# Detecting rockfall precursory movements in 3D point clouds using a new method based on a local ICP registration

Marie-Aurélie Chanut, Yohan Peru, Jerome Faillettaz, Laurent Dubois, Alexandre Carotte, Pierre Azemard

► To cite this version:

Marie-Aurélie Chanut, Yohan Peru, Jerome Faillettaz, Laurent Dubois, Alexandre Carotte, et al. Detecting rockfall precursory movements in 3D point clouds using a new method based on a local ICP registration. 2023. hal-05120768

HAL Id: hal-05120768

https://hal.science/hal-05120768v1

Preprint submitted on 19 Jun 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
1 Detecting rockfall precursory movements in 3D point
2 clouds using a new method based on a local ICP
3 registration

4 Marie-Aurélie Chanut *

5 Cerema, Team GeoCoD, 25 avenue François Mitterrand, Bron, France

6 Yohan Peru

7 Cerema Centre-Est, Département Risques Infrastructures et Matériaux, 25 avenue François

8 Mitterrand, Bron, France

9 Jérôme Faillettaz

10 Cerema, Team GeoCoD, 25 avenue François Mitterrand, Bron, France

11 Laurent Dubois

12 Cerema Centre-Est, Département Risques Infrastructures et Matériaux, 25 avenue François

13 Mitterrand, Bron, France

14 Alexandre Carotte

15 Cerema Centre-Est, Département Risques Infrastructures et Matériaux, 25 avenue François

16 Mitterrand, Bron, France

17 Pierre Azemard,

18 Cerema Méditerranée, Team GéoCoD, Avenue Albert Einstein, Aix-en-Provence, France

19 * Corresponding author : marie-aurelie.chanut@cerema.fr

20

21
22

**Abstract:**

23

A new method (called L-ICP method) is proposed for tracking precursory movements of rocks prior to failure through the comparison of 3D point clouds. This method is based on a local ICP registration of point clouds neighborhoods to determine the 3D displacement, i.e. both the value and direction of the movement. The aim of local registration is to locally follow the same geometric pattern from one point cloud to another. Knowing at all points the 3D displacements enables us to understand the underlying mechanisms involved. A detection level is also derived from stable zone analysis, providing further insights into the results.

24

25

26

27

28

29

30

The L-ICP method is validated using synthetic data with an imposed known displacement and a variable noise level. Results demonstrate that the method is able to detect the “real” 3D displacements in any direction up to a signal to noise ratio equal to 0.5. Compared to the conventional methods such as M3C2 and C2M distances, the proposed method exhibits superior performance, especially in detecting in-plane movements whereas conventional are not able to detect them.

31

32

33

34

35

The second application on an unstable rock (500 m³ column) in a rocky cliff confirms its effectiveness to detect precursory movements. The obtained 3D displacements are of the same order of magnitude as field measurements. The L-ICP method tracks actually the deformation of the mass before its failure.

36

37

38

**Keywords:** 3D point cloud, terrestrial laser scanning, local ICP registration based method, 3D displacements, precursory movements, cloud-cloud comparison

39

40

**Highlights:**

41

* The L-ICP method is designed to match the local neighborhoods of 3D point clouds.

42

* The L-ICP method provides both value and direction of 3D movement.

43

* The L-ICP method enables rockfall precursory movements to be detected and tracked.

44

**Declarations**
45 Funding: this research received no external funding.

46 Conflicts of interest/Competing interests: The authors declare no conflict of interest

47 Availability of data and material: the images used are accessible on specific request

48 Code availability (software application or custom code): Not applicable
49

# 1 Introduction

50

Quantifying surface change of soil or rocky landslides is currently a challenge in order to reduce the risk, develop appropriate mitigation measures and ensure the safety of people, buildings and infrastructures. The use of dense three-dimensional (3D) point clouds is now widely used in natural hazards (Barbarella and Fiani, 2013; Jaboyedoff et al., 2012; Rosser et al., 2005; Royán et al., 2014).

51

52

53

54

Remote sensing technologies, indeed, enable the representation of large surfaces with a dense spatial sampling (Casagli et al., 2017). Remote data can be acquired through radar interferometry (Casagli et al., 2010; Nagler et al., 2002; Tantianuparp et al., 2013), terrestrial laser scanning (Abellán et al., 2010; Jaboyedoff et al., 2012; Monserrat and Crosetto, 2008; Remondino et al., 2005), mobile laser scanning (Michoud et al., 2015) or imaging ((Blanch et al., 2020; Delacourt, 2004; Kaab, 2000; Samodra et al., 2020; Stumpf et al., 2015).

