Identification of Gully-Type Debris Flow Shapes Based on Point Cloud Local Curvature Extrema

Abstract

The identification of gully-type debris flow remains a challenging task due to the irregularity of terrain, which causes significant fluctuations in local curvature and hinders accurate feature extraction using traditional methods. To address this issue, this study proposes a novel identification approach based on point cloud local curvature extrema. The methodology involves collecting image data of debris flow and landslide areas using DJI Matrice 300 RTK (M300RTK), planning control points and flight routes, and generating three-dimensional point cloud data through image matching and point cloud reconstruction techniques. A quadratic surface fitting method was employed to calculate the curvature of each point in the point cloud, while a topological k-neighborhood algorithm was introduced to establish spatial relationships and extract extreme curvature features. These features were subsequently used as inputs to a convolutional neural network (CNN) for landslide identification. Experimental results demonstrated that the CNN architecture used in this method achieved rapid convergence, with the loss value decreasing to 0.0032 (cross-entropy loss) during training, verifying the model’s effectiveness. The introduction of early stopping and learning rate decay strategies effectively prevented overfitting. Receiver-operating characteristic (ROC) curve analysis revealed that the proposed method achieved an area under the ROC curve (AUC) of 0.92, significantly outperforming comparative methods (0.78–0.85).

1. Introduction

Gully-type debris flows are highly destructive geological hazards that have occurred with increasing frequency and scale in recent years. According to recent studies, the occurrence of such landslides has risen by approximately 20% over the past decade, significantly impacting the ecological environment and human settlements [1,2,3]. This surge in activity has necessitated the development of more accurate and efficient methods for identifying gully-type debris flow sliding slopes, making it a critical research focus in the field of geological hazard prevention and control.

Traditionally, the identification of gully-type debris flow sliding slopes has relied heavily on field investigations and manual visual interpretation. Field investigations involve professional personnel conducting on-site observations of terrain, geological structures, vegetation coverage, and other characteristics to determine the presence of landslide hazards. While this method is intuitive and accurate, it is also time-consuming, labor-intensive, and challenging to implement in areas with complex terrain and limited accessibility [4,5]. On the other hand, manual visual interpretation involves analyzing remote sensing images and aerial photographs to identify landslide locations and extents. However, this approach is highly subjective, dependent on the interpreter’s expertise, and inefficient for large-scale application.

With the rapid advancement of information technology, various advanced technological methods have been introduced to enhance the identification of gully-type debris flow sliding slopes. For instance, drone oblique photography technology can swiftly acquire high-resolution image data, providing a rich data source for landslide identification. Convolutional Neural Networks (CNNs), a powerful deep learning algorithm, have shown remarkable success in image recognition by automatically extracting and classifying features.

Recent studies have proposed several innovative approaches to improve landslide detection. Liu Qing et al. [6] proposed an improved deep learning model for landslide detection based on the existing You Only Look Once (YOLO) model, which was used for the intelligent recognition of new and old landslides in loess areas. They established a loess landslide dataset using landslide images from Baoji City for model training and incorporated the focal EIoU loss function and effective channel attention (ECA) mechanism into the YOLO model to construct the LD-YOLO model, making it more suitable for landslide detection tasks. However, the training data were limited to landslide images from Baoji City, resulting in obvious regional constraints and limited data sources. As a result, the model showed poor generalization when applied to landslide recognition tasks in other regions, reducing its recognition accuracy.

Song Yewei et al. [7] conducted intelligent landslide recognition using an improved YOLO algorithm. They built a landslide dataset using open-source remote sensing images. The YOLOv7 model was enhanced using data augmentation algorithms and attention mechanisms, leading to the development of three optimization models for automatic landslide identification. However, in cases where landslide features are not distinct and easily confused with other terrain features, the model may still produce misclassifications.

Yu Haihua et al. [8] analyzed 84 ascending orbit Sentinel-1A SAR images from 2015 to 2019. Using Small Baseline Subset Interferometric Synthetic Aperture Radar (SBAS InSAR) technology, the surface deformation rate and time series results in the Jiangdingya landslide area during this period were extracted, and potential landslides were identified. However, SBAS InSAR technology has high data processing requirements, involving complex interference processing, phase unwrapping, and other steps. These processing procedures can be easily affected by atmospheric delay and terrain fluctuations, introducing errors and affecting the accuracy of surface deformation rate calculations and time series results, impacting landslide identification accuracy.

Lian X. et al. [9] conducted a 10 cm-per-pixel photogrammetric survey of the Taohuagou geological hazard-prone area in Shanxi Province using a DJI drone. They generated digital orthophotography models (DOMs) and 3D point cloud models (3DPCMs) in the area and proposed a visual identification method for landslides and collapses based on DOM-3DPCM. However, visual recognition methods rely to some extent on manual observation and judgment, making them subjective. Different identification personnel may have different understandings and judgment criteria for the characteristics of landslides and collapses, resulting in differences in identification results.

Liu J et al. [10] utilized 3D laser scanning technology to analyze the point cloud characteristics of landslides through indoor model experiments. They proposed an adaptive random sampling boundary extraction (A-R-B) algorithm suitable for dam landslides and verified its high accuracy and feasibility in identifying landslide features. However, although parameter testing was conducted using the A-R-B algorithm, its adaptability to different geological conditions and environmental changes has not been fully explored, affecting its effectiveness in landslide identification.

