[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Next Article in Journal
Reconstructing Long-Term, High-Resolution Groundwater Storage Changes in the Songhua River Basin Using Supplemented GRACE and GRACE-FO Data
Previous Article in Journal
Estimation of Arctic Sea Ice Thickness Using HY-2B Altimeter Data
You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Remote Sensing
Volume 16
Issue 23
10.3390/rs16234563
remotesensing-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Calculating the Optimal Point Cloud Density for Airborne LiDAR Landslide Investigation: An Adaptive Approach

by
Zeyuan Liao
,
Xiujun Dong
* and
Qiulin He
State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, China
*
Author to whom correspondence should be addressed.
Remote Sens. 2024, 16(23), 4563; https://doi.org/10.3390/rs16234563
Submission received: 6 November 2024 / Revised: 30 November 2024 / Accepted: 4 December 2024 / Published: 5 December 2024
Browse Figures
Figure 1
<p>Overview of the study area. (<b>a</b>) The province and its boundaries where the survey area is located; (<b>b</b>) 3D terrain model of the survey area; (<b>c</b>) optical image of the Limushan landslide; (<b>d</b>) characteristic vegetation of the region (trees); (<b>e</b>) shrubs; (<b>f</b>) grassland.</p> "> Figure 2
<p>Work flow chart.</p> "> Figure 3
<p>Data acquisition and processing process (The numbers in the figure indicate the order of the processing steps).</p> "> Figure 4
<p>ICP-NN algorithm framework.</p> "> Figure 5
<p>Location map of micro-topographic features (Region a in the yellow box shows the crack at the back edge of the landslide; region b in the red box shows the right boundary of the landslide; and region c in the blue box shows the gully at the front edge of the landslide).</p> "> Figure 6
<p>Visually interpreted results–DEM comparison chart.</p> "> Figure 7
<p>Quantitative analysis of elevation RMSE.</p> "> Figure 8
<p>Quantitative analysis of elevation RMSE. ** indicates significant differences at <span class="html-italic">p</span> &lt; 0.01.</p> "> Figure 9
<p>Results of terrain complexity calculation. (<b>a</b>) Relatively flat area; (<b>b</b>) area of high terrain complexity.</p> "> Figure 10
<p>Complexity error fitting curve.</p> "> Figure 11
<p>The elevation RMSE curve discrete difference peak-seeking plot (a–d is an enlarged detail view of the last peak on the error curve).</p> "> Figure 12
<p>The TCI error curve discrete difference peak-seeking plot (a–d is an enlarged detail view of the last peak on the error curve).</p> "> Figure 13
<p>Overview of canopy density by 2D canopy height model. (<b>a</b>) Overall vegetation cover in the DOM; (<b>b</b>) canopy density inversion result.</p> "> Figure 14
<p>The loss curve of the trained model.</p> "> Figure 15
<p>Distribution of MPIW under different CLs.</p> ">
Versions Notes

Abstract

:
Ensuring that ground point density after raw point cloud processing meets the accuracy requirements for subsequent DEM construction represents a challenge for field operators during airborne LiDAR data acquisition. In this study, we propose a method to quantify DEM quality by combining the RMSE of elevation and terrain complexity, analyzing the DEM quality error curves constructed with different point cloud densities by a discrete difference peak-seeking method, to determine the optimal ground point density, and then constructing an ICP-NN algorithm for predicting the collected point cloud density. After analysis of DEM quality at eight point cloud dilution levels, the optimal ground point cloud densities were determined to be 2.43 pts/m2 (0.2 m resolution), 2.08 pts/m2 (1 m and 0.5 m resolution), and 1.84 pts/m2 (2 m resolution). Using the obtained optimal ground point densities, survey area slopes, canopy density, and elevation differences as eigenvalues, the ICP-NN model can be used to directly predict the collected point cloud density intervals in other regions, and the model has interval lengths ranging from 36 to 70.33 pts/m2 at 5 CLs. This method solves the problem of determining point cloud density in landslide surveys using airborne LiDAR and provides direct guidance for practical applications.

1. Introduction

Airborne LiDAR (Light Detection and Ranging) technology enables the rapid and precise acquisition of extensive ground surface data [1]. By utilizing multiple-echo data collection techniques, airborne LiDAR can “penetrate” vegetative cover to produce high-resolution, three-dimensional models of the ground surface [2]. Consequently, it has been widely employed in landslide investigation [3]. The digital elevation models (DEMs) constructed from LiDAR-acquired point clouds are crucial for the manual annotation of landslides, the automatic identification of cracks or disaster extents using machine learning, and the extraction of geological information for risk assessment [4]. Therefore, the accuracy and visualization quality of these DEMs directly affect the precision of identification and analysis. The density of point clouds is a critical determinant of DEM quality [5]. At the time of data acquisition, relying solely on the experience of the operator is insufficient for assessing whether the ground point cloud density, after processing the raw point cloud, meets the precision requirements for DEM construction [6]. Excessively high point cloud density necessitates higher laser point frequencies, increased flight path overlap, or reduced flight speed, all of which contribute to elevated costs for flight operations, data storage, and processing [7]. Conversely, too low a point cloud density results in striping artifacts and the omission of micro-topographic features (such as cracks, gullies, and landslide boundaries) during the triangulated irregular network (TIN) interpolation of DEMs [8].
In order to ascertain the appropriate ground point cloud density for constructing a DEM, it is necessary to conduct a comparative point cloud density test. Prior to this, a scientific method must be employed to evaluate the quality of the DEM. Some researchers utilize statistical measures, such as Mean Squared Error (MSE) or Root Mean Square Error (RMSE), to assess DEM accuracy [9], but it does not account for the preservation of micro-topographic features. Razak [10] proposed incorporating expert qualitative scoring of micro-topographic features into DEM accuracy assessment, but the method is highly subjective and depends heavily on the expertise and experience of the evaluators. Subsequent researchers have attempted to use factors such as slope, fractal dimension index, and terrain location index to quantitatively reflect terrain complexity [11], yet few studies have applied terrain complexity in DEM micro-topography evaluation. A synthesis of the aforementioned evaluation methods reveals a lack of a DEM quality evaluation system for use in geohazard identification.
In addition, the ‘appropriate point cloud density’ should be the point at which the data quality can no longer be significantly improved by increasing the point cloud density, all other conditions being held constant [12], which achieves a balance between the data quality and the costs associated with data processing and storage. It is similar to the marginal effect in economics [13], which is also referred to as the ‘appropriate point cloud density’ in this paper. Ordinary curve search optimization methods, such as Bayesian criterion [14], cross-validation [15], and L-curve methods [16], involve human subjective intervention, and it is also a challenge to objectively determine the ‘optimal’ point on the experimental error curve of a point cloud [17].
In practice, to obtain the optimal ground point cloud density, it is necessary to control the acquisition point cloud density to have a sufficient number of laser points reaching the ground [18,19,20]. Several countries have established specifications [21,22,23] for airborne LiDAR data collection to determine suitable point cloud densities for acquisition (Table 1). However, US guidelines do not specify how to determine the quality level (QL) of the DEM, and Japanese standards are too broad to offer precise guidance for field personnel based on specific project requirements. Furthermore, none of these specifications consider the need to identify micro-topographic features beneath vegetation cover. As a result, there is still a lack of guideline values for collected point cloud densities that take into account differences in topography and geomorphology in remote sensing surveys of geological hazards.
To address the aforementioned challenges, we developed a highly automated method for calculating the optimal acquisition point cloud density using the Limushan landslide in Guilin, China, as the study area. The optimal ground point cloud density was determined through a DEM quality evaluation framework that integrates both quantitative and qualitative approaches. A machine learning method [24] was then employed to predict the required acquisition point cloud density for the LiDAR data acquisition phase, using factors such as canopy density, slope, elevation variation within the survey area, and the desired ground point density as input variables. This methodology provides direct support for data collectors, allowing them to avoid the problem of finding ground point densities that do not meet the accuracy requirements for constructing DEMs after data processing.

