mean) and standard deviation (Std) of the 30 runs were recorded. For the multi-threshold segmentation problem, the population size was uniformly set to N = 40. All experiments were conducted on test images with varying threshold numbers (TH = 4, 8, 15, 20), with each threshold level undergoing 30 independent runs with a runtime of 30 s per iteration. The best-performing data are highlighted in bold for clarity.

3.2. Performance Measures

The experiments employed Mean and Std as evaluation metrics for assessing algorithm performance. The mean value assesses the algorithm’s convergence accuracy, while the standard deviation quantifies its stability. The algorithm performs better with a smaller mean value, and a smaller standard deviation indicates more stability.

In the image segmentation experiments, peak signal-to-noise ratio (PSNR) [46], structural similarity (SSIM) [47], and IoU [48] were used to evaluate the performance and quality of the algorithm for segmenting images at different thresholds. Greater picture similarity and superior image segmentation performance are indicated by higher PSNR, SSIM and IoU values. The specific mathematical models are as follows:

$$\mathit{PSNR}=10{\log }_{10}\left({\displaystyle \frac{{255}^2}{MSE}}\right)$$

(15)

$$MSE={\displaystyle \frac{{\displaystyle \sum _{j=1}^M{\displaystyle \sum _{k=1}^N{\left[I(j,k)-I^{\prime }(j,k)\right]}^2}}}{M\times N}}$$

(16)

$$\mathrm{SSIM}\left(I,I^{\prime }\right)={\displaystyle \frac{\left(2{\mu }_I{\mu }_{I^{\prime }}+C_1\right)\left({\sigma }_{I{I}^{\prime }}+C_2\right)}{\left({\mu }_I^2+{\mu }_{I^{\prime }}^2+C_1\right)\left({\sigma }_I^2+{\sigma }_{I^{\prime }}^2+C_2\right)}}$$

(17)

$$\mathrm{IoU}={\displaystyle \frac{TP}{TP+FP+FN}}$$

(18)

where I and I′ are the original image to be evaluated and the segmented image, respectively; and M and N represent the length and width of the image, respectively. μ_I and μ_I’ are the meaning of the gray scale values of the original image I and the segmented image I’, respectively, and σ_II′ is the covariance between the gray scale values of the original image I and the segmented image I’. ${\sigma }_I^2$ is the variance of the gray value of the original image I, ${\sigma }_{I\prime }^2$ is the variance of the gray value of the I′ after segmentation, C₁ = 6.502, and C₂ = 58.522. The number of true examples (TP) refers to the number of pixels where both the real label and the predicted label are i; the number of false positive examples (FP) refers to the number of pixels where the predicted label is i but the true label is not i; the number of false counterexamples (FN) refers to the number of pixels where the true label is i but the predicted label is not i.

Moreover, two non-parametric tests were introduced to statistically examine the experimental data. A non-parametric statistical technique called the Friedman rank sum test [49] was used to rank the compared algorithms’ overall performance and determine whether there were any notable differences between them. The Wilcoxon rank sum test [50], another non-parametric test, was utilized for pairwise comparisons between algorithms. The significance level for the Wilcoxon rank sum test was set to α = 0.05. The p-value represents the error probability of accepting the validity of the observed results, and h was used to indicate whether there was significance between algorithms. If h = 1, it means the algorithm is significant; otherwise, there is no significance.

4. Results

4.1. Statistical Results for CEC 2017

Table 2. Experimental results of different algorithms with D = 30.

Image	TH	NCHHO	ABGWO	JSBWO	RTH	PSOSHO	MGOA	DSBWO
Friedman mean rank		2.625	3.6	4.68	4.75	2.9375	2.5	7
Rank		6	4	3	2	5	7	1

records the test results of DSBWO and other advanced optimization algorithms used to address CEC 2017 testing functionality, with specific details included in the Supplementary File.

Table 3. The results of Friedman test for various algorithms.

