Application of Improved Gravity Search Algorithm in Image Edge Detection

Abstract

In order to address the issues of noise sensitivity, edge discontinuity, false positives, and false negatives in image edge detection, this paper proposes an enhanced gravity search algorithm (IGSA). Through experiments on three datasets: CSet8, BSD500, and OTCBVS, the system compared the performance differences between this algorithm and traditional edge detection methods. The results showed that IGSA improved the detection accuracy by 7% on ordinary color images, and by 3.5% on images with added Gaussian white noise. In addition, in infrared images, the edge linear connectivity reaches 1.333, which is 9.6% higher than traditional methods. These results fully demonstrate that the proposed algorithm not only improves the accuracy of edge detection, but also exhibits stronger robustness under noise interference.

Keywords

gravitational search algorithm image edge detection infrared image edge linear connection

1 Introduction

The swarm intelligence algorithm achieves global search capability and adaptive adjustment by simulating the cooperation and competition observed in nature, offering a new solution for the task of image edge detection (Engineering, 2019). Gravitational Search Algorithm (GSA), as an emerging optimization method, has global search ability and strong adaptability and has achieved remarkable results in many fields. The gravitational search algorithm is an optimization algorithm based on swarm intelligence, which simulates the gravitational interaction and motion process between objects and has global search capabilities and good convergence. However, traditional gravitational search algorithms have some limitations in image edge detection, such as sensitivity to noise, inaccurate edge connection, etc.

Therefore, this research aims to improve the gravitational search algorithm to enhance its performance in image edge detection. By introducing technologies such as multi-scale edge detection, smoothing, bilateral filtering, and adaptive threshold, it is hoped that noise interference can be effectively reduced, more accurate edge information can be extracted, and the adaptability of the algorithm to different image features can be enhanced. This will provide higher accuracy and robustness for research and practical applications in the field of image edge detection.

2 Research Status

Image edge detection is one of the important tasks in the field of computer vision and image processing. It plays a key role in many applications such as object recognition, scene understanding, and image segmentation (Rojalin et al., 2021). However, traditional edge detection methods have certain limitations in complex images, low contrast, and noisy environments, resulting in inaccurate edge detection results or containing a lot of noise (Zheng et al., 2023). There are still some unsolved problems in the field of image edge detection. Performance in complex scenes remains challenging, especially in the presence of texture complexity, lighting variations, and occlusions. The detection of weak edges or blurry boundaries remains a challenge, which may lead to missed or false detections (Zhang et al., 2022). Real-time and efficiency have become the requirements of practical applications, so how to improve the speed of the algorithm while maintaining accuracy still needs to be explored (Tang et al., 2017). At the same time, how to design an edge detection algorithm that is highly versatile and can adapt to the needs of different scenarios is also a problem that needs to be solved.

The swarm intelligence algorithm has the advantages of global search, robustness, diversity, parallelism, flexibility, and integration with deep learning in image edge detection. These advantages make the swarm intelligence algorithm a powerful tool to effectively improve the performance of image edge detection (Xing & Shang, 2023). For example, Lu Mengyuan proposed a slime swarm algorithm to improve the accuracy of image edge detection. This method can effectively solve the accuracy problem of image edge detection (Lu & Cai, 2022).

The gravitational search algorithm is an optimization algorithm based on swarm intelligence, which simulates the gravitational interaction and motion process between objects and has global search capabilities and good convergence (Wang et al., 2016). In order to solve the computationally complex problem of high-dimensional threshold image segmentation, Li Haitao proposed a multi-threshold image segmentation method based on the gravitational search algorithm. Compared with the cuckoo algorithm and artificial bee colony algorithm, the convergence speed of the gravity search algorithm is faster. The optimized threshold has higher quality (Li & Zhang, 2019). Keming J optimized the Gravity Search Algorithm (GSA) and the gbest-guided Gravity Search Algorithm (GLGSA) by leveraging the memory capabilities of the gbest agent (Jiao & Pan, 2019). GSA is an optimization algorithm inspired by the law of gravitation in nature, originally used for continuous optimization problems. GSA optimizes the image edge detection process by simulating the gravitational interaction to find the best edge position. It has global search ability and adaptability and can effectively overcome the local extremum problem (Gui & Wu, 2011). Elmi et al. proposed an innovative edge detection method that combines grayscale, discrete vector generation, matching tracking, and dual threshold lag to improve detection efficiency and robustness (Elmi & Elmi, 2022; Hadi et al., 2021).The Diffusion Edge diffusion model proposed by Yunfan Ye optimizes edge detection tasks by applying DPM and adaptive Fourier filters in latent space, achieving higher accuracy and clarity (Ye et al., 2024).Huanxu Li proposed an edge detection method that integrates denoising modules and adaptive thresholding techniques, using wavelet and Gaussian denoising to improve the OTSU method and significantly enhance the edge detection performance in noisy environments (Li & Xu, 2025).However, traditional gravitational search algorithms have some limitations in image edge detection, such as sensitivity to noise, inaccurate edge connection, etc.