2. Materials and Methods

2.1. Study Area

The study area is located in Limushan Village, Guilin, in northeastern Guangxi, China (Figure 1), with geographical coordinates of 110°23′59″E, 24°40′56″N. It is situated in a typical tectonic erosional low-mountain landscape characteristic of Guangxi. The region features diverse vegetation, including shrubs, trees, and grasslands. Continuous rainfall has led to partial sliding in the central part of the area, resulting in a well-defined landslide with clear boundaries. The site exhibits multiple cracks along the rear edge, gullies along the front edge, and scarps and secondary sliding within the central zone. This makes the study area ideal for conducting experiments on optimal point cloud density, as it encompasses a variety of micro-topographic features.

2.2. Methods

The overall methodology of this research is illustrated in Figure 2. Digital orthophoto model (DOM) and point cloud data were first acquired [25], and then this study mainly focused on determining the optimal ground point cloud density and predicting the expected acquisition density.

2.2.1. Data Acquisition and Pre-Processing

Data acquisition was performed using Feima D20 hexacopter UAV (Shenzhen Feima Robotics Co., Ltd., Shenzhen, China) with a DV-LiDAR10 module (equipped with a 42-megapixel full-frame high-definition camera), and the ground base station was a Feima RTK100 GNSS reference station, with 7 Ground Control Points (GCPs) collected according to the size of the study area. During the acquisition, the LiDAR point frequency was set to 200 Hz, with a side overlap of 35%. The flight altitude and speed were maintained at 250 m and 10 m/s, respectively. This configuration resulted in an average point cloud density of 144.84 pts/m2, significantly exceeding the density typically used in conventional remote sensing surveys of landslides. This ensures that high-density point cloud experiments are performed. The data acquisition and pre-processing workflow is illustrated in Figure 3.
The point cloud data are acquired by LiDAR, and the point cloud data that can be used in this study are obtained through data calculating, point cloud denoising, strip adjustment, etc. The synchronously acquired optical image is processed by feature point matching, ortho-correction, and other processes to obtain the DOM. Firstly, the point cloud was diluted to 80%, 60%, 40%, 20%, 10%, 5%, and 1% by an equal interval random thinning method [26]. Subsequently, the point cloud was classified, and the ground points were used to construct a TIN to generate DEMs at 0.2 m, 0.5 m, 1 m, and 2 m resolutions. The optimal point cloud density test was based on these models.

2.2.2. Elevation Quality Evaluation

To quantitatively evaluate the DEM constructed at each point cloud density, the commonly used RMSE was first selected as the evaluation index [27]. The smaller the value, the closer the DEM is to the real terrain. The calculation formula is as follows:
R M S E = ∑ i = 1 n Z i − Z i ^ 2 n
where Z i —elevation value of sampling point in the DEM; Z i ^ —elevation of the actual sampling point; and n —number of sampling points.

2.2.3. Terrain Complexity Evaluation Metrics

The second step of the quantitative analysis involves calculating the terrain complexity index by extracting relevant terrain factors. Since a single terrain factor cannot adequately capture the characteristic variations in different landforms, Lu [28] proposed a multi-factor combination approach to quantify terrain complexity. In this study, four commonly used terrain factors were selected based on ease of quantification and relative independence: Slope of Slope (SOS), Terrain Ruggedness (TR), Relief Degree of Land Surface (RDLS), and Terrain Position Index (TPI). The corresponding raster calculation tool in ArcGIS was employed to extract these terrain factors from the DEM at varying resolutions and point cloud retention rates [29]. Pearson product–moment correlation coefficients were analyzed using SPSS 27.0 statistical software, where correlations were considered very low if |r| < 0.3 [30]. Based on this analysis, two topographic factors were ultimately selected for this study: SOS and TPI.
This study employs the CRITIC method to calculate the coefficient weights for terrain complexity metrics [31]. This method assigns weight coefficients based on the contrast intensity and conflict among the factors. Contrast intensity is calculated to determine the degree of variation in the non-dimensionalized samples of each factor (Equation (2)). The greater the variation, the more surface information the factor contains [32]. Here, m is the number of factors, n is the number of samples, Z ¯ i is the mean value of the samples for the i th factor, and Z i j is the j -th sample value of the i -th factor.
S i ˙ = ∑ j = 1 n Z i j − Z ¯ i 2 n − 1 i = 1,2 , … , m
Next, conflict calculation is performed to quantify the combined effect of the relationship strengths among all factors (Equation (3)). Here, m is the number of factors, and r i k is the correlation coefficient between the i -th and k -th factors. The greater the correlation between factors, the lower the conflict.
δ i = ∑ k = 1 m 1 − r i k i = ( 1,2 , … , m )
The product of the contrast intensity and conflict results yields the comprehensive weight coefficient c i for each factor. To objectively represent the weight proportion of each factor, the computed comprehensive weight coefficients are normalized.
ω i ′ = c i ∑ i = 1 3 S i ⋅ δ i
In these equations, c i is the comprehensive weight coefficient for the i-th terrain factor, S i is the contrast intensity, and δ i is the conflict. Afterward, the inverse non-dimensionalization operation is performed to obtain the final true coefficients ω i .
ω i = ω i ′ x i ¯ i = ( 1 ,   2 ,   3 )
Among them, ω i is the normalized weight coefficient for the i-th terrain factor, and x i ¯ is the sample mean of the i -th terrain factor.
The final formula for calculating the local terrain complexity index in the experimental area, constructed using SOS and TPI, is shown in Equation (6).
T c l = ω S O S ⋅ S O S + ω T P I ⋅ T P I
The SOS and TPI values of DEMs at different diluting rates and resolutions are substituted into the above formula, and the calculated arithmetic mean values are expressed using a fitted curve, preparing for the subsequent determination of the optimal ground point cloud density.