55

56

57

58

59

60

The processing of point clouds enables various applications in the field of landslides (Jaboyedoff et al., 2012), including landslide detection, structural analysis, and monitoring. (1) The delineation of a landslide is made possible by the detection of characteristics such as roughness or curvature of the topography (Wang et al., 2013). (2) Once the landslide has been identified, it is possible to characterize sets of discontinuities (for a rocky massif) using adjustment planes or plane orientation indicators (Fanti et al., 2013; Spreafico et al., 2015). These data provide insights into the underlying mechanisms of the studied rocky landslide. (3) Finally, monitoring has several applications (Crosta et al., 2017): pre-failure deformation, quantification of large displacements in slow-moving landslide and rockfall detection, and frequency analysis from multitemporal point clouds. In addition to 3D geometry, attributes like reflectance or intensity data can be considered to implement segmentation and enhance the analysis (Franceschi et al., 2009).

61

62

63

64

65

66

67

68

69

70

71

In this paper, we focus on the study of the precursory movements observed during pre-failure deformation before rockfalls, specially the small displacements that are of the order of millimeters.

72
Unfortunately, the monitoring of deformation before failure consists in identifying displacements whose values are of the same order of magnitude as the measurements noise (R. Kromer et al., 2015). The ability to detect such change by comparing point clouds is thus limited by several factors (R. Kromer et al., 2015; Mayr et al., 2020) such as the point cloud accuracy and precision (instrument specification), the ground factors (vegetation, surface reflectance and surface roughness), the conditions of acquisition (distance, incidence angle) and the registration error between clouds. All these factors lead to the definition of a minimum magnitude where geometric surface change can be confidently detected called the level of detection (LoD).

The remote sensing technique used in this paper is the terrestrial laser scanning (TLS). As discussed in the review by (Abellán et al., 2014), TLS proves to be a challenging effective method for studying rock slopes, particularly in detecting precursory deformations and possibly assisting the prediction of future rock failures. TLS is a terrestrial Lidar (Light Detection and Ranging) and consists of a laser transmitter and receiver and a scanning device. The laser beam is reflected directly onto the rock slope surface eliminating the need of reflector. This technology enables the generation of high resolution point cloud (up to a millimeter scale) and can be easily deployed (Day et al., 2013; Williams et al., 2018). A series of point clouds is thus required to detect precursory deformations before failure. Previous studies have used monitoring at different time range: from monthly or more intervals (Abellán et al., 2010; Lague et al., 2013; Oppikofer et al., 2009; Williams et al., 2021) to weekly intervals (R. A. Kromer et al., 2015; Zahs et al., 2022) and hourly intervals with real-time acquisitions from a permanently installed terrestrial laser scanner (Kromer et al., 2017; Williams et al., 2018). Such monitoring are expensive, require a permanent installation with an energy supply and are adapted in case of a crisis during a short time. For operational cliff monitoring at a reasonable cost, cliff point cloud series are rather acquired at several times adapted to the kinematics of the movement (between weeks and months) (Royán et al., 2014). Our work is conducted within this context with a series of point clouds acquired approximatively at the same position.
From these series of TLS point clouds, change can be detected according to two main classes of methods: (1) local deformation or (2) object based methods. (1) Local deformation methods: first, the differentiation of the digital terrain model (DTM) (Bitelli et al., 2004; Giacomini et al., 2020) can be used to detect rockfalls. However, this approach seems not to be suitable to track precursors due to the step of rasterization and the loss of information. Second, point clouds can be compared using different definitions of distance calculation, for instance cloud to mesh distance (C2M distance), Multiscale Model to Model Cloud Comparison (M3C2) distance (Lague et al., 2013) or the concept of shortest distance (Oppikofer et al., 2009). Refinements, such as the use of the M3C2 algorithm with precision maps option, have been proposed (Blanch et al., 2021). Along with distances computations, filtering methods are necessary to detect precursors and decrease LoD. In (Abellán et al., 2009), the filtering method consists in averaging the C2M distances over a neighborhood for which the dimension has to be calibrated. On the other hand, (R. Kromer et al., 2015) used a denoising and calibration approach that takes advantage of point redundancy in both space and time (4D) and calibration point clouds to remove systematic errors. For the M3C2 distances, filtering is intrinsic to the method because of the averaging of the point coordinates before the calculation of the distance (Lague et al., 2013). The main difficulty with the use of distance computation lies in the definition of direction of change. Typically, the normal direction is chosen (Abellán et al., 2009; Lague et al., 2013), but this may lead to underestimation of change magnitude if precursory movements occur in different directions. In the aim of estimating the direction of change, (Kromer et al., 2017) calculates distances between clouds according to a slope-dependent normal. Another recent approach (Williams et al., 2021) allows to compute a dominant movement direction at each point based on multi-scale, multidirectional change quantifications to best assess the real movement with the M3C2 distance.