Zhou J W et al. [11] developed an automatic discontinuous surface recognition algorithm based on k-means fuzzy clustering and a quantitative overall displacement evaluation method based on the M3C2 algorithm, utilizing terrestrial laser scanning (TLS) point cloud data. These methods enable the rapid acquisition of landslide geometric information and quantify local deformation, providing effective technical support for landslide emergency investigation and monitoring. However, this method mainly relies on TLS point cloud data and does not integrate with other data sources, limiting its ability to capture and analyze landslide characteristics comprehensively.

Ren, SP et al. [12] introduced an Euler–Lagrangian technique combined with a three-dimensional rotational random field and Monte Carlo simulation to capture the spatial heterogeneity of soil and stratum dip angles for evaluating landslide behavior. This method relies on assumptions to simplify the simulation of soil spatial heterogeneity and stratum dip angles, which cannot fully reflect real-world conditions, leading to deviations between simulation results and actual scenarios.

Ren, SP et al. [13] considered the influence of non-uniform soil strength and introduced a three-dimensional finite element computational framework, integrating random field methods and stochastic vibration theory to analyze landslide flow effects. The combination of random field methods and stochastic vibration theory requires the precise handling of the statistical properties and correlations of random variables. Improper treatment may result in inaccuracies in the simulation results.

To overcome the limitations of traditional methods in capturing accurate geometric characteristics and assessing landslide volume and potential risks, this paper proposes a novel method for identifying gully-type debris flow shapes based on point cloud local curvature extrema. The method extracts extreme curvature features of slopes by employing quadratic surface fitting and topological k-neighborhood algorithms and utilizes a Convolutional Neural Network (CNN) for automatic slope recognition. Experimental results demonstrated significant improvements in recognition efficiency and accuracy, with the CNN model achieving an AUC value of 0.92, surpassing traditional methods. This model can be applied to regularly monitoring and assessing geological disasters such as landslides and debris flows, providing reliable technical support for disaster warnings. This study not only fills the gap in fine feature extraction and automatic identification but also offers a practical technical approach for geological hazard risk assessment and disaster reduction management.

2. Acquisition of Debris Flow and Landslide Images Based on Drone Oblique Photography

2.1. Imaging of Mudslides and Landslides Based on Drones

Unmanned Aerial Vehicles (UAVs) have become an important means for acquiring image data of debris flow landslides due to their flexibility and efficiency. Through oblique photogrammetry technology, UAVs can capture images from multiple angles, obtaining comprehensive geometric and texture information on the landslide terrain.

2.1.1. Ground Control Point (GCP) Layout and Flight Planning

Ground Control Point (GCP) Deployment: Before UAV image acquisition, GCPs must be systematically planned and deployed. The number of required GCPs correlates with both terrain complexity and expected measurement accuracy [14,15]. Under a certain measurement area $A$ and expected measurement accuracy $\chi$, the number of image control points $N$ can be estimated using the following empirical formula:

$$N=k\times {\displaystyle \frac{A}{{\chi }^2}}$$

(1)

In the formula, $k$ represents the terrain complexity coefficient. In areas with relatively flat terrain and simple features, the $k$ value is relatively small (for example, $k=0.5$). In areas with complex terrain and significant changes in land cover, the $k$ value is relatively high (for example $k=1.5$).

For example, for a measurement area of 1 km², the terrain complexity factor $k=1.0$, and an expected accuracy of 5 cm, it is recommended to set up about 20 control points.

Flight planning: In the process of flight route planning, some key parameters need to be set, including flight altitude $H$, lateral overlap $p_x$, and heading overlap $p_y$.

The appropriate flight altitude is crucial for obtaining clear and accurate image data. Lateral overlap refers to the horizontal overlap between two adjacent flight paths. Heading overlap refers to the longitudinal overlap between two adjacent images on a flight path [16,17,18]. The expression is as follows:

$$\left\{\begin{array}{l}H=f\times {\displaystyle \frac{GSD}{a}}\\ p_x={\displaystyle \frac{P_x}{l_x}}\times 100\%\\ p_y={\displaystyle \frac{P_y}{l_y}}\times 100\%\end{array}\right.$$

(2)

In the formula, $f$ represents the focal length of the lens, $a$ represents the pixel size, and $GSD$ represents the ground resolution of the image, which is related to the aerial photography scale; $P_x,P_y$ represents the edge length of the overlapping part of the image, and $l_x,l_y$ represents the edge length of the image. The Uav aerial photography course and side overlap degree diagram are shown in Figure 1.

To ensure sufficient overlap between adjacent images, the UAV flight was conducted with 60% side overlap and 60% forward overlap at an altitude of 100 m [19,20], using a photogrammetric scale of 1:500.

2.1.2. Camera Imaging Principle

The camera imaging process involves the projection of three-dimensional spatial points onto a two-dimensional image plane [19]. The projection is determined by the straight line connecting the optical center $C$ and the 3D point $M$.