2.2.4. Discrete-Difference Peak-Seeking Method

The discrete difference peak-seeking method involves taking each ( x i ,   y i ) point and moving forward and backward on the x axis by b steps with a unit step size of a . Within a total step size of l , search for the corresponding x i − a ,    y x i − a , x i − 2 a ,    y x i − 2 a … x i − a b ,    y x i − a b and x i + a ,    y x i + a , x i + 2 a ,    y x i + 2 a … x i + a b ,    y x i + a b values. The variance s i − l 2 of the i -th point on the curve, moving forward by l steps, is calculated as shown in Equation (8). The difference in variance between the front and back halves of the interval is used to obtain D i , which is then plotted as a discrete difference curve using x i ,   D i . The first peak that appears on this curve is considered the optimal ground point cloud density.
l = a · b
s i − l 2 = 1 b ∑ n = 1 b y x i − n a − y i − l ¯ 2
D i = s i + l 2 − s i − l 2
where a is the unit length of each calculation step; b is the total number of calculation steps; s i − l 2 is the variance within the forward step size l of the i -th point on the curve; y i − l ¯ is the average value of the points within the forward step size l of the i -th point on the curve; and D i is the discrete variance difference at the i -th point on the curve.
In the experiment, to ensure there are enough points on the curve for forward and backward difference calculations, we first applied denser resampling to the elevation RMSE and terrain complexity error curve under different point cloud densities. Then, the discrete difference peak-seeking method was used to find the optimal ground point cloud density.

2.2.5. Prediction of Collected Point Cloud Density Using Machine Learning Algorithms

To achieve optimal ground point density, it is necessary to adjust the collection density. Given the complexity of the survey area during data acquisition, the relationship between ground point density and collection density is nonlinear, and varies with changes in terrain and vegetation within the survey area. Previous work has shown that the ground point density obtained during point cloud collection is influenced by multiple factors: the penetration capability of the laser largely depends on the performance of the LiDAR sensor itself [33]; the vegetation cover, which significantly affects the amount of emitted point cloud that reaches the ground [34]; terrain undulations, which affect the distance between the ground and the sensor; the fact that when the sensor is closer to the ground, more laser points are received per unit area [35]; slope variations within the survey, which area also influence the area receiving the laser; and the fact that steeper slopes result in fewer laser points being received on those surfaces [36].
Therefore, we propose using a neural network to estimate the collection density, with canopy density, elevation difference, slope, and expected ground point density as the input features to calculate the mapping between ground point density and collection density in different geographic environments. This method involves training a neural network using a database containing terrain data, actual ground point density, and corresponding collection density for prediction. In practice, users need to first estimate the geographic environment data (i.e., canopy density, elevation difference, slope) and the optimal ground point density recommended in this paper. Then, by inputting these data into the trained neural network, the collection density required to achieve the desired ground point density can be obtained.
1.
Preparation of the Dataset for Training the Neural Network
The dataset used for training the model in this study was derived from previously collected data from Limushan landslide. Each data point in the database represents the geographic features and the number of point clouds within a 1 × 1 m2 statistical unit. The number of collected point clouds and ground point clouds within the unit area were extracted using the Point Cloud Density Calculator toolbox in FME 2021.0 software. Vegetation cover was expressed as canopy density, with a two-dimensional canopy height model used to estimate canopy density [37], and the vegetation height threshold was set to 2 m based on the actual growth of plants in the surveyed area. Canopy density was classified as low (0–0.2), medium (0.2–0.69), and high (0.7–1) [38]. Additionally, slope and elevation were extracted using ArcGIS, with the elevation difference calculated by subtracting the minimum elevation from the maximum, representing terrain undulation within the survey area.
2.
Considering Uncertainty in Neural Networks
Neural networks are considered powerful function approximators, and their strong nonlinear fitting capabilities have led to significant performance across various application domains [39], making them popular machine learning algorithms. This success is often measured by the overall accuracy of point predictions, such as MSE in regression problems. However, in the context of this study, relying solely on the collection density suggested by a neural network may not be reliable. Neural networks have limited interpretability [40], and when faced with data samples outside the distribution of the training set, they can produce predictions that deviate significantly from true values [41,42]. Blindly trusting such predictions could result in incorrect UAV data collection, leading to economic losses and reduced data quality.
To mitigate this issue, uncertainty quantification using prediction intervals (PIs) can be highly effective. In various real-world applications, such as autonomous driving [43], financial systems [44], and medical diagnosis, PIs have been employed to account for the uncertainty of individual predictions. PIs offer lower and upper bounds for predicted values, along with the probability that the true value falls within the interval. This probability is typically pre-set by the user and is referred to as the confidence level (CL). For example, a CL of 0.8 indicates that 80% of the generated intervals are expected to capture the true value. Two metrics are used to measure the quality of PIs: Mean Prediction Interval Width (MPIW) and Prediction Interval Coverage Probability (PICP).
Given a dataset with n instances, where the i -th input feature and target are represented as x i and y i , respectively, for i ∈ { 1 , … , n } . Prediction intervals (PIs) can be expressed using the upper and lower bounds y l i ^ and y u i ^ . The Prediction Interval Coverage Probability (PICP) and the Mean Prediction Interval Width (MPIW) can be expressed by the following formulas:
P I C P = 1 n ∑ i = 1 n k i
where k i = 0 if y l i ^ ≤ y i ≤ y u i ^ ; otherwise, k i = 1
M P I W = 1 n ∑ i = 1 n ( y l i ^ − y u i ^ )
High-quality PIs should meet the following two criteria: the resulting PICP should be as close as possible to the user-defined confidence level; the MPIW should be as small as possible.
3.
Constructing Prediction Intervals Using ICP-NN
In this study, we propose using the Inductive Conformal Predictor (ICP) framework to assist neural networks in generating high-quality PIs. Using ICP, one first needs to train a standard machine learning regression model to predict the label values, followed by training another machine learning model of the same structure and type to predict the error of the first model. We used neural networks as the base model, and ICP acts as a wrapper built on top of the neural network. ICP has many advantages; firstly, it theoretically guarantees that the PICP of the generated PIs meets the user-defined confidence level [45]. Secondly, compared to the bootstrap ensemble method, which typically requires training more than 50 models, ICP has very mild requirements regarding data distribution and only requires training two models, providing higher computational efficiency.
The data requirements and computational process for the ICP algorithm are as follows: Let Z 1 ,   Z 2 … Z n represent a set of independent and identically distributed data points, where each data point Z i consists of an input variable x i and a target label y i . For 1 ≤ k ≤ l ≤ n , use the data points from 1 to k as the training set, from ( k + 1 ) to 1 as the calibration set, and from ( l + 1) to n as the test set. The Nonconformity Measure (NCM) for a data point x , y depends on the value itself and the data in the training set, represented by the function A x , y .
A x , y = A ( Z 1 , Z 2 … … , Z k , x , y )
The order of the calibration data does not affect the function value. Let the NCM for data point i be α i = A ( x i ,   y i ). Typically, we assume that the NCM is generated based on a machine learning algorithm using the underlying training set.
At a confidence level of ε , the ICP prediction set for new, unlabelled data x is:
Γ ε x = y ϵ R , ∑ j = k + 1 l H A x , y − A x i , y i + 1 ≤ ε ( l − k + 1 )
where H is the Heaviside step function. Assuming that all data points from Z k + 1 to Z n are exchangeable, it can be proven that the generated dataset satisfies:
Pr ⁡ y i ϵ Γ ε x i ≥ 1 − ε
for all i ϵ l + 1 , … , n [46]. This result guarantees the validity of ICP because it shows that the probability of the true value being within the prediction set is greater than or equal to the CL.
In this paper, the NCM used is a normalized NCM [47],
A ( Z 1 , … … , Z k , ( x , y ) ) = | y − m η ; X | ⁄ σ ( θ ; X )
where m and σ are typically two models with parameter vectors η and θ , respectively. m usually corresponds to the point estimation model of the target label, and σ corresponds to the uncertainty model in that point estimation, which is generally positive. σ can be regarded as the model of the absolute value of the residual of m, and it is necessary to estimate the parameter vectors η and θ . η and θ . are the sets of weights used in the neural networks in this paper.
Combining the above equation, the prediction set becomes a PI with upper and lower bounds,
Γ ε x = [ y l i , ^ y u i ^ ]
where y l i ^ = m η ; X i − q σ ( θ ; X i ) ; and y u i ^ = m η ; X i + q σ ( θ ; X i ) , with q being the ε quantile of all the NCM values in the calibration set (i.e., α k + 1 , … … , α l ) .
The detailed process of the ICP adopted in this paper, normalized NCM, has been proven effective in various models, including neural networks. The overall ICP-NN algorithm framework is shown in Figure 4.

