Rapid non-contact detection of aggregate gradation based on stereo vision

The size and gradation of aggregates strongly influence the performance of asphalt concrete. They directly affect the deformation characteristics and fatigue resistance of asphalt concrete pavements. During production, transportation, and storage, granular aggregates are accumulated in bulk. When allowed to settle naturally, gradation segregation may occur. This leads to an uneven spatial distribution of coarse and fine particles. As a result, traditional screening methods cannot achieve rapid and accurate gradation detection. This paper proposes an intelligent identification method for aggregate heap gradation based on binocular machine vision and deep learning. We use a binocular stereoscopic vision system to reconstruct the three-dimensional model of the heap. The actual height of the heap is determined by acquiring a disparity map using Semi-Global Block Matching stereoscopic matching. Top-view images of the conical heap are captured, and deep learning algorithms segment aggregate particles and quantify the area proportion of coarse particles on the surface. By analyzing the concentration gradient of coarse particles in radial zones, we develop a multiple linear regression model linking surface distribution to the overall coarse aggregate gradation. Experimental results show that the proposed method is much more efficient than the manual screening method in the laboratory environment. The average relative error for aggregate pile height from three-dimensional reconstruction is less than 5%. The coefficient of determination for the prediction model of aggregate gradation is 0.970. This study thus provides a low-cost, high-efficiency approach for detecting aggregate gradation.

1 Introduction

Aggregates make up over 70% of the volume in asphalt concrete. According to relevant statistics, the global use of mineral aggregates has surpassed 2 billion tons annually since 2020. Proper control of gradation can optimize asphalt concrete performance at the source, reduce early pavement defects, extend road lifespan, and decrease the frequency and cost of future maintenance. Aggregates essentially form a discrete, disordered system composed of particles of various sizes (Wang and Xiao, 2022; Nejem and Akhtar, 2025). In stockyards, aggregates are typically piled into heaps by stackers rotating around fixed points near the top. However, significant differences in particle size, density, shape, and material properties can easily cause segregation and uneven distribution of coarse and fine aggregates during stacking (Wu et al., 2019; Hamza et al., 2025). This uneven distribution has a significant impact on the key performance features of asphalt concrete, including workability, mechanical properties, and durability (Abuowda et al., 2024; Wu et al., 2023; Wang et al., 2022; Wang and Huang, 2017).

Many scholars have extensively studied the distribution patterns of particle composition in granular accumulations. Research has shown that the accumulation, spatial volume distribution, and two-dimensional planar distribution of particles during fragmentation and transportation are closely linked to their particle size composition (Liu et al., 2020; Grasselli and Herrmann, 1998; Hernán et al., 1997; Li et al., 2021). Drahun and Bridgwater (1983) investigated the separation process of free-flowing particles during granular accumulation, which leads to surface segregation. Their research findings revealed that particle diameter and density greatly affect the likelihood of particles’ positions: larger or less dense particles tend to settle at the bottom of the surface, while smaller or denser particles often gather near the dumping point within the pile. Balancing particle size and density can improve the surface distribution. Furthermore, the velocity of particles colliding with the surface enhances the influence of size on distribution, whereas the effect of density on surface distribution remains unaffected by impact velocity. Salter et al. (2000) investigated the formation of piles in storage silos and found that the feed rate, silo geometry, and storage silo filling angle all influence particle segregation. The research above suggests that the specific distribution patterns of particle segregation on aggregate surfaces provide a feasible basis for inferring the overall gradation based on surface characteristics. This not only highlights the limitations of traditional sieving methods but also underscores the urgent need for new, rapid, non-contact detection techniques.