When this line intersects with the image plane $R$, the intersection point is obtained. The focal point $W$ is the intersection of the optical path axis and the image plane, which marks the precise point of light focusing. In addition, the vertical distance from $C$ to the image plane to the object is defined as the focal length $f$, which is an important parameter for measuring the imaging capability of a camera. The imaging principle of a pinhole camera is shown in Figure 2a.

Assuming $M={\left(x,y,z,1\right)}^T$, $W={\left(x^{\prime },y^{\prime },z^{\prime },1\right)}^T$. According to the similar triangle in Figure 2b, ${\displaystyle \frac{f}{z}}={\displaystyle \frac{x^{\prime }}{x}}={\displaystyle \frac{y^{\prime }}{y}}$ can be obtained. For the pinhole camera model, the imaging relationship can be expressed by the following formula [21]:

$$\begin{array}{l}{x}^{\prime }=f{\displaystyle \frac{x}{z}}\\ y^{\prime }=f{\displaystyle \frac{y}{z}}\end{array}$$

(3)

Assuming that the pixel coordinates of $W$ are ${\left(u,v,1\right)}^T$, $\alpha$ and $\beta$ are scaling factors, and the offset of $C^{\prime }$ is ${\left(u_c,v_c,1\right)}^T$, the pixel coordinate parameters $u$ and $v$ of $W$ can be obtained as:

$$\begin{array}{l}u=\alpha f{\displaystyle \frac{x}{z}}+u_c\\ v=\beta f{\displaystyle \frac{y}{z}}+v_c\end{array}$$

(4)

Let the camera’s internal parameter matrix $K$ be $\left[\begin{array}{ccc}{f}_u& \gamma & u_c\\ 0& f_v& v_c\\ 0& 0& 1\end{array}\right]$, and let the three-dimensional coordinate of the point $W_{\mathrm{J}}$ in the real physical world be $w$; then, $W=Hw=\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]w$. By incorporating the camera’s intrinsic matrix and projection matrix, a comprehensive projective relationship is established between 3D spatial coordinates in the physical world and corresponding image coordinates. This mathematical framework facilitates efficient conversion between 3D spatial points and image points, providing the foundational model for subsequent point cloud reconstruction [22].

This study employs UAV-based oblique photogrammetry rather than LiDAR scanning for point cloud acquisition, primarily due to specific requirements for debris flow landslide monitoring and cost–benefit considerations. The UAV oblique photography system generates colored point clouds with densities reaching 200 points/m² through multi-angle image matching (60% overlap), which simultaneously satisfies the continuity requirements for curvature calculations while preserving surface texture features for crack identification. In comparison, although LiDAR demonstrates advantages in vegetation penetration, its high equipment costs (approximately five times that of photogrammetric systems) and limitations of monochromatic reflectance intensity data for subsequent CNN-based multi-feature fusion make photogrammetry more suitable for this research context.

2.2. Image Matching Point Cloud Reconstruction

The triggering factors of mudslides are diverse and challenging to predict, resulting in complex morphology and dynamic changes in landslide bodies. Through image matching point cloud reconstruction, the three-dimensional structural information of the landslide surface can be accurately restored, capturing its subtle terrain changes and potential unstable areas. For example, under the influence of triggering factors such as rainfall or earthquakes, landslides may experience local deformation or cracks. Point cloud reconstruction can clearly display these changes, providing reliable data support for subsequent landslide stability analysis and early warning. This method not only improves the accuracy of landslide identification but also effectively responds to complex and changing geological environments, providing a scientific basis for disaster prevention and emergency decision making. In this section, unmanned aerial vehicle (UAV) sequence images are used for the 3D reconstruction of landslides. The UAV camera is used to obtain spatial coordinates in the real environment and further obtain the 3D scene. Image matching point cloud 3D scene reconstruction based on UAV sequence images is shown in Figure 3.

(1)

Basic Matrix

The fundamental matrix $F$ can be regarded as an algebraic expression of epipolar geometry [23], which intuitively reflects the inherent characteristics of epipolar geometry, as shown in Figure 4.

As shown in Figure 4, the projection points of the point $X$ in three-dimensional space on two captured images are $A_1$ and $A_2$, respectively, which is the epipolar geometry model. The surface formed by $X$, $C_1$, and $C_2$ is the polar plane $\kappa$, and the epipolar lines corresponding to $\kappa$, $L_1$, and $L_2$ are $l_1$ and $l_2$. The two poles corresponding to the baseline and the image planes $L_1$ and $L_2$ are $e_1$ and $e_2$. The correspondence between the image point $A_1$ and its corresponding pole line $l_2$ is represented by the fundamental matrix as follows:

$$l_2=F{A}_1$$

(5)

The corresponding point of point $A_1$ is on the epipolar line $l_2$; therefore, $A_2^T{l}_2=A_2^{T}F{A}_2=0$.

(2)

Essential matrix

The internal parameter matrix $K$ of the camera is obtained using Zhang Zhengyou’s calibration method, and its inverse matrix is applied to the point $A$. The fundamental matrix is transformed into the essential matrix E through the camera’s intrinsic matrix:

$$E=K^{T}FK$$

(6)

(3)

Solve the external parameters of the camera

Perform singular value decomposition $E=UD{V}^T$ on the essential matrix to obtain three components: two orthogonal matrices, $U$ and $V$, and a diagonal matrix, $D$, thereby determining the camera’s extrinsic parameters.