3. Results

3.1. Qualitative Evaluation Results

The visual interpretation results of DEMs with different point cloud densities at a 0.2 m resolution for various micro-topographic features are compared in Figure 5 and Figure 6. By comparing the representation of features such as rear edge displacement, cracks, and gullies in DEM generated with different point cloud densities, it is observed that the ability of the DEM to express details gradually decreases with diluting, eventually resulting in irregular triangular meshes. Micro-topographic features related to the landslide begin to be lost when the point cloud density is reduced to 4.07 pts/m2. When the point cloud density drops below 1.77 pts/m2, the DEM can no longer be visually interpreted. Similarly, the optimal ground point densities of 1.77 pts/m2~4.07 pts/m2 at 1:500 and 1:1000 scale, and 1.15 pts/m2~2.54 pts/m2 at 1:2000 scale can be obtained comparatively. In order to further narrow down the optimal point density intervals, a quantitative evaluation is subsequently conducted.

3.2. Quantitative Evaluation Results

Using the DEM elevation constructed from the highest density ground point cloud as a baseline, the elevation errors were calculated for different levels of point cloud dilution in the study area. The RMSE of the elevation ranges from 0.0278 m to 0.3068 m, and as the resolution changes from 2 m to 0.2 m, the errors gradually reduced. Additionally, as the point cloud density decreased for each resolution, the elevation errors exhibited a trend of gradual increase (Figure 7).
A correlation analysis is conducted on all extracted terrain factors (Figure 8). The lower left part shows the calculation results and distribution of the topographic factors for all sample units, and the upper right part shows the results of the Pearson correlation analysis. Very low correlation topographic factors with p-values that should be less than 0.05 and |r| less than 0.3 should be used, so TPI and SOS were chosen for this study.
The weight coefficient results are shown in Table 2.
The normalized weight coefficients are then subjected to dimensionalization (with TPI taking the mean of absolute values), yielding the true weight coefficients for the SOS and TPI terrain factors as follows:
ω S O S = ω S O S ′ x s o s ¯ = 0.5816 79.5182 = 0.0073
ω T P I = ω T P I ′ x T P I ¯ = 0.4184 77.8204 = 0.0054
The resulting calculation formula for the final terrain complexity index is as follows:
T C I = 0.0073 · S O S + 0.0054 · T P I
The rendered details of the local terrain complexity are shown in Figure 9, where the boundaries of terraces, roads, slopes, and depressions are highlighted in red, indicating that the terrain complexity in these areas is higher. In contrast, the central positions of the roads, which have smoother terrain, are shown with lower complexity.
The TCI for all sample units in the Yangshuo study area is averaged to obtain the mean local terrain complexity for different resolutions. Then, the highest point cloud density (16.08 pts/m2) was used as the basis for error calculation, and the complexity error fitting curve (Figure 10) was calculated to obtain error values ranging from 0.018 to 0.282. As both resolution and point cloud density increased, the DEM’s ability to preserve micro-topographic features improved, leading to a gradual decrease in the complexity error curve.

3.3. Error Curve Analysis

The discrete difference peak finding method requires that the original data points be resampled, and after resampling in steps of 20, a total of 1494 sample values are obtained. A detailed discussion of the parameter settings is provided in Section 4.2. The discrete difference values for all samples are shown in Figure 11 and Figure 12. The y-axis represents the magnitude of the error over the range of steps around each point, rather than the rate of change, focusing on the x-axis value where the largest error occurs. Observing the overall trend of the discrete difference curves, the maximum values consistently appear between 1.5 and 2.5 pts/m2. Figure 11 and Figure 12 show the points of maximum dispersion for both the elevation rms error curves and the TCI error curves, with both the 0.2 m and 2.0 m resolutions taken as the greater of the peak of the elevation rms error curves and the peak of the TCI error curves, so that 2.43 pts/m2 is taken for the 0.2 m resolution and 1.84 pts/m2 for the 2 m resolution. However, the values of both error curves were almost the same for both 0.5 m and 1 m resolutions, so the optimum ground point density was considered to be 2.08 pts/m2 for both resolutions. These optimal values are also consistent with those determined through visual inspection. The peak of the elevation RMSE curve is consistently higher than that of the TCI error curve, likely because elevation accuracy continues to improve over a wider range, whereas the retention of micro-topographic features declines rapidly beyond a certain point as point cloud density increases.

3.4. Prediction of Acquisition Point Cloud Density

Figure 13b shows the inversion to obtain canopy density. Compared to the actual vegetation cover in the DOM (Figure 13a), evergreen broad-leaved forests were classified as high canopy density, coniferous forests as medium canopy density, and sparse shrubs, fruit trees, and roads as low canopy density. This comparison indicates accurate inversion results overall.
After removing NoData, negative values, and outliers, 94,970 datasets remained for analysis. Of these, 40% were used for the training set, 20% for the validation set, and 20% for the test set; the remaining 20% of the data were used to adjust the hyperparameters. A neural network (NN) with 30 hidden neurons, a learning rate of 10−4, and 1000 epochs was employed as the regression prediction model, and the loss curve of the trained model is presented in Figure 14. The prediction interval width, calculated by the ICP-NN algorithm on the test set, is illustrated in Figure 15, where the x-axis represents the actual acquisition point cloud density, and the y-axis represents the predicted value. When the predicted value aligns with the true value, the red prediction curve coincides with the 45° line. Prediction error is minimal for acquisition point cloud densities between 100 and 175 pts/m2 but increases significantly when densities exceed 250 pts/m2. Furthermore, as the CL increases, the interval width expands. The MPIW and PICP values for different CLs are detailed in Table 3.

4. Discussion

4.1. Terrain Complexity

In this study, terrain complexity was used as an indicator to evaluate the DEM micro-topographic expression ability when determining the point cloud density required for DEM interpolation in landslide surveys. The Pearson correlation analysis was used to select terrain factors, ensuring both the comprehensiveness and independence of micro-topographic characterization. The two factors selected for the study area are SOS and TPI. SOS represents the rate of change in terrain slope, reflecting the variation in surface elevation and highlighting sudden undulations on an otherwise smooth surface, such as landslide boundaries, cracks, and depressions. TPI characterizes the difference between the elevation of a point and the average elevation of its surrounding points, indicating the intensity of topographic variation within a localized area. Two factors describe the geomorphic changes from integral and local perspectives, and both possess the property of being easy to extract, which is in line with the principle of terrain factor screening [48].
When applying this method to determine optimal point cloud density in other regions, the topographic factors can be re-selected according to the specific conditions of the survey area, such as terrain cutting depth, terrain roughness, contour density, and runoff length [49].

