A Block-Wise ICP Method for Retrieving 3D Landslide Displacement Vectors Based on Terrestrial Laser Scanning Point Clouds

Highlights

What are the main findings?

• A block-wise ICP approach is proposed to directly retrieve 3D displacement vectors from multi-temporal TLS point clouds.
• Compared with M3C2, it produces a more continuous displacement field and clearer deformation boundaries, which were validated using a tower target and a seasonal vegetation change scene.

What are the implications of the main findings?

• The method improves interpretable deformation mapping under occlusion, heterogeneous point density, and vegetation disturbances, which are common in field landslide monitoring.
• It supports practical boundary delineation and target-based displacement verification and can be extended via adaptive multi-scale blocking and uncertainty quantification.

Abstract

Terrestrial laser scanning (TLS) provides dense point clouds for landslide monitoring, yet occlusion, heterogeneous point density, and seasonal vegetation introduce noise and unstable deformation boundaries in multi-temporal change detection. To overcome the limitations of the multiscale model-to-model cloud comparison (M3C2) method under dominant downslope tangential motion and vegetation disturbance, we propose a block-wise ICP method to retrieve 3D displacement vectors. The scene is partitioned into local sub-blocks; rigid registration is performed within each sub-block, and the estimated translation is assigned to the sub-block center. A two-stage matching and quality control procedure removes under-constrained sub-blocks, enabling the direct retrieval of 3D displacement vectors and interpretable boundaries. Applied to the Longxigou landslide in Wenchuan using RIEGL VZ-2000i surveys on 1 November 2023 and 23 May 2024, the proposed method produces a more continuous displacement field and clearer boundaries than M3C2. For a tower target, manual measurements indicate a displacement of 0.41–0.63 m; our estimates are within 0.33–0.40 m, whereas M3C2 mostly falls between −0.25 and 0.25 m. In a seasonal vegetation change scene, we detect a canopy envelope expansion of approximately 0.20–0.40 m, while M3C2 shows scattered canopy responses that hinder boundary interpretation. A sensitivity analysis indicates a block-scale trade-off between boundary stability and peak preservation, motivating adaptive multi-scale blocking and uncertainty quantification.

1. Introduction

Landslides are widely distributed geohazards with sudden onset and strong destructive potential, posing serious threats to mountainous infrastructure and engineering projects [1]. Surface-based observation offers a cost-effective and operationally feasible approach for slope safety monitoring before failure [2]. Contact-based instruments, mainly Global Navigation Satellite Systems (GNSSs) and total stations, remain widely used in landslide monitoring worldwide [3,4]; for example, long-term GNSS observations at the Xintan and Shuping landslides in the Three Gorges Reservoir area, China, captured accelerating creep before failure and provided important evidence for risk mitigation [5,6].

Despite their broad use, contact-based monitoring can be difficult to deploy and maintain in complex field settings [7]. For large landslides, terrain constraints and monitoring costs often prevent dense sensor installation, making full spatial coverage impractical [8,9]. Moreover, such instruments report absolute displacement only at the instrumented points. If intense local deformation occurs in uninstrumented areas, such as a partial toe collapse or retrogressive sliding while sensors in the middle and head remain relatively stable, the monitoring network may not register the kinematic signal. Under sparse sampling, point-wise monitoring can therefore lead to missed alarms or misleading interpretations. The catastrophic Xinmo landslide in Maoxian, Sichuan, China, on 24 June 2017 illustrates this limitation: the steep topography hindered the deployment of conventional monitoring in the concealed high-elevation source area, and early deformation signals were not effectively captured before the collapse [10,11,12,13]. These observations highlight a persistent bottleneck of discrete monitoring in resolving spatially heterogeneous deformation and identifying critical pre-failure indicators.

To address blind spots and limited spatial coverage, non-contact techniques, particularly terrestrial laser scanning (TLS), have become important tools for landslide deformation monitoring, owing to their ability to acquire dense and precise 3D surface data [14,15]. TLS alleviates the sparse-point problem and has been widely applied on complex slopes. Oppikofer et al. used multi-temporal TLS on the Åknes rockslide in Norway to obtain 3D displacement information over the scanned area and to resolve the movement direction (and associated kinematic components) from sequential point-cloud comparisons [16], while Abellán et al. demonstrated millimetric TLS detection of precursory deformation on steep, inaccessible rock slopes [17,18]. These studies indicate the value of TLS for continuous surface characterization and precursor identification [19].

With the increasing availability of multi-temporal TLS datasets, robust deformation quantification from large point clouds has become a central topic in geomorphic and geohazard monitoring [20,21]. The key step is to estimate spatial differences between point clouds acquired at different epochs. Several change-detection algorithms are now commonly used. Early cloud-to-cloud (C2C) approaches estimate displacement by searching the nearest neighbors between two point sets, but they are sensitive to varying point density and measurement noises [22,23]. Cloud-to-mesh (C2M) methods compute point-to-surface distances after meshing a reference cloud, which can reduce the local noise but may introduce interpolation artefacts on rough natural terrain [24]. The multiscale model-to-model cloud comparison (M3C2) method proposed by Lague et al. computes orthogonal distances along local surface normals without meshing and incorporates a level-of-detection (LoD) test to distinguish significant change from noise [25,26,27,28]. However, distance-based comparison methods—including C2C, C2M, and M3C2—do not explicitly recover the true 3D motion direction of material points. They output a one-dimensional scalar distance (typically along the shortest geometric path or a local normal) rather than a displacement vector, which can complicate the interpretation in engineering monitoring. This limitation is particularly evident in three situations. First, when deformation is dominated by slope-parallel (tangential) sliding, the normal component of motion may be small, causing normal-projected distances to underestimate the actual displacement [29]. Second, long-range scanning and occlusion can lead to strong variations in the point density and local gaps between epochs; without directional constraints, nearest-neighbor pairing near sparse regions or gap edges can amplify small misregistrations and mask subtle deformation [30]. Third, seasonal vegetation dynamics can cause interpenetration of canopy points between epochs, biasing local normal estimation and generating spurious change patches that interfere with the delineation of true deformation boundaries [31,32].

To go beyond 1D distance scalars, recent work has explored point-cloud registration methods, such as iterative closest point (ICP), to estimate 3D displacement vectors [33,34]. Ning et al. applied ICP-based 3D deformation analysis to earth dam monitoring and showed that local ICP can better represent the positional changes of homologous points than scalar distance measures [35]. Pfeiffer et al. derived 3D displacement vectors for the Reissenschuh landslide in Tyrol, Austria, by registering local subsets extracted from multi-temporal long-range TLS point clouds [36]. In addition to whole-cloud co-registration, ICP-based methods have increasingly been extended to local deformation analysis using spatial windows, block domains, or piecewise patches [37,38,39]. These approaches are conceptually advantageous for spatially heterogeneous deformation because they use the geometric consistency of local neighborhoods to recover full 3D motion rather than only one-dimensional distance change. However, when applied to multi-temporal TLS data in natural landslide environments, local ICP remains challenging because of terrain occlusion, heterogeneous point density, limited inter-epoch overlap, local geometric degradation, and vegetation-induced disturbance. Under such conditions, conventional local matching with fixed subset sizes may become under-constrained or unstable, leading to mismatches, divergent iterations, or noisy displacement fields. Recent local ICP studies have also shown that the choice of local domain size can materially affect the registration stability and deformation estimation accuracy. Excessively small domains may lack sufficient geometric constraints and become unstable, whereas overly large domains may smooth local deformation signals or mix different motion patterns. However, quantitative evidence on how the local block size mediates the trade-off between deformation boundary continuity and the preservation of local displacement peaks remains limited, especially in complex landslide TLS scenes. To address this gap, this paper proposes a block-wise ICP approach for 3D displacement estimation. The scene point cloud is partitioned into local blocks; within each block, the spatial distribution of points provides constraints that help suppress non-terrain disturbances.

Rigid ICP registration is then performed at the block scale, combined with quality-control criteria to discard underconstrained blocks. The procedure directly yields a 3D displacement vector field with both magnitude and direction, mitigating the inability of scalar distance methods to represent tangential sliding. Using the Longxigou landslide in Wenchuan, Sichuan, as a case study, we validate the method with two epochs of long-range TLS data. The results indicate that under the slope-parallel movement of man-made structures and under seasonal vegetation change, the block-wise ICP approach captures tangential kinematics, suppresses spurious signals, and delineates more continuous deformation boundaries. We further quantify how the block size mediates the trade-off between boundary continuity and local peak preservation, providing guidance for multi-scale analysis and displacement uncertainty assessment in engineering practice.

2. Materials and Methods

To enable reliable deformation quantification from multi-temporal TLS surveys, this study establishes a unified processing framework linking study area characterization, point-cloud preparation, 3D change detection, and subsequent deformation interpretation. The methodology begins by defining the geological and kinematic context of the landslide to identify specific monitoring challenges. Subsequently, the multi-epoch TLS point clouds are preprocessed and rigorously co-registered into a common reference frame to minimize artifacts caused by noise and misalignment. Building upon this geometric baseline, a block-wise ICP change-detection strategy is introduced and contrasted with the conventional distance-based M3C2 approach to explicitly retrieve 3D displacement vectors. Finally, the detected spatial differences are interpreted as physical deformation patterns and verified through target-based validation and error assessment. The overall workflow encompassing data preprocessing, change detection, and validation is summarized in Figure 1.

2.1. Study Area Overview

The Longxigou landslide is situated on the hillside behind the plant site in Group 2, Lianhe Village, Bazhou Town, Wenchuan County, Sichuan Province, China. The deforming slope occupies the middle-to-upper part of the hillside and shows an irregular arcuate planform (Figure 2), overall resembling an inverted-U (∩) shape with higher elevations in the south and lower elevations in the north. Ground elevations range from 1695 to 1835 m, with a relative relief of approximately 140 m.

Figure 2 shows that the monitored slope includes exposed bedrock overlain by a surficial deposit layer, and a landslide deposit is present at the slope toe. In the present study, the displacement analysis mainly concerns the movement of the surficial cover/deposit materials, rather than the sliding of intact bedrock. At the scale of the present monitoring interval and TLS analysis, the exposed bedrock is treated as relatively stable geomorphic background terrain, whereas the main detected displacement signal is concentrated in the surficial deposit layer and toe depositional materials within the deforming zone. The principal movement azimuth of the deforming zone is approximately 352°, which is broadly consistent with the overall slope aspect. Therefore, the results presented in this study are interpreted as the 3D surface displacement field of surficial materials during the monitoring interval, rather than as direct evidence for a uniform deep-seated creep-sliding mechanism of the entire slope mass. Such tangentially dominated surface motion is poorly captured by conventional one-dimensional normal-distance algorithms, making this site well suited for validating the proposed 3D block-wise ICP method.

In the longitudinal direction, the landslide body exhibits a stepped morphology, with surface gradients of approximately 15–45°. The deformation–failure zone is about 140 m in length and 150 m in width. Deformation initiated prior to 2015 and has continued to develop. In October 2022 and November 2023, the deforming area further expanded upslope, and multiple transverse tensile cracks developed along the rear margin, suggesting ongoing retrogressive development. As of 2024, the slope remains in an active deformation stage; therefore, systematic 3D deformation monitoring is required to quantify the displacement evolution and assess the risk of instability.

2.2. Data Acquisition, Preprocessing, and Point-Cloud Characteristics

This study acquired two epochs of terrestrial laser scanning (TLS) data on 1 November 2023 and 23 May 2024 using a RIEGL VZ-2000i terrestrial laser scanner (RIEGL Laser Measurement Systems GmbH, Horn, Austria). Scan stations were deployed along a roadway on the opposite hillside across Longxigou. Four scan stations were set for each epoch to capture the scene from different elevations and viewing angles.

The geographic coordinates of four optical targets were measured using real-time kinematic (RTK) positioning. Data from one station were georeferenced using a backsight orientation procedure. The point clouds from the remaining stations were registered into the same coordinate framework using the iterative closest point (ICP) algorithm, yielding strictly co-registered point clouds for the two epochs.

To establish a unified geometric baseline and strictly constrain the comparison domain, preprocessing followed a workflow of quality screening, geometric reconstruction, and spatial normalization. First, low-confidence segments affected by scan layering, instrument shake, and dust noise were removed, and statistical filtering was applied to suppress outliers. However, preprocessing in this study did not include aggressive vegetation removal; this choice was intentional. Although vegetation filtering is common in ALS and is also often applied in TLS processing, in this long-range TLS, landslide scene vegetation is closely interwoven with rough ground, talus material, and discontinuous local slope geometry. Removing vegetation in advance could therefore also discard the valid geometric constraints needed for stable local registration. Moreover, for structurally stable woody vegetation, the local block may still carry the displacement signal of the attached ground surface, although foliage growth and defoliation can still introduce local noise. Second, the multi-station point clouds within each epoch were merged. Taking the first epoch as the reference, high-accuracy inter-epoch registration was achieved under constraints from stable bedrock areas. These stable reference areas were selected from exposed bedrock zones outside the actively deforming landslide body. The selection followed three practical criteria: (i) clear geomorphic separation from the main deformation boundary and the tension crack zone, (ii) relatively intact rock exposure with no obvious disturbance features in the scene, and (iii) full containment within the spatial overlap of the two TLS epochs to prevent edge effects. This ensured that the inter-epoch registration was constrained by non-deforming terrain within the common comparison domain. Finally, the deformation analysis area was restricted to the region with complete spatial overlap between the two epochs, avoiding edge effects induced by non-overlapping boundaries, terrain shadows, and field-of-view blind zones. This ensured spatial consistency of the comparison domain and reduced the risk of spurious deformation interpretation.

For both epochs, the scan parameters were a scan rate of 50 kHz and an angular resolution of 0.02°. The average distance from the scan stations to the main landslide area was approximately 800 m, and the farthest distance to the rear edge of the mountain hosting the landslide was approximately 1800 m. With increasing scan range, point spacing increased from 4–15 cm to 80–200 cm (Figure 3a).

Due to the rugged topography and occlusion by vegetation and houses on the landslide surface, the point cloud above the main landslide area is discontinuous, and the discontinuity becomes more pronounced with increasing distance (Figure 3b,c).

2.3. Methods for Landslide Deformation Calculation from TLS Point Clouds Using M3C2 and a Block-Wise ICP-Based Approach

Conventional point-cloud change detection is commonly based on the shortest distance (SD) concept. It does not explicitly recover the true 3D displacement vectors between homologous points; instead, deformation is approximated by the nearest geometric distance from the reference data to the comparison data. The most basic form is the cloud-to-cloud (C2C) distance. For an arbitrary point ${\mathbf{p}}^{\left(1\right)}$ in the reference point cloud, the nearest neighbor $\mathbf{q}$ is searched for in the comparison point cloud $P^{\left(2\right)}$, and the Euclidean distance is computed as follows:

$${\mathrm{d}}_{\mathrm{C}2\mathrm{C}}=\underset{\mathrm{q}\in {\mathrm{P}}^{\left(2\right)}}{\mathrm{m}\mathrm{i}\mathrm{n}}\Vert \mathrm{q}-{\mathrm{p}}^{\left(1\right)}{\Vert }_2$$

(1)

A more advanced cloud-to-mesh (C2M) method replaces the discrete point set with a triangulated mesh or a continuous surface model $\mathcal{M}$ and computes the shortest projected distance from a point to $\mathcal{M}$. When $\mathcal{M}$ has consistent normals, C2M can further output signed distances. The measurement geometries of C2C and C2M are illustrated in Figure 4. It should be noted that in steep, rough, and heavily occluded field landslide terrain, the geometric “nearest point/nearest surface” is often not the true homologous location. When the heterogeneous point density and surface roughness are superimposed, small tangential misalignments may be amplified into biases in the normal-direction distance, leading to scattered salt-and-pepper noise, spurious deformation patches, or unstable deformation boundaries.

To improve the robustness of the distance-based interpretation in complex terrain, this study adopted the multiscale model-to-model cloud comparison (M3C2) method. The key idea of M3C2 is to introduce local-normal constraints and cylindrical-neighborhood statistics. Core points ${\mathbf{x}}_i$ are selected in the reference point cloud, and their local normals ${\mathbf{n}}_i$ are estimated using neighborhood principal component analysis (PCA). A projection cylinder is then constructed with ${\mathbf{x}}_i$ as the axis origin and ${\mathbf{n}}_i$ as the axis direction, using the cylinder diameter $D$ and half-depth $H$ for bidirectional searching along the normal direction. Points within the cylinder are selected from the two epochs, projected along the normal direction, and their projected means are compared to obtain a more stable signed normal distance. For a candidate point $\mathbf{p}$, let $\mathsf{\Delta }=\mathbf{p}-{\mathbf{x}}_i$, where ${\mathsf{\Delta }}_t$ denotes the tangential distance from the point to the cylinder axis and ${\mathsf{\Delta }}_n$ denotes the distance along the normal direction. The cylinder-selection criterion is

$${\mathsf{\Delta }}_{\mathrm{t}}\le {\displaystyle \frac{\mathrm{D}}{2}} \mathrm{and} |{\mathsf{\Delta }}_{\mathrm{n}}| \le \mathrm{H}$$

(2)

After obtaining the two point sets within the cylinder and completing the normal projection, the M3C2 distance is defined as the difference between the two projected means:

$${\mathrm{d}}_{\mathrm{i}}^{\mathrm{M}3\mathrm{C}2}={\stackrel{-}{\mathrm{s}}}_{\mathrm{i}}^{\left(2\right)}-{\stackrel{-}{\mathrm{s}}}_{\mathrm{i}}^{\left(1\right)}$$

(3)

The measurement geometry of M3C2 is shown in Figure 5a. To reduce the dimensionality of parameter selection and facilitate comparative analyses, the normal-neighborhood diameter is set equal to the projection cylinder diameter, and both are set to $\mathrm{S}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}$ (i.e., $d_n=D=\mathrm{S}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}$). Multi-scale normals are used, and the normal-direction preference parameter $Y^{+}$ is set close to the main sliding direction of the landslide to ensure consistent normal orientations. Based on the field interpretation of a maximum deformation of about 5.3 m, $H=6$ m was adopted to cover this magnitude, corresponding to $\mathrm{M}\mathrm{a}\mathrm{x} \mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}=2H=12$ m. The scale parameter was set to $\mathrm{S}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}=\{20,15,10,5,2.5,1\}$ m for the comparative analysis and sensitivity evaluation. It should be emphasized that M3C2 still outputs a one-dimensional orthogonal distance scalar along the local normal direction. When landslide motion is dominated by tangential sliding along the slope surface, or when the point density is strongly heterogeneous and vegetation disturbance is pronounced, reliance on normal distances alone may be insufficient to represent true 3D motion and may lead to interference from spurious signals due to parameter choices and background disturbances.

To explicitly recover 3D displacement vectors that contain the direction and magnitude; improve the sensitivity to tangential displacements, such as slope-parallel sliding; and enhance the robustness under vegetation occlusion and sparse, discontinuous point clouds, this study further proposes a block-wise ICP method. Rigid registration is performed on a local domain basis to estimate the 3D displacement vector of the domain center and construct a displacement field. The measurement geometry of this method is shown in Figure 5b. First, voxel downsampling is applied to the epoch2 point cloud to obtain the domain-center set $\left\{{\mathbf{c}}_k\right\}$. Using ${\mathbf{c}}_k$ as the sphere center, spherical neighborhoods are extracted from the two epochs as the local-domain point sets:

$${\mathsf{\Omega }}_{\mathrm{k}}^{\left(2\right)}=\{{\mathrm{p}}^{\left(2\right)}\in {\mathrm{P}}^{\left(2\right)}\mid \Vert {\mathrm{p}}^{\left(2\right)}-{\mathrm{c}}_{\mathrm{k}}\Vert \le {\mathrm{r}}_2\},{\mathsf{\Omega }}_{\mathrm{k}}^{\left(1\right)}=\{{\mathrm{p}}^{\left(1\right)}\in {\mathrm{P}}^{\left(1\right)}\mid \Vert {\mathrm{p}}^{\left(1\right)}-{\mathrm{c}}_{\mathrm{k}}\Vert \le {\mathrm{r}}_1\}$$

(4)

To ensure sufficient overlap between the two domains when deformation exists, the neighborhood radius for the reference epoch is expanded as follows:

$${\mathrm{r}}_1=({\mathrm{r}}_2+\mathsf{\delta })\mathsf{\eta }$$

(5)

where $\delta$ is the maximum correspondence distance threshold in ICP (only correspondences within this distance are accepted) and $\eta$ is the radius expansion factor. When the number of points in a domain at either epoch is smaller than the minimum supporting point number $N_{\mathrm{m}\mathrm{i}\mathrm{n}}$, the domain is removed to avoid an under-constrained registration solution. For each domain that passes the support screening, ICP is used to estimate the local rigid transformation matrix

$${\mathrm{T}}_{\mathrm{k}}=\left[\begin{array}{cc}{\mathrm{R}}_{\mathrm{k}}& {\mathrm{t}}_{\mathrm{k}}\\ 0^{\mathrm{T}}& 1\end{array}\right],{\mathrm{R}}_{\mathrm{k}}\in \mathrm{S}\mathrm{O}(3), {\mathrm{t}}_{\mathrm{k}}\in {\mathbb{R}}^3$$

(6)

The epoch2 domain point set is treated as the source and registered to the epoch1 target. Given ${\mathbf{T}}_k$, the displacement of the domain center in the mapping sense (epoch2 $\to$ epoch1) is defined as follows:

$$\mathsf{\Delta }{\mathrm{c}}_{\mathrm{k}}^{(2\to 1)}={\mathrm{R}}_{\mathrm{k}}{\mathrm{c}}_{\mathrm{k}}+{\mathrm{t}}_{\mathrm{k}}-{\mathrm{c}}_{\mathrm{k}}$$

(7)

and is converted to the physical displacement vector (epoch1 $\to$ epoch2) following the displacement-direction convention in this study:

$$\mathsf{\Delta }{\mathrm{c}}_{\mathrm{k}}^{(1\to 2)}=-\mathsf{\Delta }{\mathrm{c}}_{\mathrm{k}}^{(2\to 1)}$$

(8)

This 3D displacement vector can be used to compute the planar displacement and the 3D displacement magnitude to support motion interpretation and quality control.

To compare with M3C2 in the same dimension, this study further outputs an outward-normal scalar displacement. The unit normal ${\mathbf{n}}_k$ at the domain center is estimated using PCA from neighborhood points around the domain center, and the normal orientation is unified following the strategy used in this study. With $\mathsf{\Delta }{\mathbf{c}}_k^{(1\to 2)}$ and ${\mathbf{n}}_k$, the outward-normal scalar displacement derived by the proposed method is defined as follows:

$${\mathrm{d}}_{\mathrm{n},\mathrm{k}}^{\mathrm{I}\mathrm{C}\mathrm{P}}=\mathsf{\Delta }{\mathrm{c}}_{\mathrm{k}}^{(1\to 2)}\cdot {\mathrm{n}}_{\mathrm{k}}$$

(9)

A two-stage “initial matching–block-wise matching” strategy is adopted. In the initial matching stage, the sub-block diameter was set to 20 m and the maximum search distance was set to 8 m. In the block-wise matching stage, the sub-block size was progressively reduced from 20 m, with a displacement convergence threshold $\mathsf{\tau }=0.001$ m and a minimum supporting point count of 100. For each valid sub-block, the center coordinates and the corresponding displacement components along the $\mathrm{x}$-, $\mathrm{y}$-, and $\mathrm{z}$-axes; along the $\mathrm{x}$–$\mathrm{y}$ plane; and in 3D space are recorded. Blocks that fail local registration are discarded to reduce the impact of misregistration on the displacement field. For clarity and reproducibility, the core symbols and key parameter settings for both M3C2 and the block-wise ICP method are summarized in

Table 1. Core symbols and key parameter settings for M3C2 and the block-wise ICP method.

Category	Symbol/Parameter	Description	Value
General	$\mathrm{D}\mathrm{X}\mathrm{Y}$	Horizontal displacement magnitude, $\sqrt{\mathsf{\Delta }{\mathrm{x}}^2+\mathsf{\Delta }{\mathrm{y}}^2}$	Calculated (m)
	$\mathrm{N}\mathrm{o}\mathrm{r}\mathrm{m}$	Normalization factor for segmentation threshold	0.10, 0.20
	LCC	Largest connected component	---
M3C2	$\mathrm{S}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e} (=\mathrm{D})$	Normal-neighborhood and projection-cylinder diameter	1, 2.5, 5, 10, 15, 20 (m)
	Max depth $2\mathrm{H}$	Full depth of projection cylinder	12 (m)
Block-wise ICP	Tested block diameters $\mathrm{D}$	Block-size cases used for comparison	10, 20, 30 (m)
	$\mathsf{\delta }$	Maximum correspondence distance	6 (m)
	$\mathsf{\tau }$	Displacement convergence threshold	0.001 (m)
	Iteration limit	Maximum ICP iterations	200

. The block-wise ICP procedure was implemented in Python 3.11 using the Open3D library (v0.19.0) and adopted a standard point-to-point ICP estimator. The maximum correspondence distance was set to 6 m and the maximum iteration number to 200; unreliable local matches were further rejected if the fitness score was below 0.1, the inlier RMSE exceeded 0.5 m, the valid correspondence set contained fewer than 10 point pairs, or the estimated total displacement exceeded 1.0 m.

3. Results

3.1. M3C2 Displacement Monitoring Results and Sensitivity to the Scale Parameter

In this study, M3C2 was selected from conventional distance-based methods to interpret the displacement at the Longxigou landslide. Six Scale settings—20, 15, 10, 5, 2.5, and 1 m—were compared and the monitoring results are shown in Figure 6.

Overall, deformation within the main landslide area can be identified under all Scale settings, indicating that M3C2 provides some ability to indicate the active zone. However, as Scale increases, the global noise becomes markedly stronger, and deformation signals and noise are more likely to mix spatially, resulting in scattered responses inside and around the landslide area that are difficult to interpret consistently.

Regarding the deformation morphology, when Scale is small, the main landslide area tends to exhibit an inward concave deformation pattern, as in the Scale = 1 m case in Figure 6. With increasing Scale, the main landslide area and adjacent zones gradually transition to an alternation of uplift and subsidence, with alternating red and blue patches in the Scale = 2.5–20 m cases in Figure 6, forming a pronounced “alternating-band” pattern. Noise behavior also varies with Scale: with a small Scale, widespread blue noise appears across the scene; as Scale increases, most blue noise weakens or disappears, whereas the extent of red noise gradually expands. Field investigations suggest that the blue noise mainly corresponds to low evergreen shrubs, whereas the red noise is more closely associated with differences in deciduous vegetation. Notably, under all Scale settings, the boundary between landslide and non-landslide areas remains insufficiently clear, and it is still difficult to reliably distinguish noise from true deformation and to accurately extract the boundary based on the M3C2 output alone.

3.2. Displacement Interpretation Results and Accuracy Performance of the Block-Wise ICP Method

The displacement monitoring results obtained using the improved block-wise ICP method are shown in Figure 7. In this calculation, the pre-deformation point cloud was used as the target point cloud, and the post-deformation point cloud was registered to the pre-deformation epoch via rotation and translation. The raw registration result therefore corresponds to the mapping displacement from epochs 2 to 1. For the interpretation, this paper reports the physical displacement direction, i.e., the reverse of the mapping displacement (from epochs 1 to 2). Accordingly, westward, southward, and downward are defined as positive in Figure 7. This sign convention standardizes the presentation and does not affect the interpretation of displacement magnitude or spatial patterns.

Overall, unlike the distance-field results from M3C2, the displacement field produced by the block-wise ICP method contains less noise and shows a more continuous spatial distribution, with deformation responses more concentrated within the landslide area. In particular, the boundary is clearer in the transition zone between the landslide and non-landslide areas in Figure 7, and the outer edge of the deforming zone is more readily identified; thus, the results can be directly used to delineate and quantify the landslide boundary, dimensions, or extent. Meanwhile, Figure 7 still shows locally “outward-protruding” red anomalies, appearing as scattered high-value patches. Field checks indicate that these anomalies mainly arise from point-cloud differences caused by deciduous vegetation growth and defoliation rather than stable ground-surface deformation; the causes and impacts are further discussed in subsequent sections. It should be noted that the displacement field discussed here mainly represents the 3D surface displacement of surficial materials within the deforming zone, rather than implying that the exposed bedrock sector undergoes the same style of continuous sliding. Accordingly, the vertical component should be interpreted as the vertical component of the surface 3D displacement of surficial materials, together with local surface readjustment and material redistribution, rather than as direct evidence of generalized bedrock collapse or a uniform deep-seated failure mechanism. From detailed spatial characteristics, deformation boundaries along the two flanks and the front edge of the main landslide area are pronounced, whereas a large data void occurs at the rear due to terrain occlusion during terrestrial laser scanning data acquisition.

3.3. Accuracy Analysis of Displacement Estimation: Comparison in a Downslope Sliding Scenario

To further quantify the accuracy of M3C2 and the improved block-wise ICP method, a transmission tower within the main landslide area was selected as the study target. By comparing with manually measured deformation values, the deformation measurement accuracy of the improved block-wise ICP method and M3C2 was evaluated (Figure 8 and Figure 9).

A clear relative translation between the two-epoch point clouds is visible in the direct overlay (Figure 8c). Because the point spacing in this area is relatively large (10–15 cm), exact homologous points cannot be reliably identified across epochs. Manual measurements were therefore carried out on the clearly visible overlapping part of the tower body by selecting representative rigid structural features that could be matched between the two scans, including truss-joint intersections, edge points, and corner features. A total of approximately 50 representative point-pair measurements were carried out. The range of 0.41–0.63 m (mean: 0.52 m) reported in

Table 2. Comparison of tower displacement estimates.

Statistic	Manual Measurement	M3C2	Block-Wise ICP
Repeated-measurement range (m)	0.41~0.63	−0.25~0.25	0.33~0.4
Mean (m)	0.52	0	0.37

represents the spread of these repeated measurements. Because the manually measured line segments do not necessarily coincide with the true 3D displacement direction, the manual measurements should be regarded as an approximate validation reference and are expected to slightly overestimate the physical displacement. Figure 8d shows the overlay of the pre-deformation and registered post-deformation point clouds; the two epochs are well aligned. Figure 8e presents the 3D displacement field computed by the block-wise ICP method, with magnitudes in the range 0.33–0.40 m, which are slightly lower than the manual values. The fluctuation of the ICP-based estimates is approximately 5–10 cm, while the local point spacing is 10–15 cm. This suggests that the block-wise ICP method can achieve relatively stable displacement estimates and correctly captures the deformation direction.

Figure 9 shows the M3C2 deformation results under all Scale settings. The displacement distribution derived from M3C2 is highly uneven: the displacement magnitude at the tower base is much larger than that at the tower top, indicating mismatches in the correspondence search between the pre- and post-deformation point clouds. As a result, M3C2 is essentially unable to interpret the deformation associated with downslope sliding. Table 2 compares the displacement estimates for the tower. The block-wise ICP estimates are slightly lower than the manual measurements, which is consistent with the fact that manual measurements are larger than the actual displacement. In contrast, the M3C2 results range from $-0.25$ to $0.25$ m, which clearly does not match the actual tower displacement; therefore, M3C2 shows a lower accuracy than the block-wise ICP method in this case.

The different error distributions of M3C2 and the block-wise ICP method are mainly related to their different measurement geometries. M3C2 outputs a signed distance along local surface normals, whereas the block-wise ICP method retrieves the overall 3D translation of a local rigid block. For the sparse open-lattice tower structure, the local-normal projection is more prone to mismatches with different members, local gaps, or nearby background points, especially in overlapping regions between the two epochs. As a result, the M3C2 estimates tend to fluctuate around zero. In contrast, the positive-valued block-wise ICP results mainly reflect the recovered magnitude of the actual tower displacement rather than a systematic positive bias.

3.4. Vegetation Change Analysis: Effects of Defoliation Growth Disturbance on Displacement Estimation

In the results of the improved block-wise ICP method, a large red noise region appears on the left side of the main landslide area (Figure 10(a₁)). Here, this red noise is analyzed in detail to examine whether the block-wise ICP method produces large estimation errors in vegetated areas. First, Figure 10(a₂,a₃) show field images corresponding to a selected red-noise area, representing defoliation of deciduous trees on 18 November 2023 and vegetation growth on 23 May 2024. Figure 10b shows the point cloud of a subregion, where leaves are on the top and the local ground surface is at the bottom. Figure 10c shows the overlay of the two-epoch point clouds; the tree point-cloud outline clearly expands outward due to vegetation growth. However, because the point cloud is too sparse, the expansion distance cannot be manually measured in the same way as for the tower. Figure 10d shows the overlay of the 23 May 2024 point cloud before and after registration by the block-wise ICP method; the expanded vegetation point cloud is translated inward, as shown by the white point cloud. Figure 10e presents the displacement estimate for this sub-block, approximately 20–40 cm, indicating that the block-wise ICP method effectively identifies the outline expansion caused by vegetation growth. By contrast, Figure 10f shows the M3C2 results at Scale = 1 m. The estimates near the ground surface are close to the true value, which is undeformed, whereas the displacement responses of the leaf points are highly scattered; the point-to-point distances at adjacent locations can differ by several times, suggesting that M3C2 may incur large errors in regions where the two-epoch point clouds interweave. These results indicate that the block-wise ICP method can effectively identify downslope sliding displacement and offers clear advantages over conventional methods in deformation boundary extraction, deformation interpretation accuracy, and resistance to noise interference.

4. Discussion

In the block-wise ICP framework, the block size governs the strength of the local registration constraints and the spatial resolution of the resulting displacement field. To compare the deformation extents across different block scales and parameter settings on a common basis, the horizontal displacement magnitude $\mathrm{D}\mathrm{X}\mathrm{Y}$ is adopted as the deformation intensity metric. Letting $\mathsf{\Delta }\mathrm{x}$ and $\mathsf{\Delta }\mathrm{y}$ denote the physical displacement components of $\mathsf{\Delta }{\mathrm{c}}_{\mathrm{k}}^{(1\to 2)}$ along the $\mathrm{X}$- and $\mathrm{Y}$-axes, this quantity is defined as follows:

$$\mathrm{D}\mathrm{X}\mathrm{Y}=\sqrt{{\mathrm{D}}_{\mathrm{x}}^2+{\mathrm{D}}_{\mathrm{y}}^2}$$

(10)

This definition is applied consistently throughout the text, figure captions, and segmentation procedures. Note that $\mathrm{D}\mathrm{X}\mathrm{Y}$ measures the horizontal displacement magnitude; it does not indicate the principal displacement direction. The black outlines in Figure 11 mark the boundary of the largest connected component (LCC). For a given parameter combination, the maximum $\mathrm{D}\mathrm{X}\mathrm{Y}$ over all valid blocks, denoted as $\mathrm{D}\mathrm{X}{\mathrm{Y}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$, is computed, and a relative threshold is set as

$$\mathrm{T}=\mathrm{N}\mathrm{o}\mathrm{r}\mathrm{m}\times {\mathrm{D}\mathrm{X}\mathrm{Y}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$$

(11)

where $\mathrm{N}\mathrm{o}\mathrm{r}\mathrm{m}$ is a dimensionless normalization factor. Blocks satisfying $\mathrm{D}\mathrm{X}\mathrm{Y}\ge \mathrm{T}$ are labeled as candidate deformation areas, and the connected region with the largest area is retained as the LCC. The “deformation boundary” in this study is defined as the outer contour of this LCC. Figure 12a–c reports the threshold $\mathrm{T}$, the LCC area, and the peak and mean DXY within the LCC, respectively, to quantify block-size effects and the influence of Norm.

When the block size is small, insufficient point support and limited geometric features within a domain weaken the ICP constraints, and the results are prone to boundary fragmentation. As the block size increases, within-domain constraints are strengthened, and the effects of random noise and vegetation disturbance can be more readily filtered through within-domain statistics, leading to more continuous deformation areas and more stable boundaries. Regarding identified patterns, when the block diameter increases from D10 to D30, the deformation morphology becomes more coherent under the same Norm, and the boundary of the largest connected deformation area more readily forms a smooth, closed outline, improving boundary interpretability.

Quantitative statistics further confirm the tendency that larger blocks yield more robust identification. Figure 12 shows that under Norm = 0.20, the LCC area increases from about $2.06\times {10}^4 {\mathrm{m}}^2$ for D10 to about $2.92\times {10}^4 {\mathrm{m}}^2$ for D30, an increase of about 41.45%. Under Norm = 0.10, the area increases from $8.98\times {10}^4$ to $1.10\times {10}^5 {\mathrm{m}}^2$, an increase of about 22.05%. This indicates that as the block size increases, a broader spatial extent of point clouds is more likely to be grouped into the same connected deformation unit, expanding the boundary envelope and manifesting as outward growth of the identified region. However, while larger blocks can improve the identification continuity, they also introduce systematic tendencies toward boundary overestimation and underestimation of displacement magnitudes. Figure 12 shows that the DXY peak decreases monotonically with increasing block diameter: the peak decreases from 3.918 m for D10 to 3.479 m for D30, a reduction of about 11.21%. Under larger blocks, within-domain registration and within-domain statistics exert stronger smoothing on local extrema, and true high-displacement peaks are more easily attenuated by the within-domain averaging process. Considering the boundary comparison in Figure 11 and the statistical trends in Figure 12, increasing the block size generally improves the deformation identification stability, resulting in stronger spatial coherence and more continuous boundaries; meanwhile, larger blocks are more likely to introduce outward-expansion effects, leading to an overextended boundary and reduced deformation magnitudes due to smoothing.

In addition, because the threshold $\mathrm{T}$ is proportional to Norm, the difference between Norm = 0.10 and Norm = 0.20 essentially corresponds to different segmentation criteria: with a smaller Norm, such as 0.10, the threshold is lower and tends to include more peripheral blocks with low-to-moderate displacements, yielding a larger LCC; with a larger Norm, such as 0.20, the threshold is higher and the boundary tends to enclose the high-displacement core, making the identified region more compact. Therefore, in engineering applications, the block scale should be matched to the task objective: for risk delineation and rapid screening, medium-to-relatively large blocks can be prioritized to obtain stable deformation regions; for detailed boundary mapping and peak estimation, smaller blocks should be used, or a coarse-to-fine multi-scale fusion strategy can be adopted to preserve the peak information while maintaining the spatial displacement completeness.

5. Conclusions

To address the need for 3D landslide deformation identification in complex natural scenes, this study proposes a block-wise ICP-based 3D displacement estimation method. Unlike distance-based methods represented by M3C2 that report orthogonal distances along local surface normals, the proposed method performs rigid registration with local domains as the basic units and directly computes 3D displacement vectors. Because the 3D displacement estimation no longer relies on the assumption that the local normal direction is consistent with the true motion direction, the method better reflects the actual kinematic mechanism when tangential components, such as sliding along the slope surface, dominate. Meanwhile, local-domain constraints and registration consistency help mitigate adverse effects from vegetation disturbance, heterogeneous point density, and occlusion-induced gaps, thereby facilitating the extraction of continuous deformation boundaries with clear physical meaning.

Comparative experiments and scenario-based validation demonstrate good effectiveness and engineering applicability. In the calibration sample of a tower sliding along the slope surface, the manually measured displacement magnitude is 0.41–0.63 m, whereas the estimated 3D displacement from this method is 0.33–0.40 m. The magnitudes are consistent and align with the tendency for manual measurements to be overestimated. In contrast, the M3C2 results concentrate within $-0.25–0$.25 m, which is clearly lower than the true displacement magnitude and cannot support interpretation of this type of along-slope sliding. In this area, the displacement fluctuations produced using this method are about 5–10 cm, while the point spacing is about 10–15 cm, indicating that the method remains stable and interpretable in this sparse-point tower validation scenario.

In the seasonal vegetation-change scene, this method identifies an outward expansion of the vegetation envelope of about 0.20–0.40 m and shows relatively continuous spatial responses. By comparison, M3C2 tends to produce cluttered and dispersed high and low responses in canopy areas, interfering with the deformation boundary interpretation. Overall, the method performs more stably in terms of the boundary continuity, noise suppression, and displacement verification for key targets, providing a more interpretable technical route for deformation boundary identification, motion characterization, and early warning analysis in engineering landslide monitoring.

Despite these positive results, further improvements remain necessary. The current uniform blocking strategy with a fixed diameter cannot simultaneously achieve precise boundary localization and peak preservation in regions with strong spatial heterogeneity of deformation, leading to a scale trade-off in which boundaries become more stable but envelopes are larger and extreme values are smaller. Deformation area segmentation based on a relative threshold depends on the peak value and the normalization factor, whereas the peak value is sensitive to data noise, block scale, and local-registration smoothing; this may cause the threshold $\mathrm{T}$ to vary with monitoring conditions, increasing the risk of outward boundary bias or missed detections. In addition, due to occlusion viewpoint, point-cloud gaps, and seasonal vegetation changes, TLS data may exhibit a low overlap, insufficient geometric features, or strong nonrigid changes, in which local-domain ICP can still suffer from unstable convergence or mismatching. Future work can focus on adaptive multi-scale blocking, more robust quality control and uncertainty quantification, and integration with ground vegetation classification and stable-target constraints to improve the generalization and engineering reliability in more complex environments.