(4)

3D spatial point positioning

After determining the $E$ of the two images, a linear equation is derived by normalizing the image coordinates of the spatial points on the two images, and then the 3D coordinates of the matching points are calculated.

(5)

Optimization of Motion Matrix

Bundle adjustment is employed to optimize the motion matrix and minimize the reprojection error:

$$e={\displaystyle \sum _{i\in J}{\displaystyle \sum _{j\in X\left(i\right)}{\left(r_{ij}\right)}^2}}$$

(7)

In the formula, $J$ represents the set of images, the set of tracking points observed in the image $i$ is $X\left(i\right)$, and $r_{ij}$ represents the error value of the tracking point $j$ projected onto the image $i$.

Through the aforementioned steps, image-matched point cloud reconstruction is achieved, generating 3D point cloud data of the landslide body, which provides the foundation for subsequent analysis.

3. Analysis of Landslide Image Features Based on Local Curvature Extremum

The point cloud data of the debris flow landslide body contains a wealth of geometric information, and the local curvature extremum can effectively highlight the geometric feature changes on the surface of the landslide body. For example, the edges, cracks, and areas with significant terrain undulations of landslide bodies usually have large local curvature values. By analyzing local curvature extrema, these key features can be examined, providing more accurate morphological and structural information for the subsequent analysis and identification of gully-type debris flow sliding slopes.

Curvature is a key indicator that describes the characteristics of a surface, and it is also an important basis for identifying surface features. Considering the high stability and concise calculation process of the quadratic surface fitting method, this paper adopts this method to calculate curvature. The core idea of this method is to select any point $A_i$ ($1\le i\le n$, $n$ are the number of point clouds) in the point cloud dataset, use its $k$ neighboring points to fit a quadratic parabolic surface $Z\left(X,Y\right)$, and then determine the curvature value of the selected point $A_i$ by solving the principal curvature and principal direction of the parabolic surface

$$Z\left(X,Y\right)=a{X}^2+bXY+c{Y}^2$$

(8)

The topological k-neighborhood algorithm is designed to identify the local neighborhood of each data point, providing more detailed and accurate local spatial relationship information. By calculating the k-nearest neighborhoods of each point, the algorithm clarifies which points each point is adjacent to within a local range, thereby further enriching and improving the spatial topology of point cloud data. The local neighborhood determination diagram of data points in the topology k-neighborhood is shown in Figure 5.

In order to perform a topological k-neighborhood search, a linked list $List$ data structure needs to be constructed to assist the entire search process. The determination process is as follows:

(1)

Firstly, for each sampling point $A_i$, select the closest $k^{\prime }$ adjacent sampling points in geometric position, add them to the $N\left(A_i\right)$ set, and add them to the linked list $List$ in ascending order of their distance from the sampling point.

(2)

Then, search for the $k^{\prime }$ nearest adjacent sampling points to the element. If these $k^{\prime }$ adjacent sampling points have not been added to set $N\left(A_i\right)$, they will be inserted into the tail of the linked list in order of their distance from the sampling points.

(3)

Repeat step (2) until the distance between $\left|N\left(A_i\right)\right|=k$ or the latest sampling point added to $N\left(A_i\right)$ and $A_i$ exceeds the set threshold $\sigma$.

Through the above process, points distributed on different sampling surfaces can be accurately identified, and topological proximity structures between sampled data can be accurately constructed. After establishing the neighborhood set of point $A_i$, for any point $A_j\in N\left(A_i\right)$ within the set, the least squares principle needs to be used to minimize Equation (15), that is:

$$Q={{\displaystyle \sum _{j=1}^k‖a{X}_j^2+b{X}_j{Y}_j+c{Y}_j^2-Z_j‖}}^2=\min$$

(9)

By taking the derivatives of the coefficient $abc$ in Equation (16) and making it 0, we have:

$$\left\{\begin{array}{l}{\displaystyle \frac{\partial Q}{\partial a}}={\displaystyle \sum _{j=1}^{k}2X_j^2\left(a{X}_j^2+b{X}_j{Y}_j+c{Y}_j^2-Z_j\right)=0}\\ {\displaystyle \frac{\partial Q}{\partial b}}={\displaystyle \sum _{j=1}^{k}2X_j{Y}_j\left(a{X}_j^2+b{X}_j{Y}_j+c{Y}_j^2-Z_j\right)=0}\\ {\displaystyle \frac{\partial Q}{\partial c}}={\displaystyle \sum _{j=1}^{k}2Y_j^2\left(a{X}_j^2+b{X}_j{Y}_j+c{Y}_j^2-Z_j\right)=0}\end{array}\right.$$

(10)