4.2. Discrete-Difference Peak-Seeking

In this study, a new discrete difference peak-seeking method is proposed to solve the problem of optimal ground point cloud density calculation, which originates from the marginal theory in economics, and scholars in many fields have solved the problem of searching for the optimum based on it. Li et al. explored the relationship between marginal land use and economic growth in China, and calculated that the optimal use of construction land will be reached in 2047 [50,51]. Wang et al. investigated the ‘inflection point’ of the aging population that leads to the change in social life pattern in a low-carbon direction [52]. These studies demonstrate the feasibility of identifying inflection points based on marginal effects; instead of relying on second-order derivatives, the ‘optimal point’ is identified by finding the peak of the discrete difference within a specified range of calculation steps.
In the point cloud experiments, it was found that continuously increasing point cloud density does not lead to indefinite improvements in DEM accuracy, and the quality of the DEM fluctuates beyond a certain threshold. On the one hand, this is due to limitations of the LiDAR sensor, where higher emission frequencies may introduce more noise; on the other hand, it may be due to the limitation of the DEM grid size. The discrete difference peak-seeking is used to find the optimal value before which the DEM quality improves rapidly with increasing point cloud density, but beyond which the rate of improvement slow down significantly. In the peak-seeking process, step sizes (i.e., the length of the interval before and after each point) ranging from 10 to 50 were tested. When the step size is 10, the initial part of the curve will have abnormal fluctuations and multiple peaks, while the peak fluctuations will become less and less when step sizes range between 20 and 40. It can be seen that choosing a suitable calculation step will lead to a higher accuracy of results, and the step can be adjusted according to the preliminary results in the future use of this method.

4.3. Applicability of Interval Prediction Algorithm

Quantifying the uncertainty in point predictions can help decision-makers better manage risk, and the Conformal Prediction Algorithm, which has been extensively tested and proven to provide reliable uncertainty estimates, generates prediction intervals with a specified confidence level (with PICP being very close to the set CL when the sample size is sufficiently large). In this study, the interval prediction algorithm is enhanced and applied to the design of point cloud densities collected via airborne LiDAR. The improved model performs very well for acquisition densities from 100 to 175 pts/m2. However, prediction accuracy decreases significantly for densities below 50 pts/m2 or above 250 pts/m2. This discrepancy may be due to the limited number of samples within these density ranges, as they are infrequently used in practice. In the future, if the terrain of the survey area changes significantly or the lidar equipment changes, data under the new terrain and data collected by the new radar equipment can be added to enhance the dataset and improve the universality of the algorithm. Overall, the current ICP-NN algorithm demonstrates strong prediction performance within the commonly used range of acquisition point cloud densities.

4.4. Optimal Ground Point Cloud Density for Different Resolution DEMs

To determine the density of the collected point cloud, it is first necessary to select the appropriate DEM resolution. In this study, the optimal ground point cloud densities at four resolutions were calculated, and the optimal ground points obtained were between 1 and 3 pts/m2. Scholars conducted a study in the low mountainous terrain of Zhejiang province, and estimated that a ground point cloud density of only about 0.7 pts/m2 is needed for 2 m resolution [53], and we calculated a slightly higher recommended value of ground point density in the hilly area of Guangxi province, where the terrain is more complicated. There are also some scholars who studied the original appropriate point cloud thinning ratio; Liu found that the point cloud streamlined by 50% can still ensure a certain degree of data accuracy [54], but in this study, it is easy to see that the degree of point cloud thinning is obviously affected by the original point cloud density and the geomorphological categories, so it is difficult to make a generalization.

5. Conclusions

This study focuses on the application of airborne LiDAR technology in remote sensing surveys for landslides, specifically addressing the challenge of determining whether the acquired ground point cloud density meets the requirements for DEM interpretation during data collection. Comparative experiments using DEM generated with varying point cloud densities across different resolutions were conducted. A qualitative and quantitative DEM quality evaluation system was developed, and an algorithm for predicting the range of optimal acquisition point cloud densities was proposed. The main conclusions are as follows:
  • Optimal ground point cloud density: Comparative experiments of DEMs constructed with different point cloud densities across various resolutions identified a DEM grid density that satisfies landslide identification requirements while being cost-effective. The optimal ground point cloud densities were determined to be 2.43 pts/m2 (0.2 m resolution), 2.08 pts/m2 (1 m and 0.5 m resolution), and 1.84 pts/m2 (2 m resolution). These values provide useful references for constructing DEMs in Guangxi and regions with similar topography.
  • DEM Quality Evaluation Method: A comprehensive DEM quality evaluation method was developed for landslide remote sensing investigations. This method integrates visual interpretation, the RMSE of elevation, and terrain complexity metrics, with an emphasis on preserving micro-topographic features that are critical for accurate landslide interpretation.
  • Discrete Difference Peak-Seeking Method: A novel curve optimization technique was introduced, which identifies peaks in the elevation RMSE and terrain complexity error curves by analyzing differences in response values (y) at equal step lengths along the x-axis.
  • ICP-NN Algorithm for Point Cloud Density Prediction: Using the optimal ground point cloud densities obtained from this study, along with factors such as elevation difference, slope, and canopy density, the ICP-NN algorithm was employed to predict the required acquisition point cloud densities. The width of the prediction intervals ranged from approximately 36 pts/m2 to 70 pts/m2, depending on the chosen confidence level.

Author Contributions

Conceptualization, Z.L.; methodology, Z.L.; software, Z.L.; validation, X.D.; formal analysis, Q.H.; investigation, X.D.; resources, Q.H.; data curation, Q.H.; writing—original draft preparation, Z.L.; writing—review and editing, Q.H.; visualization, Z.L.; supervision, X.D.; project administration, X.D.; funding acquisition, X.D. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Key R&D Program Key Special Projects (No. 2022YFC3003200) and the National Natural Science Foundation of China (No. 42082306).

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Acknowledgments

The authors would like to sincerely thank Shichao Cao, Bo Deng, and Haoliang Li for their help in this study, and to Xiaoqiang Zhu and Wen Li for their help with proofreading the article.