(2) Object-based methods: this consists of tracking objects within the 3D point clouds as it is done with images in 2D as for example the computation of Scale Invariant Feature Transform (SIFT) points (Lowe, 1999). In addition to being laborious, manual points pair picking (Oppikofer et al., 2009) is not
suitable for the search of precursors because of the lack of precision in the selection of the same points in the series of point clouds. The calculation of the roto translation matrix of the selected object (Monserrat and Crosetto, 2008; Oppikofer et al., 2009) is automatic but still requires manual selection of objects. To avoid partially this manual object selection, (Zahs et al., 2022) extracts planar surfaces in point clouds of successive epochs and identifies corresponding planar surfaces between two point clouds using a binary random forest classification before calculating the M3C2 distances. This approach requires a training step with a manual definition of some similar surfaces. (Travelletti et al., 2014) first calculates the 2D displacement field by projecting the 3D point clouds, and then deduces the 3D displacements by reprojecting them back to the 3D cloud. While this method is effective for moderate to large displacements (Chanut et al., 2017), we can't apply it to detect precursory movements.

That's why we propose a new automatic method for estimating the 3D precursory displacements based on the local registration of point clouds neighborhoods. We focus on rocky slopes and cliffs in a natural environment with vegetation: some areas are known to be stable and others are potentially unstable with slight movements ranging from a few millimeters to centimeters in translation and a few degrees in rotation between two acquisitions. These movements occur in an unknown direction and can vary over time. We assume that locally the deformation is rigid as it is the case for rockfalls before failure. Through our proposed method, we aim to provide a reliable and automated approach for estimating 3D precursory displacements in rock slopes and cliffs. By leveraging local registration of point cloud neighborhoods, we can identify and track tiny movements in these areas. The comparison with in-situ measurements and conventional methods serves to validate the accuracy and effectiveness of our approach.

The paper is thus divided into 4 sections. After describing the method (section 2), we present the data used to validate it (section 3). The results obtained are presented (section 4), and the method, its limitations and future developments are discussed (section 5).
## 2 Method

The method based on a local-ICP registration aims at determining the real 3D movements in the scene that occurred between two specific dates by comparing two point clouds. We called it the L-ICP method. In this section, we first introduce the tools used for preprocessing the point clouds, and then proceed to explain the proposed method in detail and how to use it to define the level of detection (LoD).

### 2.1 Pre-processing of data

As mentioned in numerous papers (Williams et al., 2018), the comparison of point clouds is performed from cleaned point clouds (i.e vegetation removed). Several algorithms exist for cleaning vegetation: for example CSF (Zhang et al., 2016), Canupo (Brodu and Lague, 2012) or CGAL (Giraudot and Lafarge, 2023). CSF and Canupo are specific to vegetation removal whereas CGAL is a more general classifier. Considering the ease of training the classifier and the quality of the results, Canupo has been chosen for this study.

The two point clouds are then registered that is to say a spatial transformation (rotation and translation) is searched that aligns the point clouds. One cloud is thus defined as the compared cloud and the other as the reference cloud. A rigid registration is used. Clouds are first coarsely registered by selecting manually at least the same three points in both point clouds. They are then finely registered using the Iterative Closest Point algorithm ICP (Besl and McKay, 1992) developed to map two point clouds by iteratively minimizing the distance between them.

Once this pre-processing step is completed, the point clouds are ready for comparison.

### 2.2 The local ICP registration based method (L-ICP)

The method is designed to provide at each point of the point cloud, the 3D displacement. The aim of the L-ICP method is to generalize the concept of 2D image correlation in 3D (Leprince et al., 2007). To find the 3D displacement of the same material point between the two clouds, we need to find for
each point in the compared cloud its corresponding point in the reference cloud. To do this, we decide to work on the neighborhood of the point under study, and more precisely on its local geometry. We want to find the subset of the reference cloud that locally has the similar geometry. With the assumption of precursory movements, we know that these two cloud subsets are not very far apart. This is why we can use the ICP algorithm to find the part of the reference cloud that best matches the geometry in the neighborhood of the point under study. We therefore perform this local registration of point cloud subsets using the ICP algorithm, contrary to the typical use for global registration of spatial clouds or point cloud time series (Barbarella and Fiani, 2013).