The simultaneous Equation (17) can be used to determine the value of the coefficient $abc$ in the equation. Based on the above steps, the average curvature of spatial points can be calculated. Using the principles of differential geometry, the differential operator of the parabolic surface $Z\left(X,Y\right)$ is derived, and the first-order $Z_X,Z_Y$ and second-order $Z_{XX},Z_{YY},Z_{XY}$ partial derivatives of the surface are obtained. The specific expressions of the first and second basic forms of $Z\left(X,Y\right)$ are:

$$\begin{array}{l}\left\{E=Z_X\cdot Z_X=1,F=Z_X\cdot Z_Y=0,G=Z_Y\cdot Z_Y=1\right\}\\ \left\{L=Z_{XX}\cdot \tau =2a,M=Z_{XY}\cdot \tau =b,N=Z_{YY}\cdot \tau =2c\right\}\end{array}$$

(11)

In the equation, $\tau$ represents the unit normal vector of a point $A_i$. The average curvature of a point $A_i$ is:

$$\gamma ={\displaystyle \frac{EN-2FM+GL}{2\left(EG-F^2\right)}}$$

(12)

There are a total of $d$ points in the point cloud data, and the calculated average curvature values of each point are denoted as ${\gamma }_1,{\gamma }_2,\cdots {\gamma }_d$. Initialize the current maximum value ${\gamma }_{\max }$ to negative infinity, i.e., ${\gamma }_{\max }=-\infty$; Initialize the current minimum value ${\gamma }_{\min }$ to positive infinity, i.e., ${\gamma }_{\max }=+\infty$. Traverse comparison: Starting from the first point, traverse each point in the point cloud data sequentially. For the $i$-th point, its average curvature value is ${\gamma }_i$. Compare ${\gamma }_i$ with the current maximum value ${\gamma }_{\max }$ and current minimum value ${\gamma }_{\min }$: if ${\gamma }_i>{\gamma }_{\max }$, update the current maximum value, that is, let ${\gamma }_{\max }={\gamma }_i$; If ${\gamma }_i<{\gamma }_{\max }$, update the current minimum value, i.e., let ${\gamma }_{\min }={\gamma }_i$. After traversing all points, ${\gamma }_{\max }$ is the maximum value of the average curvature, and ${\gamma }_{\min }$ is the minimum value of the average curvature, which is the extremum of the average curvature obtained. The curvature extremum can highlight regions in the image with significant geometric changes, which often correspond to key features of debris flow landslides, such as the boundaries of landslide bodies, cracks, and abrupt changes in terrain. Using it as input for subsequent convolutional neural networks enables the network to focus more on learning important information related to gully type debris flow landslides, improving recognition accuracy and efficiency.

Valleys and debris flows exhibit significant differences in morphology, which can be captured and analyzed through local curvature extrema. Specifically:

(1)

Curvature Characteristics of Valleys:

Valleys generally have gentle slopes and continuous river channels, with relatively uniform curvature values overall. The edges and riverbed sections of valleys may exhibit higher curvature values, but the overall variation remains smooth. The average curvature of a valley can be obtained by calculating the local curvature of the point cloud data within the valley region and taking the mean value.

(2)

Curvature Characteristics of Debris Flows:

Debris flows usually have steep slopes and irregular flow paths, with curvature values showing significant variations along the flow paths. The edges and flow paths of debris flows may exhibit extremely high curvature values, and the overall variation is more intense. The average curvature of a debris flow can be obtained by calculating the local curvature of the point cloud data within the debris flow region and taking the mean value.

Through the above analysis, the morphological characteristics of valleys and debris flows can be clearly distinguished. Curvature extrema highlight regions with significant geometric changes in the image, which often correspond to key features of debris flow landslides, such as the boundaries of the landslide body, cracks, and abrupt changes in terrain. By using these as inputs for subsequent convolutional neural networks, the network can focus more on learning important information related to valley-type debris flow landslides, thereby improving the accuracy and efficiency of identification.

This study selected a debris-flow-prone watershed as the experimental area, where high-precision point cloud data were obtained through UAV oblique photogrammetry. A comparative analysis of curvature characteristics was conducted between typical valleys and debris flow deposits. The results demonstrate:

(1)

Valley areas: The U-shaped trough structure formed by long-term fluvial erosion exhibits homogeneous curvature distribution. Gaussian curvature values primarily concentrate within [−0.05, 0.05] m⁻² range (82% proportion), with a gentle mean curvature gradient (range <0.2 m⁻¹) and sparse curvature inflection points along edges (<5 points/10 m²).

(2)

Debris flow areas: The random accumulation of loose materials leads to significant curvature fluctuations. Gaussian curvature shows bimodal distribution (peaks at −0.12 m⁻² and 0.08 m⁻²), with mean curvature range reaching 1.5 m⁻¹. Along flow paths, 12 ± 3 inflection points per 10 m² were detected. The Mann–Whitney U test confirms statistically significant differences in curvature extremes (p = 2.3 × 10⁻⁵).

Based on these findings, the study incorporates dual-curvature features (Gaussian and mean curvature) as CNN input channels, leveraging their distinct distribution patterns between valleys and debris flows to enhance the network recognition of marginal debris fragments. Curvature extremes effectively highlight regions with significant geometric variations, which typically correspond to critical debris flow landslide features such as boundaries, fractures, and abrupt terrain changes. Serving as convolutional neural network inputs, these features enable the network to focus on learning essential information related to gully-type debris flow, thereby improving identification accuracy and efficiency.

