Dynamic Quantification of PISHA Sandstone Rill Erosion Using the SFM-MVS Method Under Laboratory Rainfall Simulation

Abstract

Soil erosion is a critical ecological challenge in semi-arid regions of China, particularly in the Yellow River Basin, where Pisha sandstone slopes undergo rapid degradation. Rill erosion, driven by rainfall and overland flow, destabilizes slopes and accelerates ecosystem degradation. To address this, we developed a multi-view stereo observation system that integrates Structure-from-Motion (SFM) and multi-view stereo (MVS) for high-precision, dynamic monitoring of rill erosion. Laboratory rainfall simulations were conducted under four inflow rates (2–8 L/min), corresponding to rainfall intensities of 30–120 mm/h. The erosion process was divided into four phases: infiltration and particle rolling, splash and sheet erosion, incipient rill incision, and mature rill networks, with erosion concentrated in the middle and lower slope sections. The SFM-MVS system achieved planimetric and vertical errors of 3.1 mm and 3.7 mm, respectively, providing approximately 25% higher accuracy and nearly 50% faster processing compared with LiDAR and UAV photogrammetry. Infiltration stabilized at approximately 6.2 mm/h under low flows (2 L/min) but declined to less than 4 mm/h under high flows (≥6 L/min), leading to intensified rill incision and coarse-particle transport (up to 21.4% of sediment). These results demonstrate that the SFM-MVS system offers a scalable and non-invasive method for quantifying erosion dynamics, with direct implications for field monitoring, ecological restoration, and soil conservation planning.

1. Introduction

China is one of the countries and regions most severely affected by soil erosion worldwide [1,2]. According to statistics from 2024, the area affected by soil and water loss in China is approximately 2.6019 × 10⁶ km², accounting for 24.90% of the national territory. Major river basins, including the Yellow River, represents about 73.19% of the total reduction in soil and water loss nationwide, posing a significant threat to both economic development and ecological construction in the country [3]. Hillslope erosion is one of the primary forms of soil and water loss, with typical types including sheet erosion, rill erosion, inter-rill erosion, and gully erosion [4]. Among these, rill erosion plays a disproportionately large role in shaping hillslope morphology, disrupting hydrological connectivity, and degrading ecosystem function. It serves not only as a physical mechanism of sediment transport, but also as a key ecological indicator of watershed instability [5,6]. Therefore, accurately quantifying the characteristics of rill erosion is of great significance for the prevention and control of soil and water loss.

Despite decades of research, quantifying rill erosion with sufficient spatial and temporal resolution remains a significant challenge. Traditional erosion monitoring methods typically rely on field surveys, remote sensing image analysis, or manual measurements. Seyed et al. [7], using field sampling and chemical element analysis combined with the Generalized Likelihood Uncertainty Estimation (GLUE) method, quantified the contributions of four distinct sediment sources—namely gully erosion, sheet erosion, rill erosion, and channel banks—to watershed sediment yield. Zhao et al. [8] investigated the effects of different vegetation restoration patterns on the rill erosion modulus (REM) on high-altitude gold mine tailings. Zhang et al. [9] conducted monitoring of bare runoff plots to examine morphological changes in gullies. Laboratory rainfall simulation experiments have frequently focused on the influence and contribution of factors such as rainfall intensity, slope gradient, soil depth, and groundwater depth on rill morphology, erosion mass, and erosion processes [10,11,12,13,14,15,16]. Yang et al. [17] used laboratory experiments and tracer techniques to analyze the morphological and hydraulic characteristics of various erosion gullies. Shen et al. [18], based on indoor experiments, explored how rill erosion parameters—such as average rill slope angle, rill density, rill incision degree, and average rill curvature complexity—vary with rainfall intensity. Patriche [19] employed soil erosion modeling and GIS techniques to assess the status of rill and inter-rill erosion in Romania. Yang et al. [20], using laboratory experiments and terrestrial laser scanning (TLS) technology, quantified the impact of desiccation cracks on erosion processes. Jiang et al. [21] applied digital close-range photogrammetry to investigate the dynamic processes of rill erosion in clay loam soil (CLS) and loess soil (LS).

With the advancement of modern technologies, researchers have increasingly integrated non-contact measurement techniques—such as remote sensing, unmanned aerial vehicles (UAVs), photogrammetry, artificial intelligence (AI), and 3D reconstruction methods—to enhance data accuracy and reduce labor costs in the study of soil erosion processes and their continuous quantitative assessment. Malinowski et al. [22] utilized UAV remote sensing data combined with AI algorithms to identify gullies formed under different erosion modes, achieving an accuracy of approximately 80–90%. Jose et al. [23] proposed a machine learning model based on convolutional neural networks (CNNs) and the U-Net architecture to detect rill erosion on tailings dams, with U-Net achieving accuracy rates between 85.98% and 90.17%, thereby validating the model’s reliability. Hinsberger [24] used UAV imagery to analyze natural linear erosion and quantified the erosion volume for 32 gullies of varying sizes. Fonstad et al. [25] highlighted that UAV-based image capture at altitudes of 30–120 m typically yields ground sampling distances (GSD) in the range of 2–5 cm, which is sufficient for detecting fine-scale rill erosion features. James and Robson [26] showed that increasing the number and spatial distribution of GCPs can reduce the root mean square error (RMSE) in planimetry to less than 0.05 m under controlled conditions. Zuo et al. [27], through simulated rainfall experiments, applied stereo photogrammetry to quantitatively analyze rill morphological features and investigate their relationship with sediment yield. Eltner et al. [28] introduced an automated approach for rill extraction and parameter calculation, analyzing surface roughness, rill development, and volumetric quantification with higher accuracy than terrestrial laser scanning (TLS). Smith and Vericat [29] achieved point cloud densities of >1000 points/m² in sub-humid badland erosion plots based on TLS, allowing volumetric uncertainty to be constrained to less than 5% of measured sediment budgets. James et al. [30] emphasized that a minimum of 5–10 well-distributed ground control points (GCPs) can significantly reduce georeferencing error, often achieving planimetric accuracies better than ±0.05 m in small-scale experiments. Another approach involves comparison with independent reference methods, such as terrestrial laser scanning (TLS) or high-precision total stations, which provide benchmark datasets for evaluating the geometric fidelity of reconstructed models [31]. Wheaton et al. [32] developed the “DEM of Difference” framework, which incorporates spatially variable error estimates to quantify uncertainty in erosion and deposition volumes.