Dimension	Significant Level	χ2	${\mathit{\chi }}_{\mathit{\alpha }}^2[\mathit{k}-1]$	p-Value	Null Hypothesis	Alternative Hypothesis
D = 30	α = 0.05	133.18	12.59	2.7508 × 10−26	Reject	Accept

shows the outcomes of the Friedman rank sum test for each algorithm.

Table 4. The comparison results of the Wilcoxon rank sum test.

Comparison	w	t	l	p-Value	Significance
DSBWO vs. NCHHO	28	0	0	4.6471 × 10−6	Yes
DSBWO vs. ABGWO	27	0	1	1.6445 × 10−7	Yes
DSBWO vs. JSBWO	23	0	5	0.03382	Yes
DSBWO vs. RTH	25	0	3	0.1469	No
DSBWO vs. PSOSHO	28	0	0	5.5521 × 10−7	Yes
DSBWO vs. MGOA	28	0	0	1.6961 × 10−5	Yes

displays the p-value results of verifying the differences of the algorithms using the Wilcoxon rank sum test.

4.1.1. Analysis of CEC 2017 Statistical Results

Table 2 provides the Friedman’s mean rank and the rank ranking. The algorithm performs better when the Friedman mean rank is smaller. The minimum Friedman mean rank of DSBWO is 1.75, ranking first among all the algorithms. DSBWO has higher computational accuracy in most test functions compared to other algorithms. The outcomes demonstrated that DSBWO performs more effectively than the other participating algorithms.

The Friedman test was chosen to assess algorithm performance further and see whether there are notable differences amongst algorithms. The Friedman test results for each algorithm at the significance level of α = 0.05 are displayed in Table 3. If k = 6 and degrees of freedom k − 1 = 5, then ${\chi }_{\alpha }^2[k-1]$ = 11.07 < χ² = 111.84 is greater than the critical value of 11.07, therefore rejecting the null hypothesis suggesting that there is an important distinction between the performances of the algorithms being compared. We verified the significance of pair-wise differences using the Wilcoxon rank sum test algorithm. As can be seen from the results presented in Table 4, most of the p-values are less than 0.05. Although the difference between DSBWO and RTH is not significant, DSBWO performs better than RTH in terms of its Friedman mean rank and the accuracy of other test functions. In summary, this indicates that DSBWO has significant superiority over other algorithms.

4.1.2. Convergence Curve Analysis

Figure 4 illustrates the convergence curves of selected test functions, where all algorithms were independently executed 30 times to record their average convergence rates. As can be seen in Figure 4, the convergence speed of DSBWO is superior to the other six algorithms at the beginning of the iteration, which indicates that DSBWO has a robust local search ability. At the same time, the best solution acquired by DSBWO is notably better than the six algorithms, demonstrating that DSBWO has excellent exploration ability. Therefore, DSBWO facilitates a more effective balance between exploration and exploitation within the algorithm. Figure 4a–c show that DSBWO has a powerful exploration ability in the beginning stages of iteration. It can also quickly converge to the optimal solution in the early stages of iteration and has better solution accuracy than the other methods. Furthermore, for (d–f), as the number of iterations increases, the comparison algorithms rapidly tackle the local optimum, leading to poor solution quality. In contrast, DSBWO exhibits a robust exploration capability, can quickly escape the local optimum, and converges rapidly, suggesting that the danger sensing mechanism and dynamic foraging mechanism can help to balance the performance of the algorithm so that the algorithm can find the best solution more quickly.

In conclusion, the DSBWO algorithm achieves an effective balance between exploration and exploitation. By integrating a danger sensing mechanism, the algorithm significantly enhances its global exploration capability while reducing the risk of becoming trapped in local optima. This improvement enables DSBWO to maintain both strong global search ability and precise local refinement, resulting in robust and reliable optimization performance across diverse problem scenarios.

4.2. Otsu Segmentation Experiment Results

The original images and their histograms are presented in Figure 5.

Table 5. Friedman mean rank of Otsu fitness values for all test images.