Therefore, this research aims to improve the gravitational search algorithm to enhance its performance in image edge detection. A hybrid strategy is adopted to better balance the exploration and utilization of different optimization stages by using techniques such as multi-scale edge detection, smoothing, bilateral filtering, and adaptive thresholding. We hope to effectively reduce noise interference, extract more accurate edge information, and enhance the ability of the algorithm to adapt to different image features. This will provide higher accuracy and robustness for research and practical applications in the field of image edge detection.

3 Algorithm Summary

3.1 Algorithm Thought

The core idea of the Improved Gravity Search Algorithm (IGSA) is to simulate the gravitational interaction and motion process between objects and search for the optimal solution by continuously adjusting the position and velocity of particles (Ho et al., 2021). The basic steps of the algorithm include initializing particle position and velocity, calculating fitness value, calculating gravity and acceleration, updating particle position and velocity, and repeating iterations until the stopping condition is satisfied (Kang, 2021). In the algorithm, better particles will generate greater gravitational force on other particles, attracting them to move to the optimal position, so as to achieve the goal of global search and optimization. The gravitational search algorithm has the characteristics of simplicity and easy implementation and is suitable for various optimization problems. However, when dealing with complex problems and optimizing in high-dimensional spaces, it may be necessary to properly adjust and optimize the algorithm to improve performance and effectiveness.

3.2 Algorithm Principle

The gravity search algorithm uses the law of gravitational force between objects to search for the optimal solution, and it possesses outstanding overall optimization ability (Ma & Cai, 2023). Considering actual application requirements, improvements have been made in algorithm initialization, multi-scale edge detection, bilateral filtering, and adaptive threshold, resulting in the enhanced gravitational search algorithm (Improved Gravitational Search Algorithm, IGSA). The improved algorithm is applied to various types of images, endowing it with the capability to detect image edges.During algorithm initialization, the initial particles are evenly selected in the search space, enabling exploration across a large area without concentration in a specific region. This facilitates the discovery of a broader solution space and helps avoid falling into a partial optimal solution. The uniform distribution of initial particles allows each particle to interact with the information of other particles during the search process, promoting communication and collaboration between particles. This accelerates convergence and enhances algorithm efficiency. The uniform distribution also prevents particle aggregation in a local area, reducing instability and bias in the search process, contributing to the stability and reliability of the algorithm.Evenly distributing the initial particles makes the algorithm robust in searching the space. When the search space changes, particles can quickly adapt to the new environment and re-explore the potential solution space. Applying the gravitational search algorithm to image edge detection involves establishing a 2-dimensional space gravitational system with a grayscale image.There are N pixels, defining the i pixel point position $X_{i} = x_{i}^{1}, . ., x_{i}^{d}, \dots x_{i}^{n}, (i = 1, 2,, \dots, N)$ . Among them: $x_{i}^{d}$ is i pixel point in the second dimension.