As mentioned above, the aim of the local registration is to locally follow the same geometric pattern from one point cloud to another. With the ICP registration, we reach this aim but we have to check that the surfaces are similar. Indeed, in some cases (e.g. rockfall, vegetation), the surfaces can have been changed and the geometrical transformation provided by the ICP algorithm minimizes the distance but the surfaces didn't match. Therefore, in addition to the 3D displacement value, we proposed to provide, as output of the method, a value, called score of the method, to indicate whether the two surfaces match.

The proposed method has been implemented in python with the libraries Open3D (Zhou et al., 2018) and CloudComPy (Rascle, 2023). The results are displayed and analyzed with CloudCompare (Girardeau-Montaut, 2022).

We now present the details of the algorithm. Let $pc_1$ be the reference point cloud and $pc_2$ the compared point cloud. The method is defined by four parameters (Table 1): the radius $r_n$, the distance $d$, the radius $r_s$ and the overlap ratio $\tau$. The algorithm is divided into two parts: A- the computation of the 3D displacements then B- the computation of the method score.

### A. Computation of the 3D displacements:

For every calculation point $i$ of $pc_2$:
- Select the neighborhood $N_2(i)$ defined by the points of $pc_2$ located inside the sphere of center $i$ and with radius $r_n$ (Figure 1-a);

- Select the neighborhood $N_1(i)$ defined by the points of $pc_1$ located inside the sphere of center $i$ and with radius $r_n + d$ (Figure 1-a);

At this step, the corresponding surface of the neighborhood $N_2(i)$ in $pc_1$ must be included in $N_1(i)$. So the value of the parameter $d$ must be chosen larger than the value of the unknown precursory displacement.

- Perform the ICP registration between $N_2(i)$ and $N_1(i)$ as reference with the overlap ratio $\tau$ to find the geometrical transformation $T$ between the two subsets (Figure 1-b);

- Compute the image of the point $i$ by $T$: $T(i)$ and the 3D vector $\overrightarrow{T(i)}$ ($T$ (Figure 1-b)). The components of the 3D displacement are thus obtained: $dx(i)$, $dy(i)$, $dz(i)$.

## B. Computation of the method score :

For every calculation point $i$ of $pc_2$:

- Select the neighborhood $N_{s2}(i)$ defined by the points of $pc_2$ located inside the sphere of center $i$ and with radius $r_s$ (Figure 1-c);

- Select the neighborhood $N_{s1}(i)$ defined by the points of $pc_1$ located inside the sphere of center $i$ and with radius $r_s + d$ (Figure 1-c);

- Apply $T$ to $N_{s2}(i)$ and compute the C2M distances between $T(N_{s,2}(i))$ and $N_{s1}(i)$ (Figure 1-d). Fit a gaussian curve of the distances of the two subsets after the ICP registration and compute the mean $\mu(i)$;

Define the limit mean distance value between registered neighborhoods $\mu_{LOD, x\%}$ with points $j$ inside the stable area in function of the confidence level as the value for which $x\%$ of the points $j$ check $\mu(j) < \mu_{LOD, x\%}$;
219

For every points i of pc₂: compute the *score* value according to:

220

$$ \text{if } \mu(i) < \mu_{LOD, x\%}, \text{ score}(i) = 1 \text{ otherwise } 0. $$

221

<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>
<figure><img src="image_5.png" /><figcaption>Figure 1: principle of the local-ICP registration based method: a- definition of the local neighborhoods for local registration, b- local ICP registration and calculation of the 3D displacement, c- definition of the local neighborhoods for score computation d- computation of C2M distances between the reference subset and the registered neighborhood</figcaption></figure>

<table><caption>Table 1 : parameters of the local ICP registration method</caption><thead><tr><td>Name of the parameters</td><td>Description</td></tr></thead><tbody><tr><td>r<sub>n</sub></td><td>Radius defining the local registered neighborhood N<sub>2</sub> at each computation point i in the compared point cloud (pc2). N<sub>2</sub> is used to compute the local ICP registration with the reference point cloud (pc1).</td></tr><tr><td>d</td><td>Distance to define of the local reference neighborhood N<sub>1</sub> inside the reference cloud (pc1). N<sub>1</sub> is defined by the points of pc1 whose distance from the calculation point i is less than r<sub>n</sub> + d</td></tr><tr><td>r<sub>s</sub></td><td>Radius defining the local neighborhood at each computation point in the compared point cloud (pc2). Used to compute the score of the method. r<sub>s</sub> ≤ r<sub>n</sub></td></tr><tr><td>τ</td><td>Overlap ratio, usual parameter used by the algorithm of the ICP registration. This is the ratio between the number of inlier correspondences divided by the number of points in the reference cloud. The higher the better.</td></tr></tbody></table>