Algorithms	NCHHO	ABGWO	JSBWO	RTH	PSOSHO	MGOA	DSBWO
Friedman mean rank	2.625	3.6	4.68	4.75	2.9375	2.5	7
Rank	6	4	3	2	5	7	1

shows the Friedman mean rank of fitness values for each algorithm obtained using the Otsu method, while

Table 6. Friedman mean rank results of PSNR and SSIM at different thresholds.

TH	NCHHO		ABGWO		JSBWO		RTH		PSOSHO		MGOA		DSBWO
	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
4	3.7	4.3	2.2	3.7	4.5	4.7	5.7	3.3	3.2	2.8	2	2.7	6.7	6.5
8	4.3	3.9	3.2	3.9	4.9	3.3	2.6	3.7	3.1	3.9	3	2.3	6.9	7
15	4.5	3.1	3.5	4.2	3.6	4.8	4.1	3.7	3.3	2.8	2.5	2.7	6.5	6.65
20	3.7	3.8	2.4	4.3	5.1	5.4	4.2	2.9	3.5	3.3	2.5	2.9	6.6	6.8

presents the Friedman mean rank of PSNR and SSIM for different algorithms.

An algorithm having a higher mean rank suggests greater effectiveness in image segmentation, with DSBWO’s Friedman mean ranking first at 6.7 in Table 5, with specific details provided in the Supplementary File. JSBWO’s Friedman mean rank result is 4.9, which is ranked second; RTH is ranked third with a rank of 4.35, and after that, the order of the rankings is as follows: NCHHO, PSOSHO, ABGWO, and MGOA. The Friedman mean rankings of PSNR and SSIM at different threshold levels using the Otsu method are displayed in Table 6. It is evident that DSBWO ranks highest in the Friedman rank ranking of several threshold experiments. The Otsu fitness value, PSNR, and SSIM demonstrate the algorithm’s excellent robustness. Additionally, as the threshold number increases, the segmentation effect of DSBWO improves. At TH = 20, the algorithm’s fitness value has a Friedman mean rank of 6.6, the Friedman mean rank of PSNR is 6.8, and the mean rank of SSIM is 6.9. The algorithm’s Friedman rank ranking is the highest when compared to the other techniques.

To further analyze the results of the experiment, the experiment was statistically tested at various threshold numbers. The outcomes of the Wilcoxon rank sum test and Friedman rank test for the participating algorithms at various thresholds are shown in

Table 7. Friedman rank test of different thresholds.

TH	χ2	${\mathit{\chi }}_{\mathit{\alpha }}^2[\mathit{k}-1]$	p-Value	Null Hypothesis	Alternative Hypothesis
4	42.77	12.59	1.2944 × 10−7	Reject	Accept
8	30.39	12.59	3.3197 × 10−5	Reject	Accept
15	27.09	12.59	1.0000 × 10−4	Reject	Accept
20	36.16	12.59	6.2733 × 10−6	Reject	Accept

and

Table 8. Wilcoxon rank sum test for the experiments based on the Otsu method.

TH	NCHHO vs. DSBWO		ABGWO vs. DSBWO		JSBWO vs. DSBWO		RTH vs. DSBWO		PSOSHO vs. DSBWO		MGOA vs. DSBWO
	p	h	p	h	p	h	p	h	p	h	p	h
4	0.0290	1	0.0409	1	0.0513	0	0.0413	1	0.0013	1	0.0172	1
8	0.0452	1	0.0113	1	0.0173	1	0.0257	1	0.0091	1	0.0091	1
15	0.0211	1	0.0211	1	0.0022	1	0.0073	1	0.0257	1	0.0257	1
20	0.0211	1	0.0173	1	0.0257	1	0.0064	1	0.0312	1	0.0036	1

, respectively. Table 7 shows that when the threshold values are 4, 8, 15, and 20, the corresponding χ² values are 42.77, 30.29, 27.09, and 36.16, respectively, with p-values of 1.2944 × 10⁻⁷, 3.3197 × 10⁻⁵, 1 × 10⁻⁴, and 6.2733 × 10⁻⁶. The ${\chi }_{\alpha }^2[k-1]$ = 12.59 < χ² for the different threshold levels; also, the p-value is less than 0.05 for the different threshold levels. This implies that when the threshold levels are set at 4, 8, 15, and 20, the null hypothesis is accepted, suggesting a noteworthy difference in performance between DSBWO and other comparative algorithms.

The Wilcoxon rank sum test results using the Otsu method are given in Table 8. When comparing algorithms at different threshold levels, it is evident that DSBWO consistently yields p-values below 0.05, unlike NCHHO, ABGWO, RTH, PSOSHO, and MGOA. The difference between DSBWO and JSBWO is not significant at a TH of only 4, and the p-values in all other cases are less than 0.05. Under high threshold conditions, DSBWO has a better p-value. Therefore, DSBWO has superior performance and significant differences to other algorithms.

4.3. Results of Otsu–Sobel Collaborative Segmentation of Potato Disease Images

The potato disease images and their histograms are presented in Figure 5.

Table 9. Results of Otsu–Sobel segmentation of diseased potato images.

Image	TH = 4	TH = 8	TH = 15	TH = 20
IM_E1
IM_E2
IM_L1
IM_L2

presents the segmentation outcomes of potato early blight and late blight images acquired through DSBWO utilizing the Otsu–Sobel edge detection method at threshold levels of 4, 8, 15, and 20. Specifically, in each image, the first row corresponds to the segmentation results obtained by combining the Otsu and Sobel methods at varying threshold levels, the second row shows the segmentation results achieved solely using the Otsu method, and the third row displays the edge detection results derived from the Sobel operator. Here, it is evident that as the threshold level increases, the segmentation quality of image thresholding significantly improves, and the detection results of using the cooperative segmentation strategy on diseased leaves become more distinct. Consequently, the threshold–edge collaborative segmentation of potato disease images can more clearly and accurately locate the positions of disease spots on the leaves.

In Table 9, when the threshold is 4 or 8, the collaborative segmentation of the early blight (IM_E1) and late blight (IM_L2) images identifies significant disease spots in the segmented images, but the detail is not well preserved. At the high threshold levels of TH = 15 and 20, by implementing more-precise threshold division and edge gradient constraints, the integrity of the lesion contour is significantly enhanced, allowing for a more detailed and accurate localization of the lesion contour. This indicates that the Otsu–Sobel collaborative strategy overcomes the limitations of single methods, thereby improving diagnostic efficiency for both early blight and late blight diseases while reducing the miss rate of early-stage lesions.

The Friedman mean ranks of Otsu–Sobel fitness values at different thresholds are presented in

Table 10. Friedman mean rank of Otsu–Sobel fitness values at different thresholds.

Algorithms	NCHHO	ABGWO	JSBWO	RTH	PSOSHO	MGOA	DSBWO
Friedman mean rank	2.625	3.6	4.68	4.75	2.9375	2.5	7
Rank	6	4	3	2	5	7	1

. The results show that DSBWO achieved the highest Friedman mean rank of 6, ranking first of all the algorithms. This indicates that DSBWO possesses stable optimization-seeking capability and delivers the best performance in segmenting potato early blight and late blight images, securing the top rank.

Table 11. Friedman mean rank of PSNR and SSIM values with different algorithms.

Image	NCHHO		ABGWO		JSBWO		RTH		PSOSHO		MGOA		DSBWO
	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
IM_E1	3.75	3	3.5	4.375	3.5	4.7	5	4.5	3.75	2.375	1.75	2.875	6.75	7
IM_E2	3	2. 875	3.25	4.375	4.5	3.3	3.25	6	4	3.875	3	2	7	6.75
IM_L1	3	3.25	4.5	4	3.25	4.8	5.75	5.25	3.5	3	1.75	1.75	6.25	7
IM_L2	3	2	2.4	3.25	2.75	5.4	4.75	6	4	4.5	3.5	3	7	7

displays the Friedman mean rank of PSNR and SSIM from potato image segmentation. By using PRNR and SSIM, the correlation between images before and after segmentation can be determined, which can help evaluate the quality of the segmentation results. A higher PRNR indicates lower segmentation error and helps reduce false positives. The higher the value of SSIM, the better the segmentation effect, indicating outstanding performance in the smoothness of lesion edges and structural integrity. The experimental results demonstrate that DSBWO consistently outperforms other methods across all threshold levels, achieving the highest accuracy and structural integrity in segmenting potato disease images.

Table 12. The IoU and CPU of diseased potato images with different threshold algorithms.

Image	NCHHO		ABGWO		JSBWO		RTH		PSOSHO		MGOA		DSBWO
	IoU	CPU	IoU	CPU	IoU	CPU	IoU	CPU	IoU	CPU	IoU	CPU	IoU	CPU
IM_E1	0.8541	1.782	0.89544	1.783	0.8409	1.793	0.8797	1.787	0.8442	1.778	0.8525	1.768	0.8769	1.763
IM_E2	0.8654	1.791	0.8614	1.846	0.8650	1.802	0.8617	1.792	0.8539	1.811	0.8607	1.782	0.8716	1.771
IM_L1	0.8613	1.867	0.8561	1.875	0.8676	1.851	0.8733	1.873	0.8685	1.855	0.8573	1.854	0.8828	1.830
IM_L2	0.8692	1.914	0.8683	1.871	0.8476	1877	0.8721	1.866	0.8613	1.872	0.8638	1.865	0.8867	1.851

presents the IoU and CPU time of different algorithms on four diseased potato leaf images. As shown in Table 12, the proposed DSBWO algorithm achieves the highest IoU values on all four images, with an average IoU of 0.8797, which is significantly higher than other algorithms such as JSBWO and PSOSHO, demonstrating superior segmentation accuracy and stability. In terms of computational efficiency, DSBWO maintains a CPU time of 1.805 s, outperforming most of the comparison algorithms. This indicates that the proposed method achieves a good balance between segmentation accuracy and runtime performance. In summary, DSBWO exhibits excellent precision, efficiency, and robustness in multi-threshold segmentation tasks for potato disease images, showing strong potential for practical application.

4.4. Collaborative Segmentation Experiments Under Different Noise Intensities

To evaluate the segmentation robustness of the proposed DSBWO method under noise interference, Gaussian noise of varying intensities (p = 0.01, 0.02, 0.03) was added to four potato disease images, and the performance was compared against six advanced algorithms. The effectiveness of the segmentation under noisy conditions was assessed using PSNR, SSIM, IoU, and CPU time.

Table 13. Images with different noise intensities and DSBWO collaborative segmentation.

Image	IM_E1	IM_E2	IM_L1	IM_L2
p = 0.01
p = 0.02
p = 0.03

presents the results of applying the DSBWO collaborative segmentation method to each image with added Gaussian noise. The first row shows the disease images after adding Gaussian noise of varying intensities, while the second row displays the corresponding segmentation results produced using the DSBWO method.

Table 14. PSNR and SSIM results of segmentation by various algorithms under different noise levels.

Image	p	NCHHO		ABGWO		JSBWO		RTH		PSOSHO		MGOA		DSBWO
		PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
IM_E1	0.01	31.08	0.8482	30.74	0.8283	30.48	0.8443	31.17	0.8760	31.02	0.8278	30.85	0.8068	31.29	0.8653
	0.02	30.73	0.8134	30.15	0.8007	30.12	0.8122	30.80	0.8541	30.64	0.8093	30.17	0.8005	31.01	0.8432
	0.03	29.68	0.7912	28.92	0.7824	29.83	0.8001	30.42	0.8223	30.20	0.8001	29.69	0.7946	30.78	0.8221
IM_E2	0.01	32.20	0.8291	32.34	0.8546	32.30	0.8342	32.37	0.8479	32.19	0.8221	32.17	0.8271	32.40	0.8571
	0.02	32.01	0.8132	31.71	0.8233	32.11	0.8240	32.15	0.8236	31.23	0.8097	32.01	0.8128	32.22	0.8468
	0.03	31.55	0.8062	31.34	0.8071	31.96	0.8102	32.02	0.8134	31.14	0.8003	31.54	0.8060	32.15	0.8324
IM_L1	0.01	33.17	0.8580	33.22	0.8619	33.07	0.8432	33.27	0.8653	33.01	0.8407	33.08	0.8432	33.30	0.8691
	0.02	33.06	0.8365	33.12	0.8434	32.86	0.8331	33.16	0.8546	32.85	0.8235	32.91	0.8331	33.22	0.8568
	0.03	32.81	0.8173	32.94	0.8208	32.53	0.8023	33.02	0.8301	32.45	0.8010	32.62	0.8023	33.14	0.8423
IM_L2	0.01	30.36	0.8617	30.32	0.8608	30.37	0.8701	30.42	0.8726	30.29	0.8602	30.35	0.8615	30.44	0.8728
	0.02	30.20	0.8562	30.11	0.8524	30.15	0.8526	30.25	0.8623	30.13	0.8515	30.21	0.8562	30.27	0.8630
	0.03	29.92	0.8513	29.88	0.8503	29.86	0.8502	30.13	0.8547	29.84	0.8501	29.94	0.8515	30.16	0.8551

shows the PSNR and SSIM statistics of each algorithm under different noise levels. In Table 14, DSBWO achieved consistently high PSNR and SSIM values under various noise intensities, indicating strong robustness. In most cases, it ranked first or second among all the algorithms. Even as the noise intensity increased and the performance of all algorithms declined, DSBWO maintained a PSNR of 30.78 and an SSIM of 0.8221, demonstrating strong anti-noise capability.

The IoU and CPU time of each algorithm at various noise levels are displayed in

Table 15. IoU and CPU results of segmentation by various algorithms under different noise levels.

Image	p	NCHHO		ABGWO		JSBWO		RTH		PSOSHO		MGOA		DSBWO
		IoU	CPU	IoU	CPU	IoU	CPU	IoU	CPU	IoU	CPU	IoU	CPU	IoU	CPU
IM_E1	0.01	0.8540	1.822	0.8544	1.830	0.8531	1.829	0.8557	1.817	0.8532	1.828	0.8534	1.819	0.8559	1.813
	0.02	0.8532	1.825	0.8537	1.833	0.8517	1.831	0.8544	1.821	0.8523	1.831	0.8526	1.824	0.8548	1.820
	0.03	0.8517	1.837	0.8518	1.846	0.8492	1.842	0.8523	1.834	0.8504	1.844	0.8505	1.835	0.8530	1.831
IM_E2	0.01	0.8643	1.841	0.8633	1.846	0.8644	1.842	0.8647	1.840	0.8554	1.841	0.8621	1.844	0.8661	1.840
	0.02	0.8626	1.850	0.8628	1.852	0.8624	1.848	0.8634	1.846	0.8543	1.847	0.8613	1.849	0.8654	1.845
	0.03	0.8608	1.857	0.8604	1.858	0.8606	1.856	0.8601	1.853	0.8529	1.855	0.8594	1.858	0.8638	1.853
IM_L1	0.01	0.8543	1.877	0.8554	1.875	0.8545	1.876	0.8556	1.875	0.8545	1.878	0.8542	1.878	0.8557	1.873
	0.02	0.8522	1.881	0.8542	1.880	0.8533	1.882	0.8547	1.881	0.8536	1.883	0.8534	1.883	0.8549	1.880
	0.03	0.8507	1.893	0.8525	1.891	0.8517	1.893	0.8521	1.891	0.8518	1.894	0.8521	1.892	0.8530	1.889
IM_L2	0.01	0.8439	1.923	0.8436	1.921	0.8422	1.923	0.8448	1.918	0.8434	1.922	0.8428	1.922	0.8450	1.915
	0.02	0.8428	1.926	0.8428	1.923	0.8418	1.925	0.8438	1.923	0.8425	1.927	0.8420	1.927	0.8442	1.922
	0.03	0.8413	1.932	0.8414	1.931	0.8406	1.932	0.8427	1.930	0.8411	1.934	0.8409	1.933	0.8331	1.930

. As shown in Table 15, DSBWO consistently achieved the highest or second-highest IoU score across all noise conditions. For example, on the IM_E2 image, DSBWO achieved IoU values of 0.8661, 0.8654, and 0.8638 under the three noise levels, outperforming all other algorithms. Additionally, DSBWO maintained the lowest or near-lowest CPU time, averaging around 1.82 s. DSBWO shows excellent segmentation and accuracy and stable performance in noisy conditions, proving its robustness and practicality.

4.5. Discussion

The potato disease image segmentation method based on DSBWO provides an effective solution to address the deficiencies of traditional image segmentation algorithms in complex agricultural environments. Through comparisons with a variety of existing algorithms, the experimental findings demonstrate that DSBWO exhibits powerful advantages in multiple aspects, especially in solving optimization problems and in terms of the accuracy of image segmentation.

Firstly, DSBWO demonstrated strong global search capabilities and fast convergence in the CEC 2017 test functions. Compared with other comparative algorithms, DSBWO can better balance global exploration and local exploitation, avoiding the risk of prematurely falling into local optimal solutions. Therefore, DSBWO exhibits higher optimization accuracy when dealing with complex optimization problems. Moreover, the results of threshold segmentation experiments indicate that DSBWO outperforms other algorithms in segmenting images depicting potato disease spots. Especially in the Otsu–Sobel collaborative segmentation experiment, DSBWO can provide clear and accurate disease spot edges under both low-threshold and high-threshold conditions.

In addition, the noise robustness of DSBWO was evaluated under different levels of Gaussian noise. The results show that, compared to other algorithms, DSBWO consistently achieved higher PSNR and SSIM values, as well as more-stable IoU scores across all noise levels. Notably, even under strong noise conditions, DSBWO maintained high segmentation accuracy and structural similarity, while keeping the CPU runtime low and stable. This demonstrates that DSBWO has excellent robustness against noise interference and can still deliver reliable segmentation results in the presence of complex environmental disturbances. These findings further validate the practical applicability and adaptability of DSBWO in real-world agricultural image analysis.

5. Conclusions

This study proposes a potato disease image segmentation method based on the beluga whale optimization algorithm with a danger sensing mechanism (DSBWO), which combines Otsu multi-threshold segmentation and the Sobel edge detection algorithm, aiming to improve the accuracy and robustness of disease spot segmentation. Through experimental verification using the CEC 2017 benchmark functions and actual agricultural images, the results show that DSBWO outperforms other comparative algorithms in multiple tests, exhibiting higher segmentation accuracy and stronger robustness.

With the addition of S-shaped control parameters, a danger sensing mechanism, a dynamic foraging mechanism, and an improved whale fall strategy, DSBWO displays effectively increased picture segmentation performance. Furthermore, the robustness of DSBWO was evaluated under varying levels of Gaussian noise. Compared to other algorithms, DSBWO achieved consistently higher PSNR, SSIM, and IoU values across all noise intensities, while maintaining a lower and more stable CPU runtime. These results confirm that DSBWO maintains excellent segmentation performance even under severe noise interference, demonstrating strong anti-noise robustness and adaptability to complex environmental conditions.

This study provides an efficient and robust solution for agricultural image segmentation. This framework serves potato disease management and can also be extended to crop phenotypic analysis and yield prediction in smart agriculture. In addition to its application in image segmentation, DSBWO can be applied to other real-world applications, such as estimating the parameters of solar cells and optimizing mechanical parameters.