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Yan, W.Y.; Shaker, A.; El-Ashmawy, N. Urban land cover classification using airborne LiDAR data: A review. Remote Sens. Environ. 2015, 158, 295–310. [Google Scholar] [CrossRef]
  2. Sun, T.; Xu, M.Y.; Dong, X.J.; Pan, X. Application of airborne LiDAR technology in geological hazard investigation in mountainous area with dense vegetation. Bull. Surv. Mapp. 2021, 0, 90–97. [Google Scholar] [CrossRef]
  3. Dong, X.J.; Deng, B.; Yuan, F.Y.; Fu, X.; Zhang, W.J.; Ju, Y.Z.; Ren, X.H. Application of Aerial Remote Sensing in Geological Hazards: Current Situation and Prospects. Geomat. Inf. Sci. Wuhan Univ. 2023, 48, 1897–1913. [Google Scholar] [CrossRef]
  4. Bonnell, R.; Mcgrath, D.; Tarricone, J.; Marshall, H.-P.; Bump, E.; Duncan, C.; Kampf, S.; Lou, Y.; Olsen-Mikitowicz, A.; Sears, M.; et al. Evaluating L-band InSAR Snow Water Equivalent Retrievals with Repeat Ground-Penetrating Radar and Terrestrial Lidar Surveys in Northern Colorado. Cryosphere 2024, 18, 3765–3785. [Google Scholar] [CrossRef]
  5. Guth, P.L.; Van Niekerk, A.; Grohmann, C.H.; Muller, J.P.; Hawker, L.; Florinsky, I.V.; Gesch, D.; Reuter, H.I.; Herrera-Cruz, V.; Riazanoff, S.; et al. Digital Elevation Models: Terminology and Definitions. Remote Sens. 2021, 13, 3581. [Google Scholar] [CrossRef]
  6. Phan, A.T.T.; Phan, Q.T.; Nguyen, A.K.V. Extracting Ground Points and Generating Digital Elevation Model (DEM) from Point Clouds. In ICSCEA 2021, Proceedings of the Second International Conference on Sustainable Civil Engineering and Architecture, Ho Chi Minh City, Vietnam, 30 October 2021; Lecture Notes in Civil Engineering; Springer: Berlin/Heidelberg, Germany, 2023; Volume 268, pp. 589–596. [Google Scholar] [CrossRef]
  7. Agüera-Vega, F.; Agüera-Puntas, M.; Martínez-Carricondo, P.; Mancini, F.; Carvajal, F. Effects of point cloud density, interpolation method and grid size on derived Digital Terrain Model accuracy at micro topography level. Int. J. Remote Sens. 2020, 41, 8281–8299. [Google Scholar] [CrossRef]
  8. Bula, J.; Derron, M.H.; Mariethoz, G. Dense point cloud acquisition with a low-cost Velodyne VLP-16. Geosci. Instrum. Methods Data Syst. 2020, 9, 385–396. [Google Scholar] [CrossRef]
  9. Wang, D.J.; Chen, B.; Sun, J.H. Study on the effects of point density on DEM accuracy of airborne LiDAR. Bull. Surv. Mapp. 2022, 140–114, 169. [Google Scholar] [CrossRef]
  10. Razak, K.A.; Straatsma, M.W.; van Westen, C.J.; Malet, J.P.; de Jong, S.M. Airborne laser scanning of forested landslides characterization: Terrain model quality and visualization. Geomorphology 2011, 126, 186–200. [Google Scholar] [CrossRef]
  11. Liu, C.; Sun, W.; Wu, H. Determination of complexity factor and its relationship with accuracy of representation for DEM terrain. Geo-Spat. Inf. Sci. 2010, 13, 249–256. [Google Scholar] [CrossRef]
  12. Zhang, D.; Li, J.C.; Wu, Z.H.; Liu, S.T.; Liu, Y. Using terrestrial LiDAR to accurately measure the microgeomorphologic geometry of active fault: A case study of fault scarp on the Maoyaba fault zone. J. Geomech. 2021, 27, 63–72. [Google Scholar] [CrossRef]
  13. Onukwugha, E.; Bergtold, J.; Jain, R. A Primer on Marginal Effects—Part I: Theory and Formulae. PharmacoEconomics 2015, 33, 25–30. [Google Scholar] [CrossRef] [PubMed]
  14. Fukahata, Y.; Nishitani, A.; Matsu’ura, M. Geodetic data inversion using ABIC to estimate slip history during one earthquake cycle with viscoelastic slip-response functions. Geophys. J. Int. 2004, 156, 140–153. [Google Scholar] [CrossRef]
  15. Xiong, W.; Yu, C.; Chen, W.; Nie, Y.S.; Tan, K. Coulomb Stress Influence of 2010 YuShu Earthquake on 2016 Zaduo Earthquake:Earthquake and Seismic Hazard Assessment on Surrounding Area. J. Geod. Geodyn. 2018, 38, 338–343. [Google Scholar] [CrossRef]
  16. Yang, Y.H.; Tsai, M.C.; Hu, J.C.; Aurelio, M.A.; Hashimoto, M.; Escudero, J.A.P.; Su, Z.; Chen, Q. Coseismic Slip Deficit of the 2017 Mw 6.5 Ormoc Earthquake That Occurred Along a Creeping Segment and Geothermal Field of the Philippine Fault. Geophys. Res. Lett. 2018, 45, 2659–2668. [Google Scholar] [CrossRef]
  17. Petras, V.; Petrasova, A.; McCarter, J.B.; Mitasova, H.; Meentemeyer, R.K. Point Density Variations in Airborne Lidar Point Clouds. Sensors 2023, 23, 1593. [Google Scholar] [CrossRef]
  18. Poux, F.; Neuville, R.; Van Wersch, L.; Nys, G.A.; Billen, R. 3D Point Clouds in Archaeology: Advances in Acquisition, Processing and Knowledge Integration Applied to Quasi-Planar Objects. Geosciences 2017, 7, 96. [Google Scholar] [CrossRef]
  19. Jakovljevic, G.; Govedarica, M.; Alvarez-Taboada, F.; Pajic, V. Accuracy assessment of deep learning based classification of LiDAR and UAV points clouds for DTM creation and flood risk mapping. Geosciences 2019, 9, 323. [Google Scholar] [CrossRef]
  20. Zhou, M.; Li, C.G.; Li, Z.; Yu, Z. Effect of UAV-LiDAR Point Density on Estimation Accuracy of Forest Inventory Attributes. For. Res. 2024, 37, 39–47. [Google Scholar] [CrossRef]
  21. National Administration of Surveying, Mapping and Geoinformation of China. Technical Specifications for Airborne LiDAR Data Acquisition (CHT 8024-2011); NASG: Beijing, China, 2011. [Google Scholar]
  22. Geospatial Information Authority of Japan. Public Survey Manual for UAVs (Draft); GSI: Tsukuba, Japan, 2016. [Google Scholar]
  23. United States Geological Survey. Lidar Base Specification; USGS: Reston, VA, USA, 2024. [Google Scholar]
  24. Krzywinski, M.; Altman, N. Points of significance: Power and sample size. Nat. Methods 2013, 10, 1139. [Google Scholar] [CrossRef]
  25. Lohani, B.; Ghosh, S. Airborne LiDAR Technology: A Review of Data Collection and Processing Systems. Proc. Natl. Acad. Sci. India Sect. A—Phys. Sci. 2017, 87, 567–579. [Google Scholar] [CrossRef]
  26. Bei, Y.X.; Chen, C.F.; Wang, X.; Sun, Y.N.; He, Q.X.; Li, K.Y. Effects of Airborne LiDAR Point Cloud Density and Interpolation Methods on the Accuracy of DEM and Surface Roughness. J. Geo-Inf. Sci. 2023, 25, 265–276. [Google Scholar] [CrossRef]
  27. Balsa-Barreiro, J.; Lerma, J.L. A new methodology to estimate the discrete-return point density on airborne lidar surveys. Int. J. Remote Sens. 2014, 35, 1496–1510. [Google Scholar] [CrossRef]