To address the limitations of traditional methods, domestic and international scholars have been working to develop rapid, non-contact systems for detecting aggregate gradation. With the continuous development of machine vision, the identification and measurement of particle size based on visual images have advanced rapidly. Wang et al. (2018) employed digital image processing (DIP) technology to investigate the separation of rubber sand mixtures, realizing the identification of material components and three-dimensional mapping of mixture segregation. Their DIP results effectively validated the simulation accuracy of the discrete element model. Building on these advancements, Wang et al. (2020) addressed the energy waste caused by fluctuations in coal transport volume on belt conveyors by developing a method integrated with stereo vision technology. This method utilizes the watershed algorithm to estimate coal block parameters and corrects the volume based on the void ratio. Experimental validation conducted with actual coal transportation images confirmed the effectiveness of the proposed method. Ding et al. (Chen et al., 2009; Ding, 2009; Ding et al., 2009) conducted experiments involving the free fall and pile formation of approximately 20 kg of mixtures with different gradations. They compared the experimental results with those from discrete element simulations and found consistency between the two. Based on image processing technology, Yao Neng (Yao, 2021) designed an automatic threshold bimodal method derived from the traditional bimodal method, optimized and segmented the image to obtain the average area of the aggregate image, and further determined the average particle size of the aggregate. This method was applied to identify the segregation degree of the pile, and the segregation of the pile in three particle size ranges with respect to volume was analyzed. Su et al. (2024) proposed a non-contact weight measurement method for aggregate piles based on stereo vision and void ratio modeling. This method achieves industrial-grade weighing precision at a low cost and high efficiency, with an error rate of less than 4%. However, two-dimensional image segmentation of sand and gravel can only collect and analyze two-dimensional information, such as particle size, shape, and area, and fails to reflect the overall depth information of the pile. This neglects the critical quality indicator of particle gradation, necessitating manual secondary screening for gradation verification. Kuo et al. (1996) captured projection images of aggregates attached to a sample tray with two vertical surfaces before and after rotating the tray by 90° to explore their 3D information, verifying that image-based methods can quantify the morphology of aggregate particles. Masad et al. (2005a), Masad et al. (2005b) proposed an angularity index based on radius and contour gradient as an aggregate particle shape evaluation parameter, developed the AIMS device (which acquires aggregate images via a digital camera on a backlit platform and performs quantitative analysis via a computer), enabling measurements of aggregate angle, texture, and size distribution as well as restoration of complete 3D information. Zhao et al. (2020) reconstructed the 3D model of rock aggregate by multi-directional image and analyzed the influence of shape on its stacking behavior. Du et al. (2022) combined target detection and binocular matching to generate a dense 3D point cloud to improve the accuracy of size measurement. Yang et al. (2021) employed a deep learning stereo matching model to achieve high-precision, real-time measurement of coal volume.

Based on the aforementioned research background, this paper proposes a method integrating stereo vision and image analysis to achieve 3D information reconstruction and rapid gradation assessment of aggregate piles. First, after camera calibration and image correction, a 3D depth map is generated via stereo matching. We then verify the reconstruction accuracy through comparative analysis, followed by surface image segmentation to determine the content ratio of coarse and fine particles, thereby clarifying the surface particle distribution pattern of binary aggregate piles. Leveraging the spatial homogeneity of aggregate piles in road engineering applications, we model the correlation between surface particle distribution patterns and overall gradation. This enables the indirect derivation of the pile’s overall gradation distribution and the development of an intelligent prediction method based on surface image analysis. Ultimately, this approach achieves rapid, non-contact, and highly efficient quantitative evaluation of the overall particle gradation of aggregate piles. As shown in Figure 1.

Figure 1

Figure 1. Intelligent identification system for aggregate accumulation and particle gradation.

2 Binocular vision depth restoration

2.1 Binocular vision principle

Stereo vision technology achieves high-precision non-contact measurement by simulating the parallax mechanism of the human eye. This technology utilizes two spatially separated cameras to capture images of the target object simultaneously. By calculating the horizontal displacement of corresponding pixels in the two pictures and integrating the camera’s geometric parameters, it is possible to compute the depth information of the scene when the optical centers of the stereo cameras are collinear, as illustrated in Figure 2.

Figure 2

Figure 2. Binocular vision schematic.

In Figure 2, b denotes the distance between the projection centers of the left and right cameras, referred to as the baseline. f represents the focal length of both the left and right cameras. The coordinates of point P in three-dimensional space are imaged at pixel coordinates $x_l$ and $x_r$ in the left and right cameras, respectively. The parallax of point P can be expressed as $d=x_l-x_r$. z is the actual depth from the camera to the point in space. Based on the principle of similar triangles. The derivation relationship is shown in Equation 1.

$\left\{\begin{array}{l}\frac{z}{f}=\frac{x}{x_l}\\ \frac{z}{f}=\frac{x-b}{x_r}\end{array}\right.\Rightarrow z=\frac{fb}{x_r-x_l}=\frac{fb}{d}(1)$

After acquiring the depth information of pixels via the parallax between the left and right cameras, three-dimensional reconstruction of the object can be carried out to obtain the height information of the stacked object, which is conducive to subsequent processing. The coordinates of a point in the image within the three-dimensional space correspond one-to-one with its coordinates in the image. To project a real three-dimensional object onto the two-dimensional plane of the camera, mutual transformations between the world coordinate system, the camera coordinate system, the image plane coordinate system, and the pixel coordinate system are necessary. The spatial relationships among these four coordinate systems are depicted in Figure 3.

Figure 3

Figure 3. Coordinate system position relation.

Among these, point $p\left(x,y\right)$ corresponds to the projection of the real three-dimensional space point $P\left(X_W,Y_W,Z_W\right)$ onto the imaging plane. Here, $O_W-\left(X_W,Y_W,Z_W\right)$ denotes the world coordinate system, which is used to describe the specific positions of the camera and the object in real three-dimensional space. $O_C-\left(X_C,Y_C,Z_C\right)$ represents the camera coordinate system, with the camera’s optical center $O_C$ as its origin, this coordinate system serves as the key hub for projecting real three-dimensional space onto the image coordinate system. $\left(x,o,y\right)$ refers to the image plane coordinate system, whose origin is located at the intersection of the camera’s optical axis $Z_C$ and the imaging plane, and the distance from this origin to $O_C$ equals the camera’s focal length. $\left(u,v\right)$ denotes the pixel coordinate system of the spatial object point after transformation, with its origin at the upper-left corner of the image and units in pixels.

During coordinate transformation, the external parameters of the camera are determined by the relative positions of the two cameras. In experiments, factors such as machine adjustments, environmental thermal expansion and contraction, and equipment damage or deformation may affect the results. Objects in space are treated as rigid bodies, which do not undergo shape-altering transformations but can only undergo translation and rotation. These motions are represented by an orthogonal unit rotation matrix R and a three-dimensional translation vector T. The transformation between the world coordinate system and the camera coordinate system can be represented in the form of a matrix of Equation 2.

$\left[\begin{array}{c}{X}_C\\ Y_C\\ Z_C\end{array}\right]=R\left[\begin{array}{c}{X}_W\\ Y_W\\ Z_W\end{array}\right]+T(2)$

When converting between the camera coordinate system and the image plane coordinate system, calculations are conducted using the image point p and the real-space point P of the object, based on the principle of similar triangles on the coordinate system plane. Its calculation is shown in Equation 3.

$\left\{\begin{array}{c}\frac{x}{f}=\frac{X_C}{Z_C}\\ \frac{y}{f}=\frac{Y_C}{Z_C}\end{array}\right.\Rightarrow \left\{\begin{array}{c}{Z}_{C}x=f{X}_C\\ Z_C\mathrm{y}=f{Y}_C\end{array}\right.(3)$

When converting between the imaging plane coordinate system and the pixel coordinate system, the conversion essentially involves transforming length coordinates into pixel coordinates. The matrix expression can be simplified in Equation 4.

$Z_C\left(\begin{array}{c}u\\ v\\ 1\end{array}\right)=KM\left(\begin{array}{c}{X}_W\\ Y_W\\ Z_W\\ 1\end{array}\right)(4)$

Where K is the camera’s internal parameter matrix, which is not affected by external factors; M is the camera’s external parameter matrix, which consists of R and T, and is affected by the relative position between the stereo cameras.

2.2 Calibration and correction of cameras

As shown in Equation 4, the transformation of the camera’s spatial coordinate system depends on the internal and external parameter matrices, which are typically obtained via camera calibration. Camera calibration is the most critical process in stereo vision; its objective is to establish the geometric relationship between 3D points in the real world and 2D image pixel coordinates through experiments and calculations, and to parameterize the projection transformation from real-world coordinate points to their corresponding image coordinate points. This process determines the camera parameters and calibrates the errors introduced during lens manufacturing and assembly, thereby providing the necessary conditions for subsequent stereo ranging solutions.

The accuracy of camera calibration is often evaluated using the reprojection error $\overline{\epsilon }$, which reflects the distance deviation between the actual pixel location and the predicted pixel location after calibration. Its calculation is shown in Equation 5.

$\overline{\epsilon }=\frac{{\displaystyle {\sum }_{i=1}^n}\sqrt{{\left(\stackrel{\wedge }{u_i}-u_i\right)}^2+{\left(\stackrel{\wedge }{v_i}-v_i\right)}^2}}{n}(5)$

Where n represents the total number of pixels in the image, $\left(u_i,v_i\right)$ denotes the actual pixel coordinates, and $\left(\widehat{u_i},\widehat{v_i}\right)$ refers to the calibrated predicted pixel coordinates. In practical applications, we consider camera parameters with reprojection coordinates less than 0.5 to be valid parameters.

During calibration, the reprojection error must be optimized through multiple iterations to minimize it. However, due to noise interference and the tendency to get stuck in local minima during iteration, the reprojection error may be small, making it difficult to evaluate the results of camera calibration fully. In this paper, the Stereo Camera Calibrator toolbox built into MATLAB R2022b is used for camera calibration. A USB stereo camera module, as shown in Figure 4, features a lens with a focal length of 2.8 mm and a baseline distance of 120 mm. Calibration was performed using synchronously acquired 1,520 × 1,520 pixel images.

Figure 4

Figure 4. USB binocular camera.

Based on the calibration results, MATLAB can further generate camera-based images and views under different camera poses. This not only helps optimize the camera’s external parameters but also intuitively displays the distinct spatial positions of the camera and the image. The average reprojection error after calibration is presented in Figure 5. The measured average reprojection error is 0.27, which is less than 0.5. This indicates that the calibration results meet the accuracy requirements and can be applied to subsequent stereo ranging tasks.

Figure 5

Figure 5. Reprojection error after calibration.

2.3 Correction and stereoscopic matching

To ensure that the same object in images captured by the left and right cameras of a stereo system appears at the same size in both images and that corresponding pixels remain horizontally aligned along a straight line, it is necessary to correct the images using the intrinsic parameter matrix, distortion coefficients, and rotation matrix obtained via calibration. During the correction process, the pixel coordinates in the original image are first transformed into camera coordinates using the intrinsic matrix. The rotation matrix derived from calibration is then employed to correct the epipolar lines in the two images. Subsequently, the distortion coefficients are used to rectify the camera coordinate system. Finally, the intrinsic matrix is reapplied to obtain the new pixel coordinates of the image, thereby achieving pixel alignment across the two images.

As shown in Figure 6, the lines in the figure represent the corresponding polar lines in the left and right images. After calibration, all matched points lie on the same horizontal line, thereby satisfying the geometric constraints of stereo matching. Epipolar constraint correction imposes a one-dimensional straight-line constraint for subsequent image matching, avoiding brute-force matching over the entire image, reducing the disparity search range, and effectively improving matching accuracy.

Figure 6

Figure 6. Image polar correction.

The stereo matching method adopted in this paper is the Semi-Global Block Matching (SGBM) (Hirschmuller, 2008) algorithm. This algorithm processes the image using a horizontal Sobel operator, maps each pixel in the processed image to a new image via a function, and acquires the gradient information of the image through preprocessing. This gradient information is then used for subsequent cost calculations. The algorithm assigns disparity values to each pixel to generate an initial disparity map. Subsequently, it minimizes the global energy function related to the disparity map to determine the optimal disparity for each pixel. The energy function employed in the SGBM algorithm is in Equation 6.

$E\left(D\right)={\displaystyle \sum _p}\left(C\left(p,D_p\right)+{\displaystyle \sum _{q\in N_p}}{p}_{1}I\left[\left|D_P-D_q\right|=1\right]+{\displaystyle \sum _{q\in N_p}}{p}_{2}I\left[\left|D_P-D_q\right|>1\right]\right)(6)$

In the equation, E(D) denotes the global energy function corresponding to the disparity map D. p and q represent two corresponding pixels in the left and right images, respectively. $N_p$ denotes the pixels within the eight-neighborhood of pixel p. $C\left(p,D_p\right)$ denotes the pixel cost corresponding to the disparity value of pixel p when $D_p$ is the corresponding disparity value. $p_1$ and $p_2$ represent the penalty coefficients applied when the disparity values of the neighboring pixels of p differ from the disparity value of p by one and by more than one, respectively.

The process of finding the optimal solution using the above energy function in a two-dimensional image plane constitutes an NP-hard problem, characterized by high computational complexity and time consumption. To address this, we consider reducing the dimensionality of the pixels within the eight-neighborhood and continuing the solution using dynamic programming, is shown in Equation 7.

$L_r\left(p,d\right)=C\left(p,d\right)+\min \left\{\begin{array}{l}{L}_r\left(p-r,d\right)\\ L_r\left(p-r,d-1\right)+p_1\\ \underset{i}{\min }{L}_r\left(p-r,i\right)+p_2\end{array}\right\}-\underset{k}{\min }{L}_r\left(p-r,k\right)(7)$

Where r is the current path direction, and when the disparity value is d, $L_r\left(p,d\right)$ is the minimum value on the current path direction. After calculating the energy values in eight directions and superimposing them, the final energy value of pixel point p is obtained, and the disparity value with the smallest final energy value is taken as the final calculated disparity of the point, denoted as $S\left(p,d\right)$, is shown in Equation 8.

$S\left(p,d\right)={\displaystyle \sum _r}{L}_r\left(p,d\right)(8)$

This paper adopts a Sobel gradient-based matching cost for SGBM stereo matching to enhance edge and detail robustness. The window size is set to 5 × 5, with smoothing parameters P1 = 8×number of channels × window size = 600 and P2 = 32×number of channels × window size = 2,400.

3 Intelligent identification system for aggregate heaps gradation distribution

3.1 System overview

To verify the consistency between the height of the reconstructed aggregate heaps and the actual pile height using the binocular vision system, images of the pile after stacking were captured with a binocular USB camera. This camera features a left and right camera, and the baseline distance between the two is adjustable. A smaller baseline distance results in a larger measurable area. Additionally, a higher camera stand height leads to a longer shooting distance, which not only increases the photographed area but also enlarges the actual distance represented by a single pixel. The camera stand was positioned approximately 100 cm above the ground. The image acquisition device is shown in Figure 7.

Figure 7

Figure 7. Binocular vision image acquisition.

After obtaining the disparity map via the SGBM algorithm, the depth information of the image is derived, as shown in Figure 8. The figure uses false color coding to indicate the height distribution of the aggregate heaps. Different color ranges correspond to distinct depth intervals. This visualization provides a quantitative basis for subsequent region segmentation based on height thresholds.

Figure 8

Figure 8. Depth image of accumulation.

This paper adopts the method proposed in Reference (Zang et al., 2023) for two-dimensional image processing and analysis. This approach enables rapid segmentation and identification of aggregate particle sizes. The algorithm proceeds as follows. First, it leverages the YOLO v4 object recognition neural network to extract features of aggregate particles and make judgments, thus locating each aggregate particle within the global image. In this process, the centroid of the anchor box is taken as the feature point of the aggregate particle, and the coordinates of these feature points are obtained. Next, considering the overlapping characteristics of manufactured sand particles, a distance transformation is performed using a topology. Here, the feature points of the manufactured sand serve as seed points, which helps to approximately divide the regions where the manufactured aggregate particles are located. Finally, based on the approximate region segmentation results of the manufactured aggregate particles, morphological extraction is conducted on the encoded regions using local thresholds. This process produces the particle segmentation and extraction results, thereby determining the particle size distribution range of the aggregate particles. The method process is shown in Figure 9.

Figure 9

Figure 9. Framework for particle gradation identification and shape evaluation of aggregate.

Acquire multi-angle, randomly stacked aggregate images. Crop these images and augment the dataset using random rotation, scaling, and similar techniques to produce 2,500 aggregate particle images. Use the labelimg tool to label particles within each image, and then split the dataset into training and testing sets at a 9:1 ratio. Train the center point coordinate acquisition model using transfer learning, with pre-trained weights from Reference (Zang et al., 2023), to suit the specific imaging traits of these aggregates. In order to better measure the performance of target detection and positioning, the precision when the threshold is 0.5 is used as the measurement index to evaluate the target detection effect. The formula is in Equation 9.

$Precision=\frac{TP}{TP+FP}(9)$

Where: TP (True Positive): the number of detection frames with IoU = 0.5; FP (False Positive): the number of detection boxes with IoU = 0.5 (false detection); FN (False Negative): the number of aggregates not detected (missed detection); Used in model training, the NVIDIA GeForce RTX 3060 GPU-accelerated training. The model achieved an average accuracy of 91% on the test set. The precision is shown in Figure 10.

Figure 10

Figure 10. Precision at a threshold of 0.5.

To validate this method for acquiring aggregate particle size, 400 manually selected aggregates (3–5 mm and 6–8 mm) were mixed and placed in a 15 cm × 15 cm acrylic container covered with white cardstock. The aggregates were evenly spread across the bottom for size measurement. Aggregates within the target gradation were collected using matching sieve sizes, and a random selection served as ground truth. Three experimental runs were conducted, using the count within the range as the statistical criterion. Comparison results are shown in Table 1.

Table 1

Table 1. Comparison of recognition results with ground truth.

The results show strong consistency between the model’s outcomes and manual grading. The model demonstrates stable predictive performance in binary aggregate particle size identification, with average relative errors below 8% for the 3–5 mm and 6–8 mm ranges. This meets engineering-grade gradation testing requirements.

3.2 High-accuracy recognition result verification

The heights of the aggregate heaps under different operating conditions, reconstructed using binocular stereoscopic vision, were compared with the maximum heights measured in actual experiments. The results and comparison are shown in Figure 11. As seen from the figure, increasing in the proportion of coarse particles causes a significant decrease in the pile’s height. This occurs because, first, as the mass fraction of coarse particles increases, the total volume fraction of the pile decreases; second, segregation causes variations in the sliding of surface particles, depending on the coarse particle content, which further lowers the maximum height. Notably, the pile heights reconstructed by binocular cameras exhibit the same decreasing trend. Moreover, when compared with the actual measurements, the error remains within 5%, satisfying the experimental accuracy requirements.

Figure 11

Figure 11. Trend of the maximum height of aggregate pile with coarse particle content.

4 Research on binary aggregate accumulation tests and gradation distribution patterns

4.1 Model construction

Aggregate segregation is a prevalent phenomenon in the production, transportation, and storage processes of manufactured aggregates. When aggregates fall freely and flow along the slope of a pile, differences in particle properties, such as size, shape, and density, cause particles to segregate under gravity. This segregation leads to significant spatial heterogeneity in the distribution of coarse and fine aggregates. The concentration of surface particles shows regular variations. This paper will use image recognition technology to analyze and summarize the surface particle concentration of aggregate heaps. These heaps are formed by mixing binary aggregates at different mass ratios. Pile images will be collected at a consistent height, and the pile height will be quantitatively controlled during the image segmentation. Additionally, a data collection model will be established by partitioning and segmenting piles formed under test conditions with different particle size ratios. This model will enable the intelligent prediction of the particle size and particle distribution of aggregate heaps.