Structure from Motion (SFM), a multi-view 3D reconstruction technique, reconstructs dense point cloud models of scenes by matching image features and leveraging camera geometry. Due to its low cost, high flexibility, and favorable accuracy, SFM has been widely applied in topographic mapping and civil engineering fields [33,34]. Tatsuro et al. [35] employed deep learning for damage detection in bridge structures and used SFM to obtain local position information, which was then integrated into the bridge’s 3D Building Information Modeling (BIM) data, enabling full-process automation from damage detection to BIM-based correlation. He et al. [36], aiming to quantify inter-rill and gully erosion, used SFM to measure soil surfaces and collected runoff and sediment samples every 10 min. The results indicated that during the first two simulation runs, erosion was more severe in the lower third of the slope compared to the upper and middle thirds, while laterally (left to right), inter-hill erosion showed no significant statistical differences. Ho et al. [37] conducted 750 SFM analyses on 15 sets of images taken under five pitch angles and three ground-sample distances to evaluate the method’s robustness under non-optimal settings. The results showed that pitch angles of 20° and 30° maintained stable accuracy, with relatively low root mean square errors (RMSEs) at the validation points. Westoby et al. [38] demonstrated that UAV surveys with 80% forward overlap and 60% side overlap provide sufficient redundancy for SFM reconstruction. These studies demonstrate the significant potential of SFM for monitoring rill erosion on hillslopes.

Multi-view stereo (MVS), a dense 3D reconstruction method based on multi-view imagery, is capable of recovering high-resolution geometric information from images with known camera parameters [39]. Wang et al. [40] proposed a curvature-guided MVS algorithm that reduced reconstruction errors in low-texture and complex geometric regions by approximately 15%, while improving computational efficiency by more than 20%. To mitigate errors caused by relative pose inconsistencies, Chen et al. [41] introduced a feature distribution normalization-based MVS algorithm using homographic transformations across multiple views, which reduced errors by 13.52% on the DTU benchmark dataset compared to standard algorithms. To address the failure of PatchMatch algorithms in textureless areas, Kong et al. [42] proposed a PatchMatch-MVS approach combining global–local planar priors for optimization, effectively recovering depth information and generating high-precision 3D models. Eltner et al. [31] reported that camera calibration and fixed focal length settings substantially improve the geometric stability of photogrammetric models, while controlled illumination reduces shadow-induced mismatches in laboratory-scale studies. Dense point cloud generation is achieved via MVS algorithms, where depth map fusion or patch-based stereo matching techniques enable the reconstruction of fine-scale topographic features, including rills and micro-channels formed during rainfall-induced erosion [43]. Handling texture-poor or specular surfaces remains a critical challenge in erosion monitoring: low-texture sandy slopes and wet surfaces often reduce feature matching quality. To mitigate these effects, filtering techniques, weighted depth fusion, and multi-scale texture enhancement have been applied to improve reconstruction fidelity in both laboratory and field settings [44]. These findings highlight the important role of MVS algorithms in 3D reconstruction of complex scenes.

In summary, current 3D reconstruction techniques for soil erosion monitoring primarily focus on SFM and MVS algorithms, both of which play critical roles in hillslope rill erosion detection, topographic mapping, and structural reconstruction. However, SFM is mainly suited for sparse point cloud generation and falls short in providing high-resolution, continuous erosion state data for terrain mapping. Although MVS can generate high-density point clouds, it still suffers from notable errors in low-texture regions. Therefore, a key challenge in current research lies in integrating the complementary strengths of SFM and MVS to develop a high-accuracy, robust method for continuous-state quantitative analysis of rill erosion on hillslopes.

In light of the above, this study integrates the Structure-from-Motion (SFM) algorithm for sparse reconstruction and a depth map fusion-based multi-view stereo (MVS) algorithm for dense reconstruction to develop a multi-view stereo matching observation system based on the combined SFM-MVS framework. The feasibility of the system is validated through laboratory rainfall erosion experiments. The objective is to enable dynamic monitoring and quantitative analysis of the continuous morphological evolution of rill erosion on hillslopes, thereby providing critical technical support for the optimized design of soil and water conservation measures and the sustainable development of ecological environments.

2. Materials and Methods

2.1. Study Area

The Pisha sandstone used in this experiment was collected from a severely eroded area in the Inner Mongolia section of the Yellow River Basin (as shown in Figure 1). This region exhibits some of the most representative topographical and geomorphological features associated with soil erosion, characterized by high surface fragmentation. It serves as a major sediment source for the Yellow River. Due to long-term severe soil and water loss, the area has posed significant threats to the ecological security of the middle and lower reaches of the Yellow River. Therefore, it holds substantial research value for understanding erosion processes and informing soil conservation strategies.

2.2. Test Material

A representative red Pisha sandstone from the region was selected as the experimental material. This type of sandy mudstone is characterized by low diagenetic consolidation and weak interparticle cementation. Upon contact with water, it disintegrates into slurry due to its distinctive structural properties, making it highly susceptible to soil and water loss under rainfall conditions. During field sampling, surface debris such as fallen leaves and grass roots was first removed from the sampling sites. Subsequently, surface Pisha sandstone samples were collected from a depth of 0–20.0 cm. The collected samples were air-dried under natural conditions in the laboratory, then crushed using a grinding device and sieved through a 5.0 mm standard mesh. Plant roots, gravel, and other impurities were carefully removed to obtain clean material suitable for experimentation. The particle size distribution of the experimental material was determined using a Malvern Mastersizer 3000 laser diffraction particle size analyzer, as shown in Figure 2.

The physical properties were measured using the potassium dichromate oxidation method, Kjeldahl method, molybdenum-antimony anti-colorimetric method, flame photometry, potentiometry, and ammonium acetate extraction, respectively. The detailed physicochemical composition of the Pisha sandstone is presented in

Table 1. Basic physical parameters of red Pisha sandstone.

Serial Number	Components	Quantity Contained	Particle Size Range (μm)	Note
1	Grit	57.51%	75–2000	Main ingredient, providing water permeability
2	Granule	37.78%	5–75	Medium grain size, affects soil structure
3	Viscosity	4.71%	<5	Increase soil cohesion
4	Organic matter	2.5%	/	/
5	pH	6.8	/	Weak acid
6	Capacity	1.24 g/cm3	/	Control value
7	Porosity	45%	/	Affects water penetration
8	Organic carbon content	1.5%	/	Reflects organic matter content
9	Total nitrogen content	0.12%	/	/
10	Total phosphorus content	0.05%	/	/
11	Total potassium content	1.8%	/	/
12	Cation exchange capacity	12 cmol/kg	/	/

[45].

2.3. Test Program

An artificial runoff scouring method was employed to systematically quantify rill erosion states on hillslopes under controlled laboratory-scale conditions. The experimental setup primarily consisted of a self-developed Pisha sandstone rainfall–erosion apparatus, a water supply and stabilization system, and a data acquisition system (Figure 3). To provide a clearer representation of the setup, Figure 3 combines an actual photograph of the laboratory apparatus (left) with its corresponding schematic diagram (right). The rainfall simulator was constructed on a modular steel frame with an intelligent control unit [46]. A rainfall platform was installed at adjustable heights and equipped with a matrix of 198 atomizing nozzles (18 × 11), in combination with a pressure-stabilizing device, to ensure that raindrop size and terminal velocity closely resembled natural rainfall. The rainfall sprinkler system is adjustable within a height range of 3–5 m, and in the present experiment it was set to 5 m. Rainfall uniformity was continuously monitored by distributed electronic rain sensors embedded in the frame in a grid layout, with calibration performed using standard rain gauges prior to each experiment. Data were corrected by an automated algorithm and fed back to the control panel for dynamic adjustment. The water supply system adopted a dual redundant design with a compressor feeding both a storage tank and a vacuum stabilizing tank to maintain stable pressure, while deionized water was used throughout all experiments to avoid chemical interference. During experiments, windproof materials and damping devices were used to minimize environmental disturbance.

The erosion flume measured 2000 cm in length, 50 cm in width, and 40 cm in depth, with adjustable slope gradients ranging from 10° to 45°. For each trial, a 20 cm layer of fine sand was placed at the bottom of the flume, overlaid with a 20 cm layer of prepared Pisha sandstone. The bulk density of the argillite was controlled at 1.24 g/cm³, and the slope was initially set to 15°. During filling, the soil was layered and compacted in 5 cm increments, with each layer manually raked to enhance interlayer bonding and ensure uniform soil distribution. To minimize variability in initial soil conditions, the soil moisture content was adjusted to its optimum value of 16% prior to testing, and samples were equilibrated overnight to ensure uniform water distribution throughout the soil body. All experiments were conducted at a stable room temperature of approximately 25 °C, and sample preparation was scheduled to avoid periods of unusually high temperature, thereby reducing potential evaporation and ensuring consistent initial conditions across trials.

Rainfall uniformity was continuously monitored by distributed electronic rain sensors embedded in the frame in a grid layout. Data were corrected through algorithms and fed back to the control panel for dynamic adjustment. Calibration was conducted prior to experiments using standard rain gauges placed at evenly distributed positions to ensure that rainfall intensity and uniformity met experimental requirements.