  28. Lu, H.X.; Liu, X.J.; Tang, G.A. Terrain Complexity Assessment Based on Multivariate Analysis. J. Mt. Sci. 2012, 30, 616–621. [Google Scholar] [CrossRef]
  29. Wu, F.; Liao, Z.Y.; He, N.; Liu, C.; Wu, Q.J.; Mo, Y.F.; Pan, X.Y.; Jiang, Y.J.; Li, C.L.; Huang, X.; et al. Airborne LiDAR for Geological Hazard Investigation in Mountainous Areas with Dense Vegetation on Point Cloud Density Optimization. Geomat. Inf. Sci. Wuhan Univ. 2023, 1–11. [Google Scholar] [CrossRef]
  30. Weisburd, D.; Britt, C.; Wilson, D.B.; Wooditch, A. Measuring Association for Scaled Data: Pearson’s Correlation Coefficient. Basic Stat. Criminol. Crim. Justice 2020, 479–530. [Google Scholar] [CrossRef]
  31. Krishnan, A.R.; Kasim, M.M.; Hamid, R.; Ghazali, M.F. A modified critic method to estimate the objective weights of decision criteria. Symmetry 2021, 13, 973. [Google Scholar] [CrossRef]
  32. Tang, Y.H. A Thin Method Based on Local Terrain Complexity Index for LiDAR Bare Earth Surface Point Cloud; Southwest Jiaotong University: Chengdu, China, 2019. [Google Scholar] [CrossRef]
  33. Michael, A.L.; Warren, B.C.; Geoffrey, G.P.; David, J.H. Lidar Remote Sensing for Ecosystem Studies: Lidar, an emerging remote sensing technology that directly measures the three-dimensional distribution of plant canopies, can accurately estimate vegetation structural attributes and should be of particular interest to forest, landscape, and global ecologists. BioScience 2002, 52, 19–30. [Google Scholar] [CrossRef]
  34. Venier, L.A.; Swystun, T.; Mazerolle, M.J.; Kreutzweiser, D.P.; Wainio-Keizer, K.L.; McIlwrick, K.A.; Woods, M.E.; Wang, X. Modelling vegetation understory cover using LiDAR metrics. PLoS ONE 2019, 14, e0220096. [Google Scholar] [CrossRef]
  35. Đuka, A.; Tomljanović, K.; Franjević, M.; Janeš, D.; Žarković, I.; Papa, I. Application and Accuracy of Unmanned Aerial Survey Imagery after Salvage Logging in Different Terrain Conditions. Forests 2022, 13, 2054. [Google Scholar] [CrossRef]
  36. Aryal, R.R.; Latifi, H.; Heurich, M.; Hahn, M. Impact of slope, aspect, and habitat-type on LiDAR-derived digital terrain models in a near natural, heterogeneous temperate forest. PFG-J. Photogramm. Remote Sens. Geoinf. Sci. 2017, 85, 243–255. [Google Scholar] [CrossRef]
  37. Zhao, X.; Yue, C.R.; Li, C.G.; Gu, L.; Zhang, G.F. Estimation of Forest Canopy Density based on Airborne LiDAR Point Cloud Data. Remote Sens. Technol. Appl. 2020, 35, 1136–1145. [Google Scholar]
  38. Soja, M.J.; Persson, H.; Ulander, L.M.H. Estimation of forest height and canopy density from a single InSAR correlation coefficient. IEEE Geosci. Remote Sens. Lett. 2015, 12, 646–650. [Google Scholar] [CrossRef]
  39. Song, L.; Fan, J.; Chen, D.R.; Zhou, D.X. Approximation of Nonlinear Functionals Using Deep ReLU Networks. J. Fourier Anal. Appl. 2023, 29, 1–23. [Google Scholar] [CrossRef]
  40. Gawlikowski, J.; Tassi, C.R.N.; Ali, M.; Lee, J.; Humt, M.; Feng, J.; Kruspe, A.; Triebel, R.; Jung, P.; Roscher, R.; et al. A survey of uncertainty in deep neural networks. Artif. Intell. Rev. 2023, 56, 1513–1589. [Google Scholar] [CrossRef]
  41. Guo, C.; Pleiss, G.; Sun, Y.; Weinberger, K.Q. On Calibration of Modern Neural Networks. In Proceedings of the 34th International Conference on Machine Learning, PMLR 70, Sydney, Australia, 6–11 August 2017; pp. 1321–1330. [Google Scholar]
  42. Wilson, A.G.; Izmailov, P. Bayesian Deep Learning and a Probabilistic Perspective of Generalization. Adv. Neural Inf. Process. Syst. 2020, 33, 4697–4708. [Google Scholar] [CrossRef]
  43. Deruyttere, T.; Milewski, V.; Moens, M.F. Giving commands to a self-driving car: How to deal with uncertain situations? Eng. Appl. Artif. Intell. 2021, 103, 104257. [Google Scholar] [CrossRef]
  44. Hansen, K.B.; Borch, C. The absorption and multiplication of uncertainty in machine-learning-driven finance. Br. J. Sociol. 2021, 72, 1015–1029. [Google Scholar] [CrossRef]
  45. Sousa, M. Inductive Conformal Prediction: A Straightforward Introduction with Examples in Python. arXiv 2022, arXiv:2206.11810. [Google Scholar]
  46. Papadopoulos, H.; Proedrou, K.; Vovk, V.; Gammerman, A. Inductive Confidence Machines for Regression. In Machine Learning: ECML 2002; Lecture Notes in Computer Science; Springer: Berlin/Heidelberg, Germany, 2002; Volume 2430, pp. 345–356. [Google Scholar] [CrossRef]
  47. Johansson, U.; Boström, H.; Löfström, T.; Linusson, H. Regression conformal prediction with random forests. Mach. Learn. 2014, 97, 155–176. [Google Scholar] [CrossRef]
  48. Zhang, L. Study on Spatial Pattern of Loess Landforms Based on Analysis of Core Topographic Factors; Nanjing Normal University: Nanjing, China, 2013. [Google Scholar]
  49. Tang, G.A.; Yang, X. An Experimental Course on Spatial Analysis in ArcGIS Geographic Information System; Science Press: Beijing, China, 2012. [Google Scholar]
  50. Li, X.S.; Zhang, S.L.; Wang, Y.H. Quantitative Study of Construction Land Increase Limit Year in the Economic Transition Stage in China. J. Nat. Resour. 2011, 26, 1085–1095. [Google Scholar]
  51. Li, X.S.; Qu, F.T.; Chen, Y.S. Hypothesis and Validation on the Logistic Curve of Economic Development and Urban Sprawl--Based on the Investigation of the Typical Cities in East China. J. Nat. Resour. 2012, 27, 713–722. [Google Scholar]
  52. Wang, F.; Zhou, X. Population Structure, Urbanization and CO2 Emission: An Empirical Study Base on Cross-country Panel Data. Chin. J. Popul. Sci. 2012, 2, 47–56, 111. [Google Scholar]
  53. Chen, B.S.; Sima, J.S.; Zhao, G.Z.; Dong, X.J.; Lei, W.Q.; Chen, T.X.; He, Q.L. Optimal Point Density of Airborne LiDAR Data Collection for Hazards in Mountainous Areas. Geomat. Inf. Sci. Wuhan Univ. 2024, 1–14. [Google Scholar] [CrossRef]
  54. Liu, X.Y.; Zhang, Z.Y.; Peterson, J.; Chandra, S. The effect of LiDAR data density on DEM accuracy. MODSIM07-Land, Water and Environmental Management: Integrated Systems for Sustainability, Proceedings. 2007. Available online: https://api.semanticscholar.org/CorpusID:18995152 (accessed on 3 December 2024).
Remotesensing 16 04563 g001
Figure 1. Overview of the study area. (a) The province and its boundaries where the survey area is located; (b) 3D terrain model of the survey area; (c) optical image of the Limushan landslide; (d) characteristic vegetation of the region (trees); (e) shrubs; (f) grassland.