4.1.1 Test equipment

An indoor test was conducted to observe how aggregates of different sizes fall and accumulate on the surface of a pile after falling. The test setup is shown in Figure 12. The falling device consists of two parts: an upper cylindrical section and a lower conical funnel. The cylindrical section has a radius of 300 mm, a height of 400 mm, and a wall thickness of 5 mm. The conical funnel has an upper radius equal to that of the cylinder, a lower radius of 16 mm, an inclination angle of 45°, and a length of 50 mm.

Figure 12

Figure 12. Free fall test device.

The falling test apparatus is made of acrylic or organic glass plates; the transparency of the apparatus allows for better observation of the mixing process and the falling of the mixture inside. The height of the support frame is fixed at 100 cm, and the free-falling height can be adjusted using pulleys.

In this experiment, aggregates of different sizes were used. Sieves with varying sizes of mesh were employed for screening to obtain fine aggregate particles with a particle size range of 3–5 mm and coarse aggregate particles with a particle size range of 6–8 mm. To investigate the formation of aggregate heaps composed of binary aggregates with different particle size proportions under the same free-falling conditions, and to analyze the distribution patterns and segregation characteristics of surface particle sizes, this study designed nine experiments focused on the pile formation of coarse and fine aggregates under different proportion conditions. The two types of screened aggregate particles were mixed, with the mass proportion of coarse aggregate particles serving as the reference standard. The specific experimental groups are presented in Table 2.

Table 2

Table 2. Design of test conditions.

The total weight of coarse and fine aggregate particles in each test group is 20 kg. The required aggregates for the test are weighed according tp the proportions specified in Table 2 and then poured into a container for thorough mixing. After evenly blending the coarse and fine aggregates of different groups, they are loaded into the drop device. To minimize the displacement of the mixture during transfer, a spoon is used to move the mixture in small batches. Once the drop device has stabilized, the funnel valve is opened to allow the aggregates to fall freely and accumulate. To enhance the reliability of experimental comparisons and improve overall experimental accuracy, each group of mixtures with different proportions undergoes three repeated natural free-fall accumulation tests.

4.1.2 Image capture

This paper employs machine vision technology to analyze the overall particle distribution of aggregates after accumulation statistically. Images of the accumulated pile formed after the falling process are captured. When using a dual-lens USB camera for image capture, dual-side LEDs are utilized for supplementary lighting to ensure uniform illumination during shooting, thereby avoiding any adverse impacts on subsequent image processing results. The shooting angle is from top to bottom, with a top-down perspective. In the top-down image, the pile exhibits a circular contour, and the separation of particles on the surface is clearly visible. Therefore, the captured images are cropped such that the circular edge of the pile is tangent to the image edge, which facilitates subsequent processing and extraction of the pile. Additionally, the actual diameter of the pile is measured, and particle size conversion analysis is conducted.

4.1.3 Image segmentation

In the collected images, sand and gravel particles randomly overlap after aggregate pilling. The boundaries between particles are blurred. To better apply the method above to machine vision-based identification and classification, the surface pile is analyzed through zonal and block division. Accordingly, the images are segmented as shown in Figure 13 This reduces the number of pixels in each photo and lowers the computational load during algorithm processing. The procedure is simplified, which facilitates the identification and segmentation of particle boundaries. This enables faster and more efficient image processing.

Figure 13

Figure 13. Block diagram of accumulation image.

Depth information of the pile is obtained using a stereo camera, which provides 3D data by capturing images from two slightly different perspectives. The pile is then zoned based on its height. Meaning sections are determined by their height. After removing the influence of the outermost edges (edge effects, which refer to distortions or inaccuracies at the pile’s boundaries), the circular pile is divided into three zones (inner, middle, and outer) according to the average depth, which correspond to positions 3, 2, and 1, respectively, as shown in the figure. Each zone is further partitioned into blocks at a 45° angle, with each zone evenly divided into eight blocks. Each block (e.g., 1.1, 2.1, 3.1) forms a strip; these strips are numbered sequentially and subjected to particle image recognition.

Building on this spatial division, in the test, aggregates fall from rest and undergo free-fall motion. The distribution of particles on the pile surface is random, ensuring that each region and block in the image is independent and non-interfering. Their positions are characterized by randomness and arbitrariness, which facilitates subsequent statistical analysis and data interpretation.

4.2 Analysis of the distribution pattern of particles on the surface of aggregate heaps

4.2.1 Test results

The ratio of the actual diameter of aggregates to their pixel diameter in the two-dimensional coordinate system is calculated to determine the correspondence between unit pixels and exact dimensions in the image. This ratio is then used to define the pixel ranges for coarse and fine aggregate particles for statistical analysis. Using the previously mentioned two-dimensional image surface particle segmentation method, image recognition and particle segmentation are performed. The minimum particle size, area, and area proportion of particles within different size ranges are calculated, and the area proportion of coarse particles is statistically analyzed. The results are shown in Table 3. The standard deviation across the three experimental groups is less than 0.1, the mean absolute error is 1.22%, and the root mean square error is 1.53%, indicating a low degree of dispersion and suggesting that the segmentation method produces results with a certain level of accuracy. Additionally, the data obtained through this method can be used for more in-depth, specific analyses.

Table 3

Table 3. Results of the area proportion of coarse aggregate on the accumulation surface.

We conducted three independent experiments under similar conditions and collected the data. Next, we compared the percentage of coarse particles on the surface of the accumulated body with the initial mass percentage of coarse particles. As shown in Figure 14, a strong correlation exists between these two values. When the initial coarse particle content increases, the proportion of coarse particles on the pile’s surface also rises. This proportion tends to align with the initial coarse particle content. To assess segregation on the surfaces of different sections of the pile under varying mass ratios of binary particles, we defined the concentration of coarse particles T in each section. This definition is based on the proportion of coarse particle aggregate on the pile’s surface, is shown in Equation 10.

$T=\frac{S_C}{S}(10)$

Figure 14

Figure 14. Overall distribution of coarse particles on accumulator surface.

Where $S_C$ is the area occupied by coarse aggregate in the region, and S is the total area of the region.

4.2.2 Distribution pattern of particles on the surface of the pile

To investigate and compare variations in aggregate segregation across different partitioned regions, experiments were performed. In these experiments, the proportion of coarse aggregate particles was gradually increased. After binocular stereoscopic reconstruction, the total height of the pile was divided into three equal segments. The concentrations of coarse particles in the inner, middle, and outer rings were then statistically analyzed in sequence. These results are presented in Table 4.

Table 4

Table 4. Calculation results of particle concentration in different areas of the accumulation surface.

The data results showed minor deviations among the three sets of experimental outcomes. This indicates good experimental reproducibility and effectively reflects the distribution pattern of particle concentration changes on the pile surface. As the initial mass proportion of coarse particles increased, the concentration of coarse particles within the same ring also rose. At the same coarse particle mass percentage, the concentration of coarse particles in the outer ring was higher than that in the inner ring. This implies that the coarse particle content at the pile top was lower than that at the pile bottom. Due to free fall, coarse particles rolled to the bottom sides, making them concentrate in the edge regions. Fine aggregates are concentrated at the upper center of the pile top. Consequently, the segregation degree at the pile top was greater than that at the pile bottom.

As shown in Figure 15, the same region of the deposit, the coarse particle content in surface zones increases almost linearly as the initial coarse particle mass ratio rises. When the initial coarse particle content is 20% and 30%, the increase in coarse particle concentration in the inner circle of the deposit is relatively gradual. However, once the content exceeds 30%, the rate of change in the inner circle becomes greater than with initial mass ratios of 10%–20%. In the middle sedimentary zone, the increase in coarse particle concentration accelerates notably when the initial content is around 50%.

Figure 15

Figure 15. Concentration distribution of coarse particles in different areas on the surface of accumulation. (a) Concentration of coarse particles in the accumulative outer ring. (b) Concentration of coarse particles in the accumulative center ring. (c) Concentration of coarse particles in the accumulative inner ring.

4.2.3 Intelligent prediction of pile particle concentration

The distribution of particles on the pile surface shows a specific linear relationship with the initial particle mass ratio. By analyzing the relationship between the coarse particle concentrations in different regions of the pile surface, machine vision can rapidly identify and analyze the concentration ratios of binary particles. This approach gathers data on coarse particle concentrations in different zones within the same strip.

As shown in Figure 16, the data is fitted to obtain the aggregate gradation distribution Equation 11.

$y=0.4123x_1+0.41013x_2+0.1264x_3+0.04262(11)$

Figure 16

Figure 16. Concentration distribution of coarse particles in different blocks on the surface of accumulation.

In the equation, y represents the percentage of coarse particles in the entire deposit after prediction $x_1$ represents the concentration of coarse particles in the outer ring of the same strip block, $x_2$ represents the concentration of coarse particles in the middle ring of the same strip block, and $x_3$ represents the concentration of coarse particles in the inner ring of the same strip block. After performing multiple linear regression, the coefficient of determination $R^2$ is 0.97041, and the adjusted $R^2$ is 0.96999, indicating that the aforementioned multiple regression equation has high accuracy and good fitting performance.

The weighting coefficients show that the normalized regression coefficients for coarse particle concentrations in the outer and middle rings are highly consistent. Both contribute nearly equally to the overall prediction of graduation. During aggregate accumulation, coarse particles mainly undergo gravity-dominated free fall. Inter-particle friction then causes them to slide along the slope surface and accumulate in the middle to lower regions. This process strengthens the correlation between coarse particle concentration and overall gradation in these areas.

In contrast, coarse particle concentration in the inner ring, at the center of the pile top, shows much lower absolute values than in the middle and outer rings. This means there are weaker segregation effects, less coarse particle enrichment, and a more stable distribution in this region. As a result, the inner ring has a relatively lower weight for predicting overall gradation. The quantitative distribution of the regression coefficients matches the physical mechanism of gravity segregation. This provides direct data support for the model’s physical interpretability.

To systematically validate the proposed method, a binary aggregate mixture was prepared. The mixture consisted of particle sizes ranging from 3 to 5 mm (fine aggregate) to 6–8 mm (coarse aggregate). The aggregates were randomly blended at a set ratio, with a fixed total mass of 20 kg, to simulate common mixing conditions in engineering practice. The mixture then underwent free-fall compaction to form a stable pile. Surface images were captured using the earlier-described binocular vision system. Deep learning algorithms extracted particle distribution on the surface to calculate coarse aggregate concentration in each partition. Based on these results, the multiple linear regression model was applied to predict the coarse aggregate content ratio throughout the entire pile. The predicted values showed excellent agreement with the actual mix ratios, with a mean absolute error of less than 2%.The full identification and calculation process was completed in about 3 min. This demonstrates much higher detection efficiency compared to traditional sieving methods.

5 Conclusion

This study employs binocular vision technology to investigate the distribution patterns of surface particles and the overall concentration within aggregate piles formed by the natural fall of 3–5 mm and 6–8 mm binary aggregates, enabling their intelligent prediction. By integrating a deep learning model validated by standard metrics with traditional image segmentation algorithms and combining them with three-dimensional reconstruction technology from binocular stereoscopic vision, the study systematically analyzed the quantitative distribution characteristics of particles in gradient zones on the surface of the pile. Ultimately, an intelligent prediction model for particle distribution was established. The conclusions of this study are as follows:

1. In conical aggregate heaps formed by typical stationary accumulation, gradation segregation causes particles on the surface to exhibit regular distribution patterns, with coarse aggregate enrichment in the pile base region and fine aggregate dominance at the pile top center.

2. Within the tested range of binary particle size combinations and mix proportions, the surface area ratio of coarse particles (coarse particle area/total area) shows a significant linear correlation with the initial mass ratio of coarse to fine aggregates.

3. Through multiple linear regression, a quantitative model was established. This model predicts the overall coarse aggregate content using the concentrations of coarse particles in the outer, middle, and inner surface rings as independent variables. The model achieved a coefficient of determination (R²) of 0.970. In the three-dimensional reconstruction of pile height, the average relative error was less than 5%. These results demonstrate high predictive accuracy under the experimental conditions tested.

To ensure engineering rigor, the application scope of this method is clearly limited to specific boundary conditions verified in this study. These include: (a) a controlled laboratory environment with stable light and minimal dust; (b) binary aggregate systems (3–5 mm and 6–8 mm); (c) an axisymmetric conical pile formed by natural gravity dumping. The established linear mapping relationship has initially verified the feasibility of inferring overall gradation from surface distribution. However, further calibration is needed before direct application to complex engineering scenarios, such as continuous gradation, variable outdoor lighting, or environments with high humidity or dust. This study provides a laboratory-validated proof of concept. Subsequent work will focus on improving model robustness to environmental disturbances through systematic field tests.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

YL: Conceptualization, Methodology, Software, Writing – original draft. BZ: Writing – original draft, Writing – review and editing. ZH: Methodology, Software, Writing – original draft. JT: Methodology, Software, Writing – review and editing.

Funding

The author(s) declared that financial support was received for this work and/or its publication. The financial support from Guangdong Basic and Applied Basic Research Foundation (2022A1515011607, 2022A1515011537 and 20231515030287) and the Fundamental Research Funds for the Central Universities (2022ZYGXZR056).

Acknowledgements

Thanks to all those who contributed to the articles.

Conflict of interest

Authors YL was employed by Guangzhou cheng’an Testing LTD. of Highway & Bridge. Authors BZ and ZH were employed by Guangzhou Xiaoning Road Engineering Technology Research Office Co., Ltd.

The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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