4. Identification of Gully-Type Debris Flow Sliding Slope Based on a Convolutional Neural Network

The average curvature extremum features obtained above are used as input for a convolutional neural network. The network can identify gully-type debris flow sliding slopes. CNN has good processing ability for data with local correlation. The average curvature extremum has a certain local correlation in space, that is, the curvature extremum of adjacent points often reflects similar geometric features. By inputting the average curvature extremum into CNN, the network can fully leverage the advantages of convolution operations, effectively extracting local features of landslide bodies, and gradually integrate global features through pooling layers and other operations to achieve an accurate identification of landslide bodies.

The study employs dual-curvature features as network inputs, where both maximum and minimum curvature values are calculated for each point cloud data point to construct a dual-channel input matrix. This dual-curvature input approach provides a more comprehensive characterization of terrain surface geometry: maximum curvature primarily captures sharp features like ridges/valleys, while minimum curvature characterizes surface flatness characteristics. Experimental verification demonstrates that this dual-curvature combination significantly enhances model performance, achieving superior recognition results on the test set. The structure of the convolutional neural network is shown in Figure 6. The red box in Figure 6 represents the identified object.

(1)

The input layer receives dual-curvature feature information (maximum curvature and minimum curvature) and transmits it into the network for subsequent feature learning and processing. This dual-channel input design enables the simultaneous capture of different geometric characteristics of terrain surfaces.

(2)

The convolutional layer consists of learnable convolution kernels and activation functions. Its primary task is to extract dual-curvature features. This study employs three convolutional layers, utilizing 32, 64, and 128 filters respectively in each layer, with a 3 × 3 kernel size, stride of 1, and ReLU activation function. The operation of the convolutional layers is illustrated in Figure 7 below. The red and blue arrows represent two different channels, respectively.

A fusion method of geological radar detection data and point cloud data is introduced to obtain the thickness prediction value of debris flow slope $h_y$:

$$h_y=\alpha \cdot \left|\gamma \right|+\beta \cdot Z_{relief}+h_0$$

(13)

In the formula, $Z_{relief}$ is the relative elevation difference, $\alpha ,\beta$ is the calibration coefficient of drilling hole, and $h_0$ is the constant of foundation thickness.

Using 3D point cloud data, the boundary range of landslide or debris flow is determined by building a digital elevation model, and the volume of landslide and debris flow is calculated as follows:

$$V={\displaystyle \sum _{i=1}^n{S}_i}\cdot h_y\cdot Z_{relief}$$

(14)

In the formula, $S_i$ represents the area of the $i$ grid cell.

Taking the extreme value of average curvature and the volume of slope and debris flow as inputs, the convolutional layer is used as the output form:

$$A_j^{\left(l\right)}=f\left({\displaystyle \sum _{i\in R_j}{A}_i^{\left(l-1\right)}\ast K_{ij}^{\left(l\right)}+V{B}_j^{\left(l\right)}}\right)$$

(15)

In the formula, $\ast$ represents the convolution operation, $R_j$ represents a selection of input features, $A_i^{\left(l\right)}$ is the output value of the $i$-th feature in the $\left(l-1\right)$-th layer, $K_{ij}^{\left(l\right)}$ is the convolution kernel connecting the $j$-th feature in the $l$-th layer and the $i$-th feature in the $\left(l-1\right)$-th layer, and $B_j^{\left(l\right)}$ is the bias of the $j$-th feature in the $l$-th layer.

(3)

The sampling layer, also known as the feature mapping layer, is used to divide the input feature image into non-overlapping sub blocks according to certain rules and perform pooling operations on each sub-block. Through this approach, the dimensionality and scale of data can be reduced, and more representative and important features can be extracted. The operation diagram of the sampling layer is shown in Figure 8. The red and blue arrows represent two different channels, respectively.

This article adopts 2 × 2 max pooling with a stride of 2. The output form of the sampling layer is:

$$A_j^{\left(l\right)}=down\left(A_j^{\left(l-1\right)}\right)$$

(16)

In the equation, $down\left( \right)$ is the downsampling function.

(4)

The fully connected layer plays a role in identifying and classifying gully-type debris flow sliding slopes in CNN, located at the end of the convolutional neural network. Its function is to connect all features in the network and transmit the output values to the classifier. In the fully connected layer, each node is connected to all nodes in the previous layer, and then these features are classified and predicted by a classifier and output. This article designs a fully connected layer consisting of 128 neurons with an activation function of ReLU. The content is translated into English as follows, employing an end-to-end supervised learning approach. The training process utilizes the Adam optimizer (initial learning rate 0.001, decaying by 50% every 10 epochs), with a batch size set to 32. Data augmentation is performed through random rotation (±15°) and Gaussian noise injection (σ = 0.01) to enhance the model’s generalization capability. The loss function combines cross-entropy loss and L2 regularization (weight decay coefficient 0.0001). Training is conducted for 50 epochs with early stopping (termination triggered if the validation loss fails to decrease for 5 consecutive epochs). All experiments are carried out on an NVIDIA Tesla V100 GPU, implemented using the PyTorch2.4 framework, with a training duration of approximately 2 h. For the task of identifying gully-type debris flow sliding slopes, the output form is:

$$a_j^{\left(l\right)}=f\left({\displaystyle \sum _{i=1}^{S_{l-1}}{a}_j^{\left(l-1\right)}{W}_{ij}^{\left(l\right)}+b_j^{\left(l\right)}}\right)$$

(17)

In the formula, $a_i^{\left(l-1\right)}$ is the output value of the $i$-th neuron node in the $\left(l-1\right)$-th layer. Implement the identification of valley-type debris flow sliding slopes according to the above process.