Figure 1. Overview of the study area. (a) The province and its boundaries where the survey area is located; (b) 3D terrain model of the survey area; (c) optical image of the Limushan landslide; (d) characteristic vegetation of the region (trees); (e) shrubs; (f) grassland.
Remotesensing 16 04563 g001
Remotesensing 16 04563 g002
Figure 2. Work flow chart.
Figure 2. Work flow chart.
Remotesensing 16 04563 g002
Remotesensing 16 04563 g003
Figure 3. Data acquisition and processing process (The numbers in the figure indicate the order of the processing steps).
Figure 3. Data acquisition and processing process (The numbers in the figure indicate the order of the processing steps).
Remotesensing 16 04563 g003
Remotesensing 16 04563 g004
Figure 4. ICP-NN algorithm framework.
Figure 4. ICP-NN algorithm framework.
Remotesensing 16 04563 g004
Remotesensing 16 04563 g005
Figure 5. Location map of micro-topographic features (Region a in the yellow box shows the crack at the back edge of the landslide; region b in the red box shows the right boundary of the landslide; and region c in the blue box shows the gully at the front edge of the landslide).
Figure 5. Location map of micro-topographic features (Region a in the yellow box shows the crack at the back edge of the landslide; region b in the red box shows the right boundary of the landslide; and region c in the blue box shows the gully at the front edge of the landslide).
Remotesensing 16 04563 g005
Remotesensing 16 04563 g006
Figure 6. Visually interpreted results–DEM comparison chart.
Figure 6. Visually interpreted results–DEM comparison chart.
Remotesensing 16 04563 g006
Remotesensing 16 04563 g007
Figure 7. Quantitative analysis of elevation RMSE.
Figure 7. Quantitative analysis of elevation RMSE.
Remotesensing 16 04563 g007
Remotesensing 16 04563 g008
Figure 8. Quantitative analysis of elevation RMSE. ** indicates significant differences at p < 0.01.
Figure 8. Quantitative analysis of elevation RMSE. ** indicates significant differences at p < 0.01.
Remotesensing 16 04563 g008
Remotesensing 16 04563 g009
Figure 9. Results of terrain complexity calculation. (a) Relatively flat area; (b) area of high terrain complexity.
Figure 9. Results of terrain complexity calculation. (a) Relatively flat area; (b) area of high terrain complexity.
Remotesensing 16 04563 g009
Remotesensing 16 04563 g010
Figure 10. Complexity error fitting curve.
Figure 10. Complexity error fitting curve.
Remotesensing 16 04563 g010
Remotesensing 16 04563 g011
Figure 11. The elevation RMSE curve discrete difference peak-seeking plot (a–d is an enlarged detail view of the last peak on the error curve).
Figure 11. The elevation RMSE curve discrete difference peak-seeking plot (a–d is an enlarged detail view of the last peak on the error curve).
Remotesensing 16 04563 g011
Remotesensing 16 04563 g012
Figure 12. The TCI error curve discrete difference peak-seeking plot (a–d is an enlarged detail view of the last peak on the error curve).
Figure 12. The TCI error curve discrete difference peak-seeking plot (a–d is an enlarged detail view of the last peak on the error curve).
Remotesensing 16 04563 g012
Remotesensing 16 04563 g013
Figure 13. Overview of canopy density by 2D canopy height model. (a) Overall vegetation cover in the DOM; (b) canopy density inversion result.
Figure 13. Overview of canopy density by 2D canopy height model. (a) Overall vegetation cover in the DOM; (b) canopy density inversion result.
Remotesensing 16 04563 g013
Remotesensing 16 04563 g014
Figure 14. The loss curve of the trained model.
Figure 14. The loss curve of the trained model.
Remotesensing 16 04563 g014
Remotesensing 16 04563 g015
Figure 15. Distribution of MPIW under different CLs.
Figure 15. Distribution of MPIW under different CLs.
Remotesensing 16 04563 g015
Table 1. Airborne LiDAR data collection specifications.
Table 1. Airborne LiDAR data collection specifications.
Name of SpecificationsPublished UnitsCollect Point Cloud Density Requirements
Lidar Base SpecificationThe United States Geological Survey (USGS)QL: Quality level
QL0: ≥8.0 pls/m2; QL1: ≥8.0 pls/m2;
QL2: ≥2.0 pls/m2; QL3: ≥0.5 pls/m2
Drone Public Survey HandbookThe Geospatial Information Authority of Japan (GSI)Low vegetated areas:10~100 pts/m2
Highly vegetated areas:20~200 pts/m2
Specification for data acquisition of airborne LiDARNational Administration of Surveying, Mapping and Geoinformation1:500 scale: ≥16 pls/m2;
1:1000 scale: ≥4 pls/m2;
1:2000 scale: ≥1 pls/m2;
1:5000 scale: ≥1 pls/m2;
1:10,000 scale: ≥0.25 pls/m2;
Table 2. CRITIC weight calculation results.
Table 2. CRITIC weight calculation results.
Terrain Factor Contrast   Intensity   ( S i ˙ ) Conflict   Index   ( δ i ) Comprehensive   Weight   Coefficients   ( c i ) Normalized   Comprehensive   Weight   Coefficients   ( ω i ′ )
SOS0.1041.0930.1140.5816
TPI0.0751.0930.0820.4184
Table 3. MPIW and PICP of ICP-NN on the test set.
Table 3. MPIW and PICP of ICP-NN on the test set.
CLMPIWPICPMPIW (100–250)PICP (100–250)
0.536.000.49728.560.506
0.643.730.60134.980.598
0.752.340.70542.090.689
0.861.620.79850.800.796
0.970.330.89960.470.911
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Liao, Z.; Dong, X.; He, Q. Calculating the Optimal Point Cloud Density for Airborne LiDAR Landslide Investigation: An Adaptive Approach. Remote Sens. 2024, 16, 4563. https://doi.org/10.3390/rs16234563

AMA Style

Liao Z, Dong X, He Q. Calculating the Optimal Point Cloud Density for Airborne LiDAR Landslide Investigation: An Adaptive Approach. Remote Sensing. 2024; 16(23):4563. https://doi.org/10.3390/rs16234563

Chicago/Turabian Style

Liao, Zeyuan, Xiujun Dong, and Qiulin He. 2024. "Calculating the Optimal Point Cloud Density for Airborne LiDAR Landslide Investigation: An Adaptive Approach" Remote Sensing 16, no. 23: 4563. https://doi.org/10.3390/rs16234563

APA Style

Liao, Z., Dong, X., & He, Q. (2024). Calculating the Optimal Point Cloud Density for Airborne LiDAR Landslide Investigation: An Adaptive Approach. Remote Sensing, 16(23), 4563. https://doi.org/10.3390/rs16234563

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop