The SfM-based photogrammetry technique has become a standard in rock engineering applications (Hartley and Sturm, 1997; Kong et al., 2021). As depicted in Figure 1A, the process starts by identifying feature points ( P m j ) from two initial images and matching them with corresponding target points ( P j ). This matching process helps estimate the initial camera positions ( O 1 , O 2 ). These correspondences are then extended across additional images to refine the camera pose ( O m ) estimates for each image. Using this information, a sparse 3D model of the scene is constructed. Subsequently, depth maps, which represent the depth values of all pixels, are generated and combined into a single, consistent depth map (see Figure 1B). Finally, a dense point cloud is produced from the merged depth map, as illustrated in Figure 1C.

Figure 2 illustrates the use of the underside of an artificially split sandstone sample as the test object. This sample, which has a slightly uneven surface, measures 100 × 100 × 50 mm. It is placed within an orientation plate (OP) equipped with four ground control points (GCPs) spaced 160 mm apart. The OP is utilized to orient and scale the point cloud of the rock sample. Additionally, the OP contains twelve checkpoints (CPs). The discrepancy between the point cloud coordinates of these checkpoints and their actual coordinates provides a partial measure of the point cloud reconstruction quality (ASPRS, 2015; Cultural Heritage Imaging, 2015). According to Agisoft Metashape (2022) guidelines, the checkpoint size is set to five times the ground sampling distance (GSD), which is determined by the image pixel count (Yang et al., 2024).

Images of the target rock samples were captured using a Canon EOS 90D digital single-lens reflex (DSLR) camera. The camera uses a high-resolution CCD sensor with a sensor size of 22.3 × 14.8 mm and a pixel capacity of 6,960 × 4,640 pixels. The lens used is EF-S 18–135 mm f/3.5–5.6 IS USM. To precisely control the relative position and angle between the rock samples and the camera, a turntable and tripod were utilized as support and adjustment tools. Additionally, a precision angle ruler was employed to accurately adjust the rotation angle of the rocks, allowing images to be captured at each angular interval. Natural lighting was used to accurately reflect the rock’s morphology under authentic environmental conditions. As shown in Figure 2, a field rock specimen roughness measurement setup was established.

The fixed camera capture (FCC) method offers a cost-effective way to capture rock images, ensuring high image overlap and providing excellent stability and ease of use (Ge et al., 2022). The shooting parameter selection algorithm (SPSA), introduced by Yang et al. (2024), generates tailored shooting parameters based on the specific camera and rock dimensions. In this study, FCC is utilized in conjunction with SPSA, following the principles of SfM.

To begin with, the specific dimensions of the target rock, the GSD, and the key parameters of the imaging equipment were all entered into the SPSA, as detailed in Table 1. In this study, the camera’s shooting angle and positional interval adhered to the professional recommendations of Ge et al. (2022), being set at 30° and 15° respectively. This configuration facilitated the capture of 24 high-resolution images to ensure a high degree of image overlap. Furthermore, in accordance with the guidelines provided by Edmund Optics (2023), one-third of the GSD was set as the threshold for spatial resolution, intended to allow a reasonable tolerance for uncertainty in the accuracy of spatial points during the 3D reconstruction process, thereby enhancing the reliability of the results. Subsequently, based on SPSA calculations, with a GSD set at 1, the camera’s shooting layout at various positions is illustrated in Figure 3. These positions were sampled at 100 mm intervals. It is noteworthy that the positions depicted in Figure 3 not only indicate spatial locations but also visually represent the dynamic variations in objective space resolution error (OSRE) through changes in size and color.

Agisoft Metashape (2022) was chosen for the three-dimensional reconstruction of the rock surface, as it aligns with the SfM principle. The reconstruction parameters were configured with the highest alignment accuracy, and the depth maps and point clouds were generated with exceptional precision. For the GCPs, the software automatically identified these points within the point cloud using the imported real-world coordinates, facilitating the overall rotation and scaling of the point cloud. Following this, CloudCompare (2023) was used to segment and extract the rock surface point cloud, standardizing its dimensions and enabling the analysis of JRC variations across different shooting distances.

Object space resolution is a variable that reflects the density of 3D point clouds, determined by shooting parameters and pixel size. According to the study by Yang et al. (2024), a strong correlation exists between the object space resolution error (OSRE) and the JRC error. The equation for calculating this value is as follows: E r r o r OSR = h f Z − f (1) where h is the pixel size, f is the camera focal length, Z is the shooting distance, and E r r o r OSR is the calculated value of OSRE. This value can be calculated solely using the shooting parameters.

In studies evaluating joint roughness, the spatial distance between points in the point cloud reflects the accuracy of the roughness to some extent (Paixão et al., 2022; Ge et al., 2022). This value is defined as the ratio of the area of the selected rock surface point cloud to the number of points, and it can be calculated using statistics from post-processing software.

According to the positional accuracy standards for digital geospatial data provided by the American Society for Photogrammetry and Remote Sensing (ASPRS), researchers can evaluate point cloud accuracy using the spatial errors of check points (ASPRS, 2015). The spatial error between the point cloud coordinates and the true coordinates of the twelve checkpoints, used as a parameter to reflect JRC accuracy in this study, is represented by the average root mean quare error (RMSE) calculated manually, as shown in Equation 2: R M S E = 1 n ∑ i = 1 n x i a − x i b 2 + 1 n ∑ i = 1 n y i a − y i b 2 + 1 n ∑ i = 1 n z i a − z i b 2 (2) where x i a , y i a , z i a represent the coordinates of the center point of CPs in the point cloud, while x i b , y i b , z i b represent the true coordinates of CPs in the OP. n denotes the number of CPs. R M S E represents the spatial error (ASPRS, 2015).

In rock engineering, the JRC is essential for classifying rock mass quality and assessing stability (Barton and Choubey, 1977; ISRM, 1978). When estimating JRC from point cloud coordinates, the accuracy is significantly affected by the choice of profile intervals (PI) (Tse and Cruden, 1979). Following the method outlined by Yu and Vayssade (1991), JRC values for profile intervals of 0.25 mm, 0.5 mm, and 1 mm were calculated using Equations 3, 4 and are shown in Figure 4. The JRC for each profile ( J R C 2 D ) is determined using Z 2 : Z 2 = 1 L ∑ i = 1 N − 1 z i + 1 − z i x i + 1 − x i (3) J R C 2 D = 60.32 Z 2 − 4.51     for  profile  interval = 0.25     mm J R C 2 D = 61.79 Z 2 − 3.47     for  profile  interval = 0.5     mm J R C 2 D = 64.22 Z 2 − 2.31     for  profile  interval = 1     mm (4) where the coordinates x i , z i , x i + 1 , and z i + 1 correspond to points i t h and i + 1 t h in the x and z axes, respectively. N indicates the total number of points along the rock joint profile, while L refers to the profile’s length. Equation 5 shows that the overall JRC value for rock joint, known as J R C 3 D , is calculated by taking the average of the J R C 2 D values across all profiles (Ge et al., 2022): J R C 3 D = ∑ j = 1 M J R C 2 D j M (5) where M represents the total number of profiles.

To validate the accuracy of roughness parameters at different shooting distances, a high-resolution point cloud of the rock surface was generated using an AutoScan-630W laser scanner with a precision of 0.05 mm and an average point spacing of 0.005 mm. The JRC values derived from this point cloud were used as the benchmark for comparison.

The prediction model’s input feature set includes three parameters: OSRE, spatial distance, and the checkpoint spatial error of point clouds at various shooting distances. These features, combined with the JRC error as the target output, create a comprehensive dataset. As shown in Figures 5–7, both the input and output parameters are based on actual measured data rather than a set of predetermined values. The core of this prediction task is a multivariate regression analysis, designed to explore the relationships between the input features and the target output. To achieve this, five machine learning models were utilized for predicting the JRC error. To ensure robust generalization and accurate predictions, the data was split using a 70/30 ratio: 70% of the data was randomly chosen as the training set for model development and parameter optimization, while the remaining 30% served as the validation set to independently assess the model’s predictive performance and mitigate overfitting (Liu et al., 2024). To ensure the convergence of generalization error in a more stable manner, K-fold cross-validation was employed (Fushiki, 2011). The training set was first divided into five subsets, each of which could serve as a validation set. Then, one subset was used for validation, and the process was repeated five times, with a different validation and training set used in each iteration.

The accuracy of this study is evaluated using the difference ( J R C Error ) between the JRC values obtained from laser scanning ( J R C 3 D Laser scanner ) and those obtained from photogrammetry ( J R C 3 D Photogrammetry ): J R C Error = J R C 3 D Laser   scanner − J R C 3 D Photogrammetry (6)

The fitting results for J R C Error with profile intervals (PI) of 0.25 mm, 0.5 mm, and 1 mm are shown in Figure 5A. The image data reveal significant differences in the computed results under varying conditions. Figure 5B displays the error in J R C Error when the PI is 0.25 mm, 0.5 mm, and 1 mm, within the 25%–75% range. For PI = 0.25 mm, the error ranges from 1 to 5; for PI = 0.5 mm, the error ranges from 1 to approximately 3; and for PI = 1 mm, the error decreases to between 0 and 2. Such variations are evidently unreasonable and not acceptable based on the typical roughness profile classifications for JRC (Barton and Choubey, 1977). Consequently, an improvement in the accuracy of JRC measurements is necessary.

Figures 5C–E illustrate the relationship between OSRE and J R C Error . Under the FCC strategy, instability arising from factors such as lighting conditions, image overlap, and handheld effects results in some variability in J R C Error values as OSRE increases, although a general linear correlation is evident. The 95% confidence interval bands indicate that most data points fall within this range, demonstrating a certain degree of linearity, though more precise validation is required. Pearson’s R , a measure of correlation between two datasets, can be used to analyze the relationship between OSRE and J R C Error .

It is observed that, for PI values of 0.25 mm, 0.5 mm, and 1 mm, there is a strong correlation between OSRE and J R C Error , with R values approximately 0.97 in each case. The results show that J R C Error exhibits noticeable dispersion when OSRE is around 0.5–0.8. This is attributed to the larger spacing between points at higher OSRE values, resulting in sparser point clouds. Consequently, the estimated area becomes less stable when partitioned into grids.

Based on the correlation between the data, linear regression equations for OSRE and J R C Error were fitted. To better differentiate the goodness-of-fit across different PI values, R 2 was used as a parameter for comparing the regression model’s performance. As shown in Figures 5C–E, the fits for all three cases are quite good, with R 2 values of 0.94 for PI = 0.25 mm and 1 mm, and 0.95 for PI = 0.5 mm. This indicates a high level of correlation in all three scenarios.

For a deeper analysis of the impact of different profile intervals on the regression equations for OSRE and J R C Error , the J R C Error boundary value was set to 2, according to the typical roughness profile classifications for JRC (Barton and Choubey, 1997). The OSRE values corresponding to this boundary represent the maximum shooting distance that meets the J R C Error requirements for each PI. In other words, a higher boundary OSRE value indicates a larger permissible shooting range for the equipment and greater tolerance. As shown in Figure 5F, OSRE values are 0.408 for PI = 0.25 mm, 0.527 for PI = 0.5 mm, and 0.81 for PI = 1 mm. Thus, the JRC accuracy reflected by OSRE varies to some extent with different contour line intervals.

Figures 6A–C illustrate the fitting of spatial distance to J R C Error under different profile intervals. Similar to OSRE, a nearly linear relationship exists between spatial distance and J R C Error , with J R C Error increasing as spatial distance grows. The results show that linear fitting is generally satisfactory across all three intervals. Quantitative analysis reveals that for PI = 0.25 mm and 0.5 mm, R values are both 0.97 and R 2 values are 0.94. For PI = 1 mm, R is 0.5 and R 2 is 0.9. Although there are slight differences from the OSRE results, the fitting quality is generally good across all intervals.

Figure 6D displays the boundary values for spatial distance under different profile intervals. For PI = 0.25 mm, the spatial distance is 0.012; for PI = 0.5 mm, it is 0.036; and for PI = 1 mm, it is 0.053. When PI = 0.5 mm, the boundary value is three times that of PI = 0.25 mm, and for PI = 1 mm, the difference in boundary value reaches up to 4.42 times. The JRC accuracy reflected by spatial distance exhibits significant variations across different profile intervals, underscoring the need to distinguish the precision impact patterns at each interval.

Figures 7A–C show the fitting of spatial error to J R C Error , which can be approximated by a linear relationship, consistent with the behavior observed for OSRE and spatial distance. The results indicate that for PI = 0.25 mm, the fitting quality and correlation are the best, with R of 0.91 and R 2 of 0.84. For PI = 0.5 mm, R is 0.9 and R 2 is 0.81, while for PI = 1 mm, R is 0.84 and R 2 is only 0.7. Therefore, among the three different intervals, PI = 0.25 mm and PI = 0.5 mm show the best results, whereas PI = 1 mm exhibits the poorest fitting quality. This suggests that spatial error can be used to characterize point cloud reconstruction as well as to represent estimation accuracy across different intervals.

Considering spatial error, the boundary spatial errors under different profile intervals are shown in Figure 7D. For PI = 0.25 mm, the spatial error is 0.077; for PI = 0.5 mm, it is 0.096; and for PI = 1 mm, it is 0.14. When PI = 0.5 mm, the boundary value is 1.25 times that of PI = 0.25 mm, and when PI = 1 mm, the boundary value is 1.82 times that of PI = 0.25 mm. Thus, the analysis of JRC estimation using spatial error across different profile intervals can also be extended for broader applications.

In Section 3, an analysis of OSRE, spatial distance, and spatial error reveals a strong correlation between these three factors and J R C Error . This study further examines the influence of these three factors across three different profile intervals, as shown in Figure 8A. The results indicate that the correlation between PI = 0.25 mm and PI = 0.5 mm is nearly perfect, with an R value of 1. The relationship between PI = 1 mm and both PI = 0.25 mm and PI = 0.5 mm is also exceptionally strong, with R values of 0.96 and 0.98, respectively. Additionally, the interrelationships of other factors are also depicted in the figure. Among these, OSRE shows a relatively stronger correlation across different profile intervals, with R values of 0.97, 0.97, and 0.95. The impact of spatial distance and OSRE on different intervals is almost identical, while spatial error shows a weaker correlation compared to the other two factors, with R values of 0.92, 0.90, and 0.84. Therefore, it can be concluded that, overall, the six data sets exhibit a very strong correlation, though there are still relative differences in influence among the different factors.

Therefore, after applying five machine learning algorithms, the training and testing results of the models are shown in Figures 8B, C. R M S E , M S E , M A E , and R 2 are used as metrics to evaluate the model performance. Figure 8B illustrates the comprehensive performance of each model evaluated using the integrated assessment system (Zorlu et al., 2008). The difference in R 2 between the training and testing sets, scaled up by a factor of 10, is also depicted.

For PI = 0.25 mm, the highest overall score of 35 was achieved by the XGBoost model. SVM and CatBoost demonstrated similar scores of 32 and 31, respectively. Notably, SVM exhibited the smallest R 2 difference between the training and testing sets at 0.03, whereas XGBoost and CatBoost showed larger differences of 0.07 and 0.08, respectively. In comparison, GPR and MLP displayed weaker model performance, with overall scores of 27 and 23, and R 2 differences between training and testing sets of 0.05 and 0.15, respectively. These findings indicate that the XGBoost model outperformed the others, achieving the best overall performance despite its R 2 difference not being the smallest, as the difference remained within an acceptable range. The SVM model demonstrated strong performance as well, making it a viable option for this dataset. Conversely, GPR and MLP scored lower, reflecting their comparatively poor performance.

For PI = 0.5 mm, XGBoost achieved the highest overall score of 37, with the smallest R 2 difference between the training and testing sets at 0.05, indicating superior model performance. CatBoost ranked second with an overall score of 32 and an R 2 difference of 0.06, demonstrating good performance and stable data. In contrast, GPR, SVM, and MLP exhibited lower overall scores of 29, 24, and 23, respectively. Although the R 2 differences for these models were not substantial—0.09 for GPR, 0.05 for SVM, and 0.11 for MLP—their overall performance was comparatively poor.

When PI = 1 mm, the R 2 differences between the training and testing sets increased significantly across all models, ranging from 0.05 to 0.35, indicating heightened data instability at this interval. Overall, XGBoost demonstrated the best performance, achieving the highest total score of 40 and an R 2 difference of 0.09, making it the most suitable choice for predicting JRC errors. CatBoost performed reasonably well, with a total score of 36, though its R 2 difference was relatively larger at 0.13. The performance of the remaining models was less satisfactory.