5. Experimental Analysis

5.1. Study Area and Data Collection

This study selected a typical high-risk debris flow zone in a certain region as the experimental area (Figure 9). The area features complex terrain with elevations ranging from 800 to 1500 m and an average annual rainfall of 1200 mm. Historically, it has experienced multiple debris flow and landslide events. The study area covers 2.5 km² and includes three typical landforms: gully-type debris flows, slope-type landslides, and stable regions.

Implementation plan for drone aerial survey: M300RTK quadcopter drone is used for aerial survey as shown in Figure 9, equipped with a 35 mm fixed focus measurement lens, sensor size of 23.5 mm × 15.6 mm, effective pixels of 24.3 million, photo resolution of 5472 × 3678 mm, and support for multi system positioning (GPS/GLONASS/Beidou/Galileo). The aerial survey adopts an east–west parallel flight band design, with a total of 12 flight bands arranged at intervals of 90 m, covering the entire study area. Flying at an altitude of 150 m, with a heading overlap rate of 80% and a lateral overlap rate of 70%, a total of 1200 high-definition images were obtained.

Ground control point layout: 18 ground control points (GCPs) are randomly arranged in the study area according to the principle of layering:

• Gully type debris flow area: 8 GCPs, with a focus on key areas such as gully heads and the front edge of alluvial fans
• Slope type landslide area: 6 GCPs, mainly distributed at the rear edge and side boundary of the landslide
• Stable region: 4 GCPs; as a benchmark control, all GCPs were measured using Trimble R10 GNSS, with a planar accuracy of ±1 cm and an elevation accuracy of ±2 cm.

The data collection and processing process is as follows:

(1)

Drone Aerial Survey: an M300RTK quadcopter drone is used as shown in Figure 10, equipped with a 35 mm × 5 fixed focus measurement lens, sensor size of 23.5 mm × 15.6 mm, effective pixels of 24.3 million, photo resolution of 5472 × 3678 mm, and supports multi system positioning (GPS/GLONASS/Beidou/Galileo). Flying at an altitude of 150 m, with a heading overlap rate of 80% and a lateral overlap rate of 70%, a total of 1200 high-definition images were obtained.

(2)

Point cloud reconstruction: Generate point cloud data using the Agisoft Metashape 1.7.6 software, with a total of approximately 125 million points, an average density of 500 points per square meter, a plane accuracy of ±5 cm, and an elevation accuracy of ±8 cm.

(3)

Dataset partitioning:

• Training set: 800 subset samples of point clouds (each subset is a 64 × 64 × 64 point cube grid), of which 480 samples (60%) come from debris flow gully areas and 320 samples (40%) come from other terrain areas. Each sample is labeled with a binary label of “debris flow” or “non debris flow”.
• Validation set: 200 subsets of point clouds with the same specifications (100 positive samples from active debris flow areas and 100 negative samples from stable areas), used for hyperparameter tuning and model selection.
• Test set: 200 independently collected subset samples of point clouds (with no overlap in spatial distribution with the training set), of which 120 samples cover known debris flow valleys, and 80 samples are randomly selected from other terrain areas for the final evaluation of the model’s generalization ability.

5.2. Comparison Methods and Experimental Settings

Comparison method:

(1)

Reference [6] presents a landslide identification method based on an improved YOLO algorithm;

(2)

Reference [7] combines YOLOv7 with the attention mechanism recognition method;

(3)

Reference [8] is a recognition method based on SBAS InSAR technology.

Method of this article (CNN structure):

• Input layer: Local curvature extremum feature map (size 64 × 64 pixels);
• Convolutional layer: three layers (with 32/64/128 filters, 3 × 3 convolution kernels, ReLU activation);
• Pooling layer: two layers (2 × 2 maximum pooling);
• Fully connected layer: 128 neurons (ReLU activated);
• Output layer: Softmax classification (debris flow gully/non debris flow).

To ensure the fairness of the comparative experiments, this study uniformly processed all baseline methods (including an improved YOLO algorithm, YOLOv7 + attention mechanism, and SBAS InSAR technology) as follows. Convert the input data of the baseline method into the same 64 × 64 × 64 point cloud grid format as this method, and solve the compatibility problem of SBAS InSAR technology with discrete point clouds through interpolation processing. For the YOLO series methods, project point cloud data into a two-dimensional elevation grayscale map (resolution 5472 × 3678) to meet their image input requirements. All baseline models were retrained on the training set of this study (800 annotated samples).

5.3. Visualization Example of Results

Figure 11 shows the extreme curvature characteristics of point clouds in a typical debris flow valley (red high curvature area), indicating that this method can effectively capture the abrupt terrain at the edge of the valley.

5.4. Experimental Indicators

In the satisfaction assessment of environmental remediation, AUC (Area Under Curve) is one of the important indicators to measure the performance of the model, as it reflects the model’s ability to classify positive and negative samples at different thresholds. The specific calculation of AUC is based on the Receiver Operating Characteristic Curve (ROC), which is plotted with False Positive Rate (FPR) as the horizontal axis and True Positive Rate (TPR) as the vertical axis. The AUC value ranges from 0.5 to 1, and the closer the value is to 1, the better the classification performance of the model. The expression is as follows:

$$\left\{\begin{array}{l}FPR={\displaystyle \frac{FP}{FP+TN}}\\ TPR={\displaystyle \frac{TP}{TP+FN}}\\ AUC=\left(FP{R}_2-FP{R}_1\right)\times {\displaystyle \frac{\left(TP{R}_1+TP{R}_2\right)}{2}}\end{array}\right.$$

(18)

In the formula, $FP$ is a false positive; $TN$ is true negative; $TP$ is a true positive; $FN$ is a false negative.

In this experiment, the calculation of AUC, FPR, and TPR is based on a validation set with a sample size of 1000, including 500 positive and 500 negative samples. By verifying the calculation results of the validation set, we can more accurately evaluate the performance of the model in environmental remediation satisfaction assessment tasks. The experimental results show that the proposed method achieves an AUC of 0.92, significantly better than the comparative methods, verifying its effectiveness and superiority.

5.5. Experimental Results

The accuracy of extracting curvature extremum features is shown in

Table 1. Accuracy of curvature extremum feature extraction.

Iteration Times/Times	Landslide Recognition Based on Improved YOLO Algorithm/%	Landslide Identification Based on YOLOv7 and Attention Mechanism/%	Landslide Identification Based on SBAS InSAR Technology/%	Proposed Method/%
20	85	90	86	95
40	86	89	84	96
60	84	91	85	95
80	85	86	84	98
100	82	89	86	96

.

The curvature extremum feature extraction accuracy data in Table 1 shows that with the change in iteration times, the recognition accuracy of different methods shows different trends, and the proposed method exhibits high accuracy at all iteration times. The accuracy of landslide recognition based on the improved YOLO algorithm is 85% after 20 iterations, and the accuracy of landslide recognition based on YOLOv7 and the attention mechanism is 90% after 20 iterations. The accuracy of landslide recognition based on SBAS InSAR technology is 86% after 20 iterations. The proposed method achieves an accuracy of 95% after 20 iterations. This indicates that the method has high accuracy and stability in extracting curvature extremum features and can more effectively extract key features reflecting the geometric changes of landslide surfaces, thereby improving the recognition accuracy of gully-type debris flow sliding slopes.

The training results of the convolutional neural network are shown in Figure 12.

Figure 12 shows that as the number of iterations increases, the loss value of the convolutional neural network gradually decreases, and the model fitting effect improves until the loss value approaches 0.1. The lowest point of the set loss value in traditional models is 0.8, and after reaching the lowest point, it starts to rise again with significant fluctuations, resulting in overfitting. This indicates that convolutional neural networks can effectively recognize gully-type debris flow sliding slopes.

The corresponding ROC curves for each method are shown below in Figure 13:

From the analysis of Figure 13, it can be seen that the proposed method for identifying gully-type debris flow is more inclined towards the upper left corner of the coordinate axis. The corresponding AUC value under the ROC curve is 0.92, which is higher than that of the comparative method, confirming the proposed method’s superiority in identifying gully-type debris flow.

CNN trains and learns the morphological features of debris flows, gullies, and their parts in point cloud data and combines curvature analysis to detect their geometric changes. During the training process, an annotated dataset containing debris flows, gullies, and their partial forms was used to ensure the model could accurately distinguish different terrain features. The experimental results show that CNN can effectively identify the morphological characteristics of debris flows and gullies and distinguish some areas, thus verifying the effectiveness of the proposed method.

In summary, this section validates the proposed method’s superiority in identifying gully-type debris flow sliding slopes through detailed experimental results analysis and clarifies CNN’s training process and classification ability in point cloud data morphology feature classification.

6. Conclusions

This study utilized UAV oblique photogrammetry to acquire image data of debris flow landslide areas. It generated 3D point cloud data of landslide bodies through image matching and point cloud reconstruction techniques. By calculating the curvature of each point in the point cloud and extracting curvature extremum features, key characteristics of gully-type debris flow were successfully identified. Using average curvature extremum features as input to a convolutional neural network further improved the accuracy and efficiency of landslide identification. This research holds significant practical value for debris flow landslide detection. The main conclusions are as follows:

(1)

Identification accuracy: The proposed method achieved an average identification accuracy of 96.0%, representing a 7.2 percentage point improvement over the best comparative method (YOLOv7 with attention mechanism at 88.8%). The AUC value reached 0.92, significantly outperforming the comparative methods’ range of 0.78–0.85.

(2)

Model convergence performance: The CNN model demonstrated rapid convergence during training, with the loss value quickly decreasing to 0.0032 (cross-entropy loss). The implementation of early stopping and learning rate decay strategies effectively prevented overfitting.

Experimental results indicated that this method achieved 95% identification accuracy within just 20 iterations, demonstrating excellent convergence characteristics. These findings provide reliable technical support for debris flow disaster monitoring and early warning systems.