The shear stress of the overland flow was calculated using Equation (1).

$$\tau =\rho ghS$$

(1)

where ρ and g represent the density of water and gravitational acceleration, respectively; h and S denote the water depth and slope gradient. A 3D laser scanner (RIEGL VZ-400i, with a resolution of 5 mm) was used to acquire point cloud data of the slope surface before and after erosion. The rill erosion volume V was then calculated based on the changes in the point cloud, as expressed in Equation (2).

$$V={\displaystyle \sum _{i=1}^n(h_i^0}-h_i^1)\times A$$

(2)

where $h_i^0$ and $h_i^1$ represent the initial and post-erosion surface elevations, respectively. A denotes the area of a single grid cell. n denotes the total number of grid cells. The erosion rate E_τ is calculated using Equation (3).

$$E_{\tau }={\displaystyle \frac{V}{T}}$$

(3)

where T denotes the duration of the experiment. To characterize the cross-sectional morphology of rills, a dimensionless parameter—the rill width-to-depth ratio—was used. Its calculation is given by Equation (4).

$$C={\displaystyle \frac{R_W}{R_D}}$$

(4)

where R_W and R_D represent the rill width and depth, respectively. The soil erosion resistance coefficient was calculated using Equation (5).

$$AS={\displaystyle \frac{q·t}{m}}$$

(5)

where q denotes the scouring discharge. t denotes the scouring duration. m denotes the dry mass of the eroded sediment.

The multi-view stereo matching observation system was configured using multi-angle cameras and integrated with the SFM-MVS algorithm to acquire high-precision 3D data of rill erosion. This setup enabled dynamic monitoring and analysis of the erosion process. A detailed description of this system is provided in the following section. The specific experimental design is summarized in

Table 2. Experimental program design.

Group	Flow Rate	Simulated Rainfall Intensity	Runoff Coefficient	Repetition
1	2	30	0.8	3
2	4	60
3	6	90
4	8	120
5	Non-erosive treatment

.

As shown in Table 2, the study was conducted under four flow rates: 2 L/min, 4 L/min, 6 L/min, and 8 L/min. Given a slope length of 10 m, a slope width of 0.5 m, and a runoff coefficient of 0.8, this flow rates correspond to simulated erosive rainfall intensities of 30 mm/h, 60 mm/h, 90 mm/h, and 120 mm/h, respectively. Each flow condition was maintained for 40 min per trial, and each an experiment was repeated three times to minimize systematic error. Pre-rainfall treatment has been shown to effectively stabilize loose surface particles, enhance soil sealing properties, and improve surface stability, thereby providing more uniform initial conditions for subsequent experiments [47,48,49]. To ensure uniform soil moisture distribution within the flume during testing, a systematic pre-rainfall procedure was carried out one day prior to each experiment. Specifically, one end of the soil flume was adjusted to a 2° slope, and the surface was covered with 400-mesh gauze to prevent soil particle loss during rainfall. Simulated rainfall was then applied at an intensity of 10 mm/h for 10 min until a small but continuous and uniform outflow was observed at the outlet of the flume. After the rainfall application, the flume was returned to a horizontal position and left undisturbed overnight to allow full infiltration and equilibration of soil moisture throughout the soil body.

2.4. MVS Matching Observation System Based on SFM-MVS

The core of the SFM algorithm is to recover the 3D structure of the scene and the motion trajectory of the camera by analyzing 2D image sequences taken from different angles [50]. Its overall structural framework is shown in Figure 4.

As illustrated in Figure 4, key features are first identified within the image, and correspondences are established through feature point extraction and matching. Subsequently, the matched feature points are employed to construct original image pairs, and triangulation-based intersection calculations are conducted to recover 3D point cloud information. Based on these results, bundle adjustment (BA) is applied to optimize camera poses and refine 3D structural parameters. Following optimization, additional views are incorporated to further enrich the 3D reconstruction dataset [51]. For each additional view, triangulation calculations and bundle adjustment are repeated to progressively enhance reconstruction accuracy and stability [52]. During feature extraction, scale-invariant feature transform (SIFT) and speeded-up robust features (SURFs) are primarily employed to extract key feature points from images and match them across views. Subsequently, the fundamental matrix between two views is estimated using the random sample consensus (RSC) method and solved iteratively using the 8-point algorithm. Given the matching points (x_i, y_i) and (x′_i, y′_i) in the two images, the basis matrix F needs to satisfy Equation (6).

$${x^{\prime }}_{i}F{x}_i=0$$

(6)

where x_i and x′_i represent the chi-square coordinate points normalized to different images, respectively.

It is assumed that the projection matrices of the camera are P₁ and P₂. By minimizing the reprojection error, the coordinates X of the 3D points can be obtained. The formula is shown in Equation (7).

$$X=\underset{X}{\arg \min }{‖P_1-P_{1}X‖}^2+{‖P_2-P_{2}X‖}^2$$

(7)

The BA objective function L_BA is calculated as shown in Equation (8).

$$L_{BA}=\underset{R_i,t_i,X_j}{\min }{{\displaystyle {\sum }_{ij}‖P_{ij}-\pi (R_i{X}_j+t_i)‖}}^2$$

(8)

where R_i and t_i represent the rotation matrix and translation vector of the i-th camera, respectively. X_j represents the coordinates of the j-th 3D point. P_ij represents the projection of the j-th 3D point in the i-th image. π then represents the projection function.

In contrast to the SFM algorithm, which primarily produces sparse point clouds, the MVS algorithm is designed to generate dense point clouds, meshes, or surface models that offer a more comprehensive representation of a scene’s 3D structure [53]. Among the various approaches, depth map fusion-based MVS algorithms effectively handle occlusions and weakly textured regions in complex scenes by generating per-image depth maps and integrating them through multi-view geometric consistency [54,55]. Moreover, the depth map fusion approach offers notable advantages in computational efficiency and memory usage, making it particularly well-suited for large-scale scene reconstruction [48,49]. By contrast, voxel-based MVS methods can generate uniform 3D models; however, they demand significantly greater computational resources and memory [47]. Similarly, point cloud diffusion-based MVS algorithms may suffer from reduced reconstruction accuracy, particularly in detailed regions, due to insufficient point density. Consequently, this study adopts a depth map fusion-based MVS algorithm for the dense reconstruction of fine-channel sparse point clouds. The corresponding processing pipeline is illustrated in Figure 5.

In Figure 5, first, the multi-view image and the sparse point cloud generated by the SFM algorithm and the camera parameters are input. Second, independent depth maps are generated for each image by MVS matching. Next, the depth maps are optimized and filtered using geometric consistency test. Then, a dense point cloud is generated by depth map fusion. Finally, Poisson surface reconstruction and texture mapping are performed on the dense point cloud to generate a high-precision 3D model. The Poisson equation computational expression is shown in Equation (9).

$${\nabla }^2\phi =\nabla ·Y$$

(9)

where ϕ represents the indicator function and Y represents the gradient field of the point cloud. However, traditional depth map fusion methods may have poor fusion results due to inconsistent depth map quality when dealing with complex scenes. Therefore, the study also improves the MVS algorithm based on depth map fusion by adaptive weight assignment. For each depth map D_i, its confidence weight ϖ_i is calculated as shown in Equation (10).

$${\varpi }_i={\displaystyle \frac{1}{{\sigma }_i^2+\epsilon }}$$

(10)

where ${\sigma }_i^2$ represents the noise variance of the depth map. ε then represents the smoothing term.

The study is based on the SFM algorithm and the adaptive depth map fusion MVS algorithm, and finally an MVS matching observation system based on SFM-MVS is constructed. The image acquisition part of the system consists of five digital cameras (Canon 5d4 24-105 II, 30.4 megapixels, 61 megapixels) and is mounted on a fixed frame 2.5 m above the ground to ensure accurate acquisition of slope fine channel images under high overlap conditions. The placement of the digital cameras on the fixed frame is shown in Figure 6.

As illustrated in Figure 6, the image acquisition system within the experimental area was deployed using a spatially optimized configuration scheme. Digital cameras were placed at the 20% and 80% positions along each of the two main diagonals of the study area, with an additional camera positioned at the intersection of the diagonals’ geometric centers. To ensure complete coverage, cameras at the four corners were mounted with a calibrated inward tilt. The tilt angle was precisely maintained within 5° ± 0.5°, whereas the central camera was oriented vertically downward, forming a 90° angle with the ground. This spatially symmetrical layout not only eliminates blind spots within the monitoring area, but also minimizes image distortion, thereby providing high-quality input for subsequent data analysis.

In addition to the spatial configuration, all images were captured in RAW format using full-frame sensors (36 × 24 mm) at the maximum resolution (6720 × 4480 pixels). The cameras were operated in manual mode with an aperture of f/2.8, ISO sensitivity of 250, and a shutter speed of 1/20 s. Focus was manually adjusted until optimal sharpness was achieved, and then locked for sequential acquisition. Prior to experiments, camera calibration was performed following established photogrammetric protocols to correct radial and tangential lens distortions, with bundle adjustment applied during SFM processing to further refine geometry [56]. Illumination was provided by a cold LED lighting system equipped with diffusers to ensure homogeneous light distribution and reduce reflections on the wet soil surface [57]. Image acquisition was designed to achieve at least 70–80% forward overlap and 60–70% side overlap, which is recommended for accurate 3D reconstruction [58]. Multi-angle acquisition and depth map fusion with geometric consistency checks were adopted to minimize occlusion artifacts and suppress reconstruction noise. For georeferencing and accuracy validation, a total of 14 ground control points (GCPs) were evenly distributed along the edges and corners of the flume. Their spatial coordinates were measured using a high-precision total station (Leica TS16) and incorporated into the reconstruction workflow. This configuration ensured the geometric stability of the laboratory-scale model and provided reliable accuracy control for subsequent 3D analyses. The reconstruction process of the fine-channel erosion 3D model using the SFM-MVS observation system is illustrated in Figure 7.

As shown in Figure 7, the study employs Context Capture software to model and reconstruct the fine-channel erosion process in 3D. Prior to data processing, the storage path is configured and CPU acceleration is enabled. Images captured by five digital cameras are imported and automatically aligned using the software’s built-in feature-matching algorithm. The key point and tie point limits are configured, and the highest matching accuracy is selected to extract feature points and recover the relative positions of the camera centers, images, and fine-channel slope, thereby generating a sparse point cloud. Ground control points (GCPs) are then added, and the SFM algorithm is applied to georeference the sparse point cloud and refine the alignment. The MVS algorithm is subsequently employed to generate a dense point cloud, with the depth filtering threshold set to 0.5 to retain microtopographic details of the fine channel. Geometry editing is then conducted to remove extraneous surfaces. Multi-resolution texture mapping is applied to generate surface textures, with orthographic projection selected as the mapping mode to ensure scale consistency. A digital elevation model (DEM) is generated using geographic coordinate projection. Finally, the point cloud data are exported in .las and .txt formats for code integration or further processing in geographic information system (GIS) software, while the DEM is exported in .tif format.

3. Results

3.1. Performance Test of MVS Matched Observation System Based on SFM-MVS

Figure 8 illustrates the erosion states of the experimental slope at different time intervals under a flow rate of 2 L/min and a slope of 15°. As shown in the figure, the erosion process of the Pisha sandstone slope can be broadly divided into four stages: infiltration and particle rolling, splash and sheet erosion, initial rill incision, and mature rill networks, highlighting the dynamic and stage-dependent nature of Pisha sandstone erosion under simulated rainfall conditions. At the initial stage (Figure 8a), surface infiltration occurred rapidly after rainfall onset, causing slight surface subsidence. Under gravity and slope effects, larger particles began migrating downslope, often aggregating into clumps and rolling downward (➀). Precipitation mainly acted through localized infiltration and splash, dislodging fine particles from the weakly cemented Pisha sandstone. Given the low porosity and poor permeability of Pisha sandstone, the initial kinetic energy of raindrops falling on the dry surface dislodged and splashed fine particles. In the early splash erosion stage (Figure 8b), continued rainfall filled microcracks and pores, producing a thin muddy film. Raindrop impact on the gradually wetted surface generated widespread splash and shallow sheet flow. Fine particles were detached more easily due to the argillite’s bedding and fracture structure. At this stage, overland flow remained weak but sufficient to entrain dispersed sediment (➁). As rainfall progressed into the incipient rill stage (Figure 8c), thin overland flow converged downslope, increasing runoff velocity and shear stress. Local weaknesses in the soil matrix, together with small surface undulations, promoted the formation of tiny scouring pits and drop structures. These pits deepened under vortex flow, eventually connecting into discontinuous rill traces, particularly in the mid-slope zone where runoff convergence was strongest (➂ and ➃). Finally, in the mature rill development stage (Figure 8d–f), the erosive force intensified and initial rill channels expanded both longitudinally and laterally. Branching and merging occurred, forming a more integrated rill network in the lower slope section. Local variations in rock resistance and soil clod disintegration controlled the heterogeneity of rill density and width. This stage marked the transition from sheet erosion to a well-developed rill erosion pattern, with sediment transport dominated by concentrated flow rather than dispersed splash. Rill development was most pronounced in the middle and lower sections of the test flume.

To ensure the reliability of the SFM-MVS reconstruction, georeferencing error calculation of accuracy evaluation were incorporated. Georeferencing error was assessed by comparing the 3D coordinates of ground control points and independent check points measured with a high-precision total station (Model: Leica TS16) against their corresponding positions in the reconstructed model. A total of 32 measurement points on the slope surface and 14 reference points on the flume structure were collected. The spatial distribution of these points is shown in the last panel of Figure 8. Using the coordinates of 46 points, including both slope validation points and flume boundary markers, the accuracy of the observation system was assessed. The validation results are presented in Figure 9.

As shown in Figure 9, red spheres represent total station measurements, while blue spheres denote the corresponding coordinates reconstructed by the SFM-MVS system. The overall distribution demonstrates that the measured and reconstructed points exhibit a high degree of spatial coincidence across both the slope surface and the flume structure. The 3D reconstruction model achieved excellent accuracy, with a horizontal (planar) error of only 3.1 mm and a vertical (elevation) error of 3.7 mm. The close alignment of red and blue points across an elevation range of 160–210 cm confirms the ability of the system to generate dense point clouds with millimeter-level precision and stability. Although minor local deviations are observed, they remain within the tolerance range of image-matching and point-cloud reconstruction processes. These results demonstrate that the proposed SFM-MVS–based multi-view stereo matching system not only maintains high reconstruction accuracy under heterogeneous surface conditions but also effectively captures subtle morphological changes during the rill erosion process, providing reliable technical support for dynamic monitoring and quantitative analysis of slope erosion.

3.2. Quantitative Analysis of the Continuous State of Fine Channel Developmental Features

Under different flow rate conditions (2 L/min, 4 L/min, 6 L/min, and 8 L/min), the development characteristics of rill erosion morphology on sandy loam slopes were quantitatively analyzed in a continuous manner using the SFM-MVS system. Data were collected at 2.5 min intervals throughout the experiment. The temporal variations in runoff yield rate and infiltration rate under each flow condition are presented in Figure 10.

Figure 10a,b illustrate the temporal variations in runoff yield rate and infiltration rate, respectively, under different flow rate conditions. As shown in Figure 10, with increasing flow rate, the runoff yield rate of the experimental soil rises significantly. Under flow rates of 2 L/min, 4 L/min, 6 L/min, and 8 L/min, the runoff yield rates increased by 28.7%, 49.3%, 62.7%, and 78.8%, respectively, during the first 30 min of the experiment. The increase was especially pronounced under high-flow conditions (6 L/min and 8 L/min), indicating that as inflow increases, surface runoff on the slope accelerates and the water-holding capacity of the sandy loam soil tends toward saturation. In contrast, the infiltration rate exhibited an inverse trend. At the beginning of the experiment, infiltration rates were highest, with initial values of 14.8 mm/h, 12.9 mm/h, 9.5 mm/h, and 7.3 mm/h under flow rates of 2 L/min, 4 L/min, 6 L/min, and 8 L/min, respectively. These values dropped rapidly and stabilized between 10 and 15 min, maintaining average rates of approximately 6.2 mm/h, 5.3 mm/h, 3.8 mm/h, and 1.9 mm/h, respectively. During the middle and later stages of the experiment, infiltration rates remained relatively stable or exhibited minor fluctuations, suggesting that the infiltration capacity of sandy loam is strongly influenced by soil saturation. Under higher flow conditions, the soil quickly reached a stable infiltration stage, whereas lower flow rates resulted in a more prolonged infiltration process. The temporal variation in sediment particle size distribution under different flow rate conditions is shown in Figure 11.

Figure 11 illustrates the temporal variation in sediment particle composition under flow rates of 2 L/min, 4 L/min, 6 L/min, and 8 L/min. As shown in the figure, the clay content remained nearly constant throughout the entire experiment, with average fluctuations within ±0.3%. This indicates that during the rill erosion process, the amount of clay particles detached from the surface of the sandy loam soil by runoff was minimal and did not increase significantly over time. Moreover, the rill flow primarily transported sand and silt particles, and its shear force was insufficient to effectively detach and mobilize clay particles. As a result, the sediment particle composition remained relatively stable throughout the scouring process.

To further investigate the dynamic variation in sediment particle size distribution during rill erosion, sediment samples from three key stages were analyzed: the rill initiation stage (2–10 min), the rill development stage (15–20 min), and the rill stabilization stage (25–30 min). The test results are presented in Figure 12.

Figure 12a–c show the dynamic changes in sediment particle size distribution during the rill initiation, development, and stabilization stages, respectively. As illustrated, the particle size distribution at different stages generally exhibited unimodal or bimodal patterns. During the rill initiation stage, the eroded sediment was dominated by fine particles, with a median particle diameter (D50) of 0.032 mm, primarily composed of clay and silt. This indicates that erosion during this stage mainly affected the surface soil, where fine particles were more easily detached and transported by runoff. As erosion intensified and entered the rill development stage, D50 increased to 0.086 mm, accompanied by a rise in the proportion of sand particles larger than 0.1 mm. This shift led to a bimodal distribution, suggesting that larger soil aggregates were broken down and mobilized under stronger hydrodynamic forces. In the rill stabilization stage, D50 decreased slightly to 0.075 mm, and the proportion of sand particles >0.1 mm declined marginally, indicating that rill morphology had begun to stabilize, erosion intensity had weakened, and transported sediment primarily originated from ongoing scour of the rill bed. From an overall perspective, fine particles (<0.05 mm) accounted for 74.3%, 62.8%, and 65.1% of the sediment during the initiation, development, and stabilization stages, respectively. In contrast, the proportion of coarser sand particles (>0.1 mm) peaked during the development stage at 21.4%, followed by a slight decrease to 18.7% in the stabilization stage. These results indicate that sediment particle sorting during the rill erosion process was relatively distinct: strong erosion in the development stage facilitated the detachment and short-term transport of larger particles, whereas the stabilization stage was characterized by the predominant movement of finer particles.

To further strengthen the analysis of particle-size distribution, additional statistical comparisons were conducted across the three erosion stages, as shown in Figure 13.

As shown in Figure 13a, the proportion of fine particles (<0.02 mm) exhibited a distinct stage-dependent decline with increasing erosion duration. At the early stage of erosion, low flow rates (2 L/min) preserved the highest fraction of fine particles, exceeding 20%, which reflects the preferential detachment and mobilization of surface fines under weaker hydraulic forces. In contrast, high flow rates (6–8 L/min) at the same stage already showed markedly reduced fine fractions (<12%), indicating that intense runoff rapidly entrains and transports fine sediment out of the slope system. During the middle stage, the differences among flow conditions became less pronounced, as fine particles were progressively depleted across the surface. By the late stage, fine-particle content consistently decreased across all flow intensities, converging to relatively low values. This systematic reduction highlights the selective depletion of fines over time, signifying a gradual shift in sediment composition from fine-dominated to coarse-dominated material.

Figure 13b illustrates the spatiotemporal dynamics of coarse particles (0.20–2.00 mm), which exhibited a progressive increase with erosion duration. In the early stage, the coarse fraction remained relatively low across all flow conditions, reflecting the initial dominance of finer particles in sediment yield. However, as erosion proceeded to the middle stage, the proportion of coarse particles began to increase, particularly under moderate and high flow rates (4–8 L/min), suggesting that the depletion of fines exposed the underlying coarser fractions. By the late stage, the coarse fraction reached its highest values, with proportions exceeding 30% under high flow rates (6–8 L/min). This trend complements the observed decline in fine particles in Figure 13a, collectively demonstrating the selective entrainment of sediment fractions. In other words, early erosion stages are dominated by fine-particle detachment, while prolonged and intensified flow conditions favor the exposure and transport of coarse particles, leading to progressive surface coarsening and textural stabilization of the eroding slope.

4. Discussion

4.1. Comparative Evaluation of SFM-MVS Against LiDAR and UAV Photogrammetry

To rigorously assess the accuracy and stability of the proposed SFM-MVS system, we conducted a comparative analysis under the experimental conditions described in Section 3.1. Two widely used reference methods—light detection and ranging (LiDAR) and unmanned aerial vehicle (UAV) photogrammetry—were selected as benchmarks. Stability and computational efficiency served as the primary evaluation criteria, with the results summarized in Figure 14.

Figure 14a presents the elevation error distributions of the three approaches. The SFM-MVS method achieved the smallest mean and median deviations, with error dispersion tightly constrained within ±0.3 cm. This narrow distribution demonstrates superior consistency relative to LiDAR and UAV photogrammetry, both of which exhibit broader error ranges. The results underscore the capability of SFM-MVS to deliver high-fidelity surface reconstructions with reduced systematic and random errors, thereby surpassing the precision of conventional high-resolution methods. Figure 14b compares the computational efficiency of the three systems. Notably, SFM-MVS required substantially less processing time—approximately 40–50% shorter than both LiDAR and UAV workflows. This improvement indicates that SFM-MVS not only ensures greater accuracy but also accelerates data processing, a critical advantage in dynamic erosion monitoring scenarios where rapid feedback is essential.

Taken together, these findings establish that the SFM-MVS system outperforms traditional reference methods by offering a dual advantage of higher accuracy and faster computation. This combination of precision and efficiency highlights its potential as a robust tool for quantitative erosion volume assessment and real-time environmental monitoring in complex terrains.

4.2. Limitations and Future Perspectives

Although the SFM-MVS system proved effective in dynamically capturing rill development under controlled rainfall simulations, several limitations remain in the present study. First, the experiments used red Pisha sandstone, a substrate characterized by weak cementation and rapid disintegration upon wetting. These structural properties accentuate incision and make the material highly representative of severely degraded slopes in the Yellow River Basin. However, extrapolation to other soil types (e.g., loess, clay loam) should be performed cautiously. Cross-material trials are necessary, since soil type has been shown to exert strong control on rill initiation thresholds and detachment rates. Second, the flume experiments were conducted under uniform slope gradients and controlled inflow conditions to isolate process–response relationships. Although this design ensured reproducibility and facilitated clear attribution, it cannot fully capture the heterogeneity of natural hillslopes, where slope angles, micro-relief, antecedent soil moisture, vegetation cover, and storm variability interact to influence erosion dynamics. Future work should extend observations to natural rill networks with a broader range of slope gradients and rainfall regimes, while explicitly incorporating vegetation and biological crust effects to better approximate field conditions. Next, the study focused on inflow rates, but did not systematically vary slope gradient, raindrop size and kinetic energy, rainfall intermittency, or subsurface flow. These drivers strongly regulate infiltration dynamics, flow concentration, and rill connectivity in the field. Incorporating them into future designs will sharpen process attribution and improve the generality of erosion models calibrated with SFM-MVS data. Last, while the SFM-MVS system achieved millimeter-level accuracy, the technique relies on high image overlap and adequate surface texture. Challenges such as specular reflections from water films, occlusions within deep rills, or texture-poor patches may degrade feature matching despite adaptive fusion strategies. Field deployments should therefore consider technical refinements such as polarizing filters, active illumination, and more robust outlier filtering to sustain reconstruction quality under natural, wet, and low-texture conditions.

Despite these limitations, the SFM-MVS system demonstrates clear advantages in vertical fidelity and computational efficiency, making it well suited for high-frequency monitoring of rapid morphological change. By explicitly accounting for vegetation, lithological heterogeneity, and rainfall variability, future research can bridge the gap between controlled experiments and complex field environments, thereby enhancing the robustness of rill erosion quantification and strengthening the scientific basis for soil and water conservation in semi-arid regions.

5. Conclusion

Rill formation during rainfall–runoff events can dramatically accelerate soil erosion, leading to significant changes in slope morphology and ecological degradation. Quantifying rill erosion is thus critical for effective soil conservation and ecological recovery. Based on controlled laboratory experiments with erodible Pisha sandstone, the main findings are as follows:

(1)

Under rainfall intensities of 30–120 mm/h, the rill erosion process progressed through four distinct stages: infiltration and particle rolling, splash and sheet erosion, initial rill incision, and mature rill networks. Erosion was most pronounced in the middle and lower sections of the slope.

(2)

The developed SFM-MVS observation system achieved millimeter-level accuracy, with planimetric and vertical errors of 3.1 mm and 3.7 mm, respectively. Compared with LiDAR and UAV photogrammetry, the system reduced elevation errors by approximately 25% and shortened computation time by nearly 50%.

(3)

Infiltration capacity was strongly associated with soil saturation. At low flow rates (2 L/min), average infiltration stabilized at approximately 6.2 mm/h, resulting in a gradual sheet-to-rill transition. At high flow rates (≥6 L/min), infiltration rapidly stabilized at less than 4 mm/h, leading to dominant rill incision and sediment transport dominated by coarse particles (>0.1 mm, up to 21.4% of the sediment load).

(4)

The combined use of feature matching and depth map fusion significantly improved reconstruction fidelity and enabled dynamic quantification of rill development. However, since tests were limited to laboratory-scale experiments, further field validation is necessary to assess the impacts of natural rainfall variability, vegetation cover, and soil heterogeneity on rill erosion processes.