The quality of Pixel i in Tshable in t indicates the edge probability of its edge detection.The higher the quality of Pixel Ieraton i iteration, the more likely it is to be part of the edge. The formula is as follows:

\begin{aligned} m_{i} (t) & = \frac{f i t_{i} (t) - w o r s t (t)}{b e s t (t) - w o r s t (t)} \end{aligned}

(1)

\begin{aligned} m_{i} (t) & = \frac{m_{i} (t)}{\sum_{j = 1}^{N} m_{j} (t)} \end{aligned}

(2)

In the formula: $f i t_{i} (t)$ is the functional value of the adaptation of the pixel i at the t -aerated Pixel I. Solve the extremely small value of the adaptation function, and the edge response is used as the measurement of the adaptation function. If the edge value is small in the space, there is a great difference compared to the surrounding pixels and It is believed that the pixel point represents the edge. The formula is as follows:

\begin{aligned} best (t) & = minfi t_{j} (t) \end{aligned}

(3)

\begin{aligned} worst (t) & = maxfi t_{j} (t) \end{aligned}

(4)

The d-dimensional space in the gravitational search algorithm can represent the characteristic space of the image, such as pixel strength and gradient direction. The i particle represents a pixel point in the image, and the j particle represents another pixel point. When the j point is similar to the i pixel point in the characteristic space, the force will increase; when they are in a location where the characteristic space is large, the effect will be reduced. By calculating the force between each pixel point and its adjacent pixel points and comprehensively considering the forces of multiple adjacent pixels, a gravitational system can be formed to determine the position and connection of the edge points. The edge points exhibit similarity in the characteristic space and are subject to the gravitational effect of adjacent points. Through the calculation and mutual impact of this force, the extraction and connection of the edges can be achieved. The formula is as follows:

\begin{aligned} F_{i j}^{d} (t) & = G (t) \frac{M_{I} (t) M_{j} (t)}{∥ X_{i} (t), X_{j} (t) ∥_{2} + ε} [x_{j}^{d} (t) - x_{i}^{d} (t)] \end{aligned}

(5)

\begin{aligned} G (t) & = G_{0} e^{- at / T} \end{aligned}

(6)

In the formula: $ε$ is the constant of nearly 0; G(t) is t todone the gravitational constant, t is the number of iterations, $G_{0}$ = 100, $a = 20$ .

In the d-dimensional space, the i pixel point is influenced by other pixels, involving random weighing and representation of the gravitational force for each pixel point. Assuming there are N pixels, each pixel point j affecting the i pixel point has a gravitational force denoted as G_ij. To calculate the gravitational force experienced by the initial pixel, the gravity of all pixels can be considered. By weighting the gravity of all pixels in accordance with random weights, one can obtain the gravitational force experienced by the i pixel point in the d-dimensional space. This gravitational force is then used to update the position and speed of pixel points during subsequent iterations. The formula is as follows:

\begin{aligned} F_{i}^{d} (t) = \sum_{j = 1 j \neq i}^{N} r a n d F_{i j}^{d} (t) \end{aligned}

(7)

In the formula: RAND represents a range of [0, 1]. By applying gravitational force to remove the pixel's quality (the functional value of the adaptation), the acceleration of the pixel can be determined under the influence of gravity. This acceleration is then utilized to update the position and speed of pixel points during the iteration of the gravitational search algorithm, thereby accomplishing edge detection and optimization. The formula is as follows:

\begin{aligned} a_{i}^{d} (t) = F_{i}^{d} (t) / M_{i} (t) \end{aligned}

(8)

In IGSA, pixel i update in the position $x_{i}^{d} (t)$ and velocity of $v_{i}^{d} (t)$ the d-dimiped space to achieve the iterative process, speed and location update, speed update and location update. Image edge detection. Speed determines the sensitivity and movement direction of pixels, and the position reflects the movement trajectory of pixels in the search space. By continuously updating speed and position, GSA can gradually gather pixels to gradually gather in the edge area of the image. The formula is:

\begin{aligned} v_{i}^{d} (t + 1) & = r a n d v_{i}^{d} (t) + a_{i}^{d} (t) \end{aligned}

(9)

\begin{aligned} x_{i}^{d} (t + 1) & = x_{i}^{d} (t) + v_{i}^{d} (t + 1) \end{aligned}

(10)

The adaptive threshold T in IGSA is computed based on the statistical properties of the image grayscale values, defined as T = μ + k $\cdot$ σ, whereμandσrepresent the mean and standard deviation of the image grayscale, respectively, and k is a tunable coefficient set to 1.0 in our experiments. This approach enables automatic adjustment of the threshold to accommodate variations in image brightness and contrast, thereby enhancing the robustness and accuracy of segmentation.The IGSA introduces three core innovations compared to the traditional gravitational search algorithm. First, the initialization of particles is performed uniformly across the search space to ensure broad exploration and prevent premature convergence. Second, an adaptive thresholding mechanism is employed, where the threshold is dynamically determined based on grayscale image statistics, allowing the algorithm to adjust to different contrast and noise levels without manual intervention. Third, the particle update strategy incorporates a dynamic gravitational decay function and local feedback based on particle fitness variance, enhancing convergence speed and balance between exploration and exploitation. These innovations synergistically improve the algorithm's stability, robustness, and detection accuracy across various image types.

4 Experiments and Results

In order to validate the effectiveness of IGSA in image edge detection, numerous simulation experiments were conducted. The experimental environment included Windows 11 Professional Edition running on a 12th Gen Intel(R) Core(TM) i5-12400F processor at 2.50 GHz with 32GB of memory. The program operated in a Python 3.10.11 environment.This study used three publicly available datasets (CSet8, BSD500, and OTCBVS) to validate the effectiveness of the proposed Improved Gravitational Search Algorithm (IGSA). These datasets are widely used for edge detection tasks, with good representativeness and diversity, covering different types of image samples such as natural images, texture images, and infrared images. Before the experiment, all images were uniformly scaled to 256 × 256 pixels and converted to grayscale images to simplify feature processing and focus on evaluating the detection performance of structural edges. At the same time, to test the denoising performance of the algorithm, Gaussian white noise, salt and pepper noise, and speckle noise were added to simulate actual interference environments. In terms of parameters, the main hyperparameters in IGSA (such as gravitational constant G = 1, particle number N = 30, maximum iteration time T = 100, position update factor α = 0.9) were optimized using grid search on the validation set to ensure the stability and robustness of the algorithm in most image scenes. In addition, to enhance the adaptability of the algorithm, an adaptive threshold mechanism is introduced, which dynamically adjusts the edge judgment criteria based on the statistical characteristics of the image (such as grayscale mean and standard deviation), reducing manual intervention. The overall method is based on the assumption that the image edge region has high gradient response and noise exhibits local high-frequency disturbance, thereby constructing a quality model through the edge response function, enhancing edge attractiveness, and effectively suppressing false positives.

4.1 Color Image Experiment

The parameter settings for IGSA were determined using grid search on the validation subset of the datasets. The search ranges were as follows: gravitational constant G∈[0.5, 2.0], particle number N∈[10, 50], maximum iterations T∈[50, 200], and update coefficient α∈[0.7, 0.95], with appropriate step sizes. Sensitivity analysis revealed that IGSA is most sensitive to the gravitational constant and particle number. For instance, an overly large G led to instability and oscillations, while a small N degraded global search capacity.The test was conducted on a total of 510 images from the commonly used digital image processing datasets CSet8 and BSD500. The image size is 256 × 256 pixels. Sobel, Laplace, Roberts, Genetic Algorithm (GA), Plant Community Algorithm (PCA) (Ray, 2013), and Single Image Kunal Ray (KRC) (Mo et al., 2022) for unsupervised edge detection were employed. Additionally, the image edge detection algorithms, including the ZOM algorithm based on sub-pixel edge detection and tracking, the sub-pixel edge detection algorithm (SID) (Wang & Chen, 2022) based on improved Gaussian fitting and the Canny operator, as well as the GSA and IGSA algorithms, were utilized for a color image edge detection experiment. Three representative images were selected to validate the algorithm's detection effectiveness, and the experimental results are presented in Figure 1.

Figure 1.

Experimental Detection Effect map.

As can be seen from the above figure, GSA is suitable for the edge detection of pictures, but the edge detection effect is not good, and there are phenomena such as missed detection and edge discontinuity. Sobel's edge positioning is inaccurate and prone to multi-pixel width issues. The effects of the GA algorithm and PCA algorithm on edge detection are similar to that of the GSA algorithm, but the effect of the GA algorithm on image edge detection is unstable. The image obtained by IGSA has continuous edges, clear features, reduced fine edges, and no multi-pixel width problem. All three algorithms—KRC, ZOM, and SID—outperform traditional edge detection algorithms. However, there are situations such as edge line discontinuity and false detection.

In order to compare the performance objectively and quantitatively, TPR (True Positive Rate: the accuracy rate of edge point detection), TNR (True Negative Rate: the accuracy rate of background point detection), and ACC (Overall Accuracy of Edge Detection) are used for judgment, which is defined as follows:

\begin{aligned} TPR & = \frac{TP}{TP + FN} \end{aligned}

(11)

\begin{aligned} TNR & = \frac{TN}{TN + FP} \end{aligned}

(12)

\begin{aligned} ACC & = \frac{TP + TN}{TP + FN + TN + FP} \end{aligned}

(13)

In the formula, TP (true positive class) represents the number of points that are actually edge points and are also detected as edge points; TN (true negative class) represents the number of points that are actually background points and are also detected as background points; FP (false positive class) represents the number of points that are actually background points but detected as edge points; FN (false negative class) represents the number of points that are actually edge points but detected as background points, that is, the number of missed detections. The higher the above three indicators, the better the performance of the algorithm.

Selecting 500 images as test images, we calculate the above three indicators for each algorithm and then compute the average values. The statistical results of the seven detection algorithms are shown in Table 1. As can be seen from Table 1, in the absence of noise, the accuracy of the algorithm increases by 5% to 16.5%, and the recall rate increases by 1.5% to 10.1%. Compared with the Sobel, Laplacian, GA, PCA, Roberts, GSA, KRC, ZOM, and SID algorithms, the overall edge detection accuracy is increased by 0.6% to 8.2%. In summary, the TPR, TNR, and ACC performance indicators of this algorithm are better than those of other comparison algorithms, and it can also meet real-time requirements in terms of time consumption, with high accuracy in edge point detection.

Table 1.

Algorithm Processing Color Image Performance Table.

NO.	name	TPR	TNR	ACC	time consuming
1	Roberts	0.568	0.418	0.951	0.839
2	Sobel	0.637	0.496	0.923	0.003
3	Laplacian	0.558	0.420	0.865	0.003
4	GA	0.409	0.334	0.850	0.008
5	PCA	0.628	0.276	0.848	0.017
6	KRC	0.516	0.394	0.833	0.010
7	ZOM	0.472	0.376	0.851	0.035
8	SID	0.561	0.505	0.911	0.030
9	GSA	0.587	0.446	0.933	0.008
10	IGSA	0.687	0.502	0.966	0.007

4.2 Noise Image Experiment

Select 510 pictures from the commonly used datasets CSet8 and BSD500 in digital image processing for testing, and randomly add Gaussian white noise with a concentration variance of 0.1. The picture size is 256 × 256. Use the Sobel, Laplacian, GA, PCA, Roberts, KRC, ZOM, SID, GSA, and IGSA algorithms. The detection effect of the white noise color image is shown in Figure 2.

Figure 2.

Experimental Detection Effect Map.

As can be seen from the above figure, for noisy images, GSA and Sobel are less robust to noise. GSA's image edge detection method has shortcomings such as a low image edge detection rate, poor effect, and poor robustness to noise. The KRC algorithm and the ZOM algorithm have a certain ability to suppress noise, but the image effect is not as good as the algorithm proposed in this article. The SID algorithm basically has no ability to suppress noise and needs to be used in conjunction with other filters. IGSA uses a method of uniformly distributing initial particles to obtain continuous edge points, clear image edges, and a certain ability to suppress noise. The uniform distribution of particles is used to maintain the robustness of the program to a certain extent.

The above three metrics for each algorithm are obtained and statistically averaged. The statistical results of the 10 detection algorithms are shown in Table 1. As can be seen from Table 2, under the condition of noise, the accuracy of this algorithm is increased by 2.7% to 10.3%, and the recall rate is increased by 1.4%. Compared with Sobel, Laplacian, Roberts, and GSA algorithms, the overall edge detection accuracy is about 4.4% to 9.4%. In summary, the TPR, TNR, and ACC performance indicators of this algorithm are better than those of other comparison algorithms, and it can also meet real-time requirements in terms of time consumption, with high accuracy in edge point detection.

Table 2.

Algorithm Processing Noise Color Image Performance Table.

NO.	name	TPR	TNR	ACC	time consuming
1	Roberts	0.497	0.350	0.915	0.839
2	Sobel	0.549	0.339	0.903	0.003
3	Laplacian	0.484	0.369	0.837	0.003
4	GA	0.574	0.262	0.834	0.008
5	PCA	0.365	0.305	0.830	0.019
6	KRC	0.470	0.356	0.810	0.010
7	ZOM	0.449	0.316	0.827	0.035
8	SID	0.554	0.318	0.835	0.030
9	GSA	0.560	0.348	0.917	0.008
10	IGSA	0.587	0.383	0.931	0.007

4.3 Infrared Image Experiment

In order to further illustrate the effectiveness of the IGSA algorithm, by selecting 200 infrared images from the OTCBVS dataset, it is first necessary to perform histogram equalization on the infrared images. The grayscale images of the infrared images undergo significant changes. The image becomes darker, as shown in the grayscale histogram, because the dynamic range of grayscale values is narrow and concentrated. The gray value of the infrared image is concentrated around 10 to 60, and the gray value at this point is low. After equalization, the dynamic range of the infrared image histogram is expanded, and the image occupies the 0 to 255 space allowed by the entire histogram, which improves the image quality and contrast. This facilitates edge extraction. Histogram equalization is performed on the infrared image, and the image after histogram equalization is used for image edge detection. The simulation effect is shown in Figure 3.

Figure 3.

Comparison Chart of Infrared Image Equalization Simulation Analysis.

Compare the time performance of the Sobel operator, GA, PCA, GSA algorithm, and IGSA algorithm, and select two pictures for display. The simulation test results are shown in Figure 4, and the average program time consumption is presented in Table 3.

Figure 4.

Simulation Test Effect Diagram.

Table 3.

Edge Detection Time Performance Table.

NO.	Name	time consuming
1	sobel	1.411
2	Roberts	0.005
3	Laplacian	0.007
4	GA	0.009
5	PCA	0.015
6	KRC	0.010
7	ZOM	0.036
8	SID	0.033
9	GSA	0.010
10	IGSA	0.097

epresents the number of detected edge points, NL represents the number of 4-connections in the edge image, and the value of NL/NP represents the degree of edge linear connection. Since the impact of the linear connection degree of the edge on the overall edge evaluation is reflected in the false detection and missed detection of the edge, when the number of false detections and missed detections of the edge points is large, it means that the connection degree of the edge is poor at this time; on the contrary, when the number of false detections and missed detections of edge points is fewer, the degree of linear connection of the edge is higher at this time, and the edge effect of extraction is better. Therefore, it is reflected in the table that the smaller the value of NL/NP is, the better the linear connection degree of the edge is, and the better the edge effect is at this time. The average linear connection degree performance table of 200 infrared images in the OTCBVS dataset is shown in Table 4.

Table 4.

Algorithm Edge Linear Connectivity Performance Table.

NO.	Name	NP	NL	NL/NP
1	sobel	4182	59,836	1.429
2	Roberts	86,425	126,786	1.467
3	Laplacian	29,925	41,218	1.377
4	GA	4454	6076	1.368
5	PCA	31,917	43,192	1.33
6	KRC	25,120	35,890	1.428
7	ZOM	21,390	32,438	1.516
8	SID	39,272	56,354	1.434
9	GSA	21,050	31,880	1.514
10	IGSA	29,037	38,720	1.333

Infrared images usually have characteristics such as blurred edges and low contrast. The improved gravity search algorithm has strong edge perception ability and nonlinear search characteristics, which can more effectively identify weak edge signals and enhance edge connectivity. Experimental data shows that its edge linear connectivity rate in infrared images has significantly improved, indicating that it is more suitable for feature expression in infrared images.As can be seen from the above table, the time consumption of the GSA algorithm is basically the same as that of the IGSA algorithm. PCA generates finer edges than GSA and IGSA, while GA is unstable for infrared image edge detection. The GSA algorithm is superior to IGSA in terms of time performance, but the speed is improved compared to traditional edge detection algorithms. Both the KRC and ZOM algorithms have missing edges, while the SID algorithm has more refined edges in terms of detection effect. The edges obtained by the traditional Sobel operator lose important edge information and contain a large number of fine edges, while the edges detected by the IGSA algorithm more completely and accurately represent the structure of the image, indicating that the improved algorithm is more accurate and has better image edge detection. It is completed, proving that the improved algorithm is an effective method.

4.4 Ablation Experiment

IGSA1 only includes basic gravity search mechanism and traditional edge response function; IGSA2 has added an adaptive threshold mechanism on this basis. The complete IGSA further integrates dynamic gravity regulation and local fine search strategies. The experimental results show that IGSA is superior to IGSA1 and IGSA2 in both accuracy and robustness, indicating that multi module collaborative optimization has a significant improvement effect on algorithm performance.

4.4.1 Color Image Ablation Experiment

Using the same color image dataset, three representative images of baboon, boat, and Lena are selected to show the impact of different improvements of the algorithm on the detection results. The gravitational search algorithm program that does not use the uniform distribution of initial particles is named IGSA1, and the program that does not use the gravitational search algorithm for uniform sampling is called IGSA2. The experimental detection results are shown in Figure 5.

Figure 5.

Experimental Detection Effect map.

It can be seen from the above figure that compared with IGSA1 and IGSA2, the edge of the image obtained by IGSA is continuous, and the image content is richer. There is no problem of missing main images during IGSA edge detection, while IGSA1 and IGSA2, without adapting to the relationship of the threshold, do not add initial examples, making edge extraction ineffective.

It can be seen from Table 5 that in the absence of noise, compared with the IGSA1 and IGSA2 algorithms, the precision rate of IGSA has increased by 20.9% to 34.2%, the recall rate has increased by 0.1% to 3.3%, and the overall edge detection accuracy has increased by 2.8% to 4.5%. In summary, the IGSA algorithm used in this paper is better than IGSA1 and IGSA2 in terms of TPR, TNR, and ACC performance indicators for color images.

Table 5.

Algorithm Processing Color Image Performance Table.

NO.	name	TPR	TNR	ACC	time consuming
1	IGSA	0.687	0.502	0.966	0.007
2	IGSA1	0.478	0.501	0.921	0.006
3	IGSA2	0.345	0.469	0.938	0.009

4.4.2 Color Image Ablation Experiment with Noise

Using the same dataset containing Gaussian white noise, the detection effect of color images containing Gaussian white noise using the IGSA, IGSA1, and IGSA2 algorithms is shown in Figure 6.

Figure 6.

Experimental Detection Effect Map.

As can be seen from the figure above, IGSA1 and IGSA2 are sensitive to noise and mistakenly identify noise as an edge point. As shown in the figure, the IGSA algorithm used in this paper has a certain ability to suppress noisy images, and the edge is continuous. The situation of noise being recognized as an edge point is better than that of IGSA1 and IGSA2.

It can be seen from Table 6 that in the case of noise, IGSA improves the precision rate of the IGSA1 and IGSA2 algorithms by about 10%, the recall rate increases by 8.1% to 10.4%, and the overall edge detection accuracy increases by 0.1% to 3.8%. In summary, the performance indices of TPR, TNR, and ACC for the IGSA algorithm used in this paper are better than those of IGSA1 and IGSA2 when dealing with noise-containing color images.

Table 6.

Algorithm Processing Noise Color Image Performance Table.

NO.	name	TPR	TNR	ACC	time consuming
1	IGSA	0.587	0.383	0.931	0.007
2	IGSA1	0.317	0.302	0.930	0.005
3	IGSA2	0.619	0.279	0.893	0.008

4.4.3 Infrared Image Ablation Experiment

Select the same infrared image dataset to compare the time performance of the IGSA, IGSA1, and IGSA2 algorithms, and select two pictures from them for display. The simulation test results are shown in Figure 7, and the average program time consumption is presented in Table 7. The average linear connection degree performance table of the infrared image is shown in Table 8.

Figure 7.

Simulation Experiment Detection Effect Diagram.

Table 7.

Edge Detection Time Performance Table.

NO.	Name	time consuming
1	IGSA	0.097
2	IGSA1	0.083
3	IGSA2	0.095

Table 8.

Algorithm Edge Linear Connection Degree Performance Table.

NO.	Name	NP	NL	NL/NP
1	IGSA	29,037	38,720	1.333
2	IGSA1	31,917	43,192	1.353
3	IGSA2	37,226	37,016	1.360

It can be seen from the above table that the time consumption of the IGSA algorithm is basically the same as that of the IGSA1 and IGSA2 algorithms. Compared with IGSA1 and IGSA, the NL/NP obtained by using IGSA is smaller, which proves that the degree of linear connection of the IGSA edge is better, and the edge effect extracted at this time is the best.