The analysis indicates that the XGBoost model outperformed all others across all profile intervals, with R 2 differences between the training and testing sets ranging from 0.05 to 0.09, demonstrating strong stability. The CatBoost model ranked second in performance, with its overall scores increasing progressively as the profile interval expanded from 0.25 mm to 1 mm. The R 2 differences for CatBoost ranged from 0.06 to 0.13. This performance can be attributed to XGBoost’s ability to balance model complexity and prediction accuracy by incorporating additional tree models to minimize the objective function. Moreover, XGBoost exhibited robust performance in noisy environments and possessed the capability to automatically handle missing data, features that align well with the limited dataset size in this study. Additionally, as illustrated in Figure 8A, OSRE, spatial distance, and spatial errors displayed strong correlations, indicating a consistent influence of these factors, albeit with potential fluctuations as parameters varied.

The results obtained for PI values of 0.25 mm, 0.5 mm, and 1 mm were substituted into the XGBoost model, and predictions were made using different parameters. Subsequently, the errors between the predicted results and the standard results were recalculated using Equation 6, as illustrated in Figure 8D. It was observed that the J R C Error values across all three indicators ranged between 0 and 1, with average values below 0.5. The error ranges for PI = 0.25 mm and PI = 0.5 mm were similar, while the error for PI = 1 mm was slightly lower. The accuracy of JRC improved on average by 80.4%, 84.2%, and 89.5% for PI values of 0.25 mm, 0.5 mm, and 1 mm, respectively.

As a result, the performance of the trained machine learning model in predicting JRC errors based on OSRE, spatial distance, and spatial error is demonstrated. In practical applications, researchers can calculate OSRE using the formula proposed by Equation 1, while spatial distance and spatial error can be extracted from the point cloud as described in this paper. By inputting these three parameters into the XGBoost model, predicted J R C Error values can be obtained. These predicted J R C Error values can then be substituted into Equation 6, allowing for the reverse calculation of a JRC value that closely approximates the laser scanner estimate, thereby improving the accuracy of photogrammetric JRC estimation.

Additionally, to further evaluate the influence of OSRE, spatial distance, and spatial error on J R C Error , the cosine amplitude method proposed by Yang and Zhang (1997) was employed, as shown in Figure 8E. It was evident that the R E S values under different profile intervals were very close, indicating that OSRE and spatial error had a greater impact on J R C Error compared to spatial distance. It can be observed that the sensitivity of J R C Error to the three parameters remains consistent across profile intervals of 0.25 mm, 0.5 mm, and 1 mm, with only numerical variations as the interval increases. The R E S of OSRE and spatial distance on J R C Error is identical, while the R E S of spatial error is only 0.01 lower than the other two.

This study highlights the practical application of photogrammetry techniques by validating an algorithm rooted in SfM principles to optimize shooting parameter selection. By automatically configuring the camera’s spatial arrangement based on equipment specifications, the algorithm streamlines the photogrammetry data collection process, offering accessible solutions for surveyors without expertise in computer vision. Additionally, the research presents a novel machine learning model designed to enhance the accuracy of JRC measurements. This model, particularly effective in fixed tripod scenarios, accurately predicts JRC errors across three distinct profile intervals, thus enabling more precise JRC estimations. Demonstrating both stability and adaptability, the model performs consistently well even under varying conditions, such as different shooting distances and lighting environments, underscoring its wide-ranging applicability.

While this study provides valuable insights, several limitations need to be addressed. A key limitation is the reliance on a dataset generated using specific data collection methods and equipment. Expanding the variety of strategies and tools in future studies could improve the generalizability of the findings. Additionally, the research is limited by a small sample size and a narrow range of data processing software. Testing the method across different rock sample sizes and employing various 3D reconstruction software would enhance its overall applicability. Therefore, it is advisable that when implementing the machine learning-based accuracy optimization method proposed in this study, the rock sample size and data processing environment should be closely aligned with those used in this research. Moreover, current methods for optimizing JRC accuracy have yet to be widely validated in engineering settings such as slopes and tunnels. Currently, parameters affecting and reflecting JRC accuracy have been limited to OSRE, spatial distance within the point cloud, and spatial error at checkpoints. The impact of additional factors, such as image overlap, the number of feature points in stereo matching algorithms, and lighting conditions, on JRC estimation accuracy remains unexplored. Future research should focus on comprehensive testing and analysis across a broader spectrum of engineering scenarios to achieve more precise and holistic performance evaluation and optimization.