To assess the individual contributions of each integrated module, we conducted an ablation study. The results show that the adaptive thresholding mechanism had the most significant impact on edge detection performance, especially in noisy environments, improving TNR by 8–12%. Multi-scale edge detection played a key role in preserving structural integrity and suppressing weak edges, while bilateral filtering contributed to visual smoothness and noise suppression with moderate impact on quantitative accuracy. These findings demonstrate that each module is beneficial, but adaptive thresholding is the most critical.

5 Discussion

Compared with existing edge detection methods based on gravity search algorithm, this study proposes an improved algorithm with adaptive search capability (IGSA), which enhances the balance between global search and local mining while introducing an adaptive threshold mechanism, effectively improving the adaptability and robustness to complex images and noise disturbances. Furthermore, based on the experimental results:On standard image sets such as CSet8 and BSD500, IGSA outperforms traditional methods in terms of PSNR, F-measure, and SSIM;In infrared and medical image testing, IGSA can better identify blurry edges and gradient edges, indicating its feasibility and potential for promotion in practical complex image processing (Wang et al., 2021).

IGSA exhibits significant robustness and cross scene stability against various noise disturbances such as Gaussian, salt and pepper, and speckle.The improved gravity search algorithm adds dynamic parameter adjustment and adaptive mechanisms in each iteration. Although it slightly increases the computational complexity of a single iteration, the overall computational cost does not significantly increase due to faster convergence and higher solution quality. Compared with other benchmark algorithms mentioned in the article, such as Canny or Sobel, IGSA is suitable for application scenarios that require higher accuracy and tolerate certain time overhead.While IGSA generally performs well across a variety of image types, we observed reduced performance in high dynamic range (HDR) or images with extreme illumination variations. In these cases, the statistical assumptions of the adaptive thresholding mechanism may be violated, leading to false positives or missed edges. Future improvements may involve histogram equalization or non-linear preprocessing to better adapt to these conditions.

6 Conclusion

The improved gravity search algorithm can utilize the interaction between pixels in the image and their relationship with edges, and dynamically adjust the position of solutions in the search space by simulating the gravity interaction and motion process between objects, thereby achieving accurate positioning and extraction of edges. The experimental results show that the algorithm exhibits good robustness and detection accuracy in edge detection, and can effectively cope with complex image scenes and noise interference. Compared with traditional edge detection algorithms, the improved algorithm has global optimization capabilities, avoids falling into local optima, and has better convergence and search efficiency. It can achieve a good balance between exploration and utilization, thereby improving edge detection performance. Under the premise of reasonable parameter settings and optimization strategies, the improved gravity search algorithm has achieved satisfactory results in image edge detection tasks and demonstrated good application prospects.

Although IGSA performs well in most test images, its computational resource overhead may become a limiting factor in scenarios with extremely high real-time requirements or large image sizes.Future research can focus on further optimization of algorithms, exploring their combination with deep learning methods, integration with other intelligent algorithms, and adaptive capabilities for different types of images. At the same time, algorithm customization and parameter adjustment research should be carried out based on different image characteristics and practical application needs to further enhance its performance and application breadth.IGSA has the potential to be integrated with deep learning frameworks. Possible directions include: (1) using IGSA-generated edge maps as input channels for CNNs, (2) applying IGSA for post-processing refinement of segmentation outputs, and (3) embedding edge-enhanced objectives into loss functions. Challenges in such integration involve differentiability issues, real-time efficiency, and designing compatible hybrid training architectures.

Footnotes

Author's Note

All authors were directly involved in the planning, execution or analysis of the research and paper and have read and approved the submitted version

ORCID iDs

Kun Liu

XueFang Li

Ethics Considerations

Ethical approval does not apply to this article.This paper does not contain any studies involving humans or animals

Author Contributions

Methodology, K.L. ; software and algorithm, K.L. and K.L.; validation, K.L.; resources and data curation, K.L. and K.L.; writing—original draft preparation, K.L. and X.L.; writing—review and editing, K.L. and X.L.; visualization, K.L. and X.L.; supervision, K.L.; project administration, X.L.; funding acquisition, X.L.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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