## 2.3 Definition of the level of detection

The outputs of the method at each calculation point are the 3D displacements and the method score. Only points with a score equal to 1 (the local surface match) are used in the following to track and quantify precursory movements. A precursory movement is detectable within the comparison of clouds if it is higher than the minimum detectable movement called level of detection (LoD). LoD can be
estimated either locally (Lague et al., 2013; Wheaton et al., 2009) or constant within the entire cloud (Abellán et al., 2009; Williams et al., 2018). In this paper for reasons of simplicity, we decide to use a constant level of detection (Abellán et al., 2009): the LoD is typically determined by computing the standard deviation of distribution of compared point clouds where no change has occurred (stable zones) and defined by 1.96-times this standard deviation corresponding to the 95% confidence level.

## 3 Datasets

We applied the L-ICP method proposed above on two types of data. First, synthetic data were built by moving a part of the point cloud to a chosen 3D displacement in order to control the change in the clouds. In the second dataset, data were acquired on a cliff and precursory deformations before failure were followed. In both cases, results obtained with the L-ICP method were compared with the knowledge we had about the ground truth (imposed 3D displacements or in-site measurements) and with two classical processing methods: averaging of the C2M distance (Abellán et al., 2009) and the M3C2 distance (Lague et al., 2013).

### 3.1 Synthetic data

A portion of a point cloud representing the face of a limestone block was selected (Figure 2- a and b). This selection consisted of 120000 points with an average point spacing equal to 3 cm. This point cloud was called the reference cloud. Within this reference point cloud, an area was selected (in blue Figure 2- c and d) and was translated along a vector $\vec{t}$ with three components ($t_x, t_y, t_z$). The remaining part as well as the translated part were merged and a gaussian noise was added to this cloud. The noise was defined by a mean $\mu$ equal to 0 and a variable standard deviation $\sigma$. This cloud was called the compared one.

Three configurations of translation were investigated with the same norm of vector $\vec{t}$, $||\vec{t}|| = 0.005 m$:
- $C_{1,\sigma} : (t_x = 0, t_y = 0, t_z = \|\vec{t}\|)$ where the displacement was globally perpendicular to the mean surface (the mean surface is in the plane Oxy in this example);

- $C_{2,\sigma} : (t_x = \|\vec{t}\|, t_y = 0, t_z = 0)$, where the displacement was in the plane of the mean surface;

- $C_{3,\sigma} : (t_x = \frac{\|\vec{t}\|}{3}, t_y = \frac{\|\vec{t}\|}{3}, t_z = \frac{\|\vec{t}\|}{3})$ for a more general displacement.

Five values of standard deviation $\sigma$ of the gaussian noise were used to assess the effectiveness of the proposed method in detecting precursors based on the noise level: 0.001 m, 0.002 m, 0.005 m, 0.01 m and 0.02 m. This corresponded to signal noise ratio (SNR) equal to 5, 2.5, 1 0.5, 0.25 respectively.

<figure><img src="image_6.png" /><figcaption>Figure 2: description of the synthetic data: a- and b- reference point cloud, c- the changed subset of point cloud before translation, d- the changed subset of point cloud after translation which forms the compared cloud</figcaption></figure>

## 3.2 Unstable rock in a rocky cliff

The proposed method was also applied to investigate the movement of a unstable mass in a rocky cliff overhanging the well known Sechilienne landslide in the French Alps (Dubois et al., 2014; Kasperski et al., 2010) (Figure 3-a). The unstable mass consisted of a 500 m³ column. The aim was to track and
analyze the 3D deformations occurring prior to failure (the failure has not yet occurred). The initial
data acquisition was conducted on December 17, 2019. A total of ten different data acquisitions were
carried out at various time intervals (see Table 2) over a study period of slightly more than two years.
Two terrestrial laser scanners were used during this campaign: TRIMBLE SX10 and RIEGL VZ 2000i.
The repositioning of the laser scanner was approximately the same between the different acquisitions.
The scanners were positioned at a distance ranging from 80 to 100 meters from the cliff (Figure 3-b).
The average point spacing of the scans ranged between 1 and 3 cm. The standard deviation of the
instrumental and methodological error (alignment, merging and surface generation) was calculated as
0.003 m based on a comparison between two scans acquired consecutively (Abellán et al., 2010). The
analysis was carried out on the entire unstable rock mass, called area A₀, and on two more localised
areas of the mass, called A₁ and A₂, which were located at different heights (Figure 3-c).

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>
<figure><img src="image_9.png" /><figcaption>Figure 3: Location of the unstable rock: a- inside the Séchilienne landslide, b- view of the acquisition of the cliff, c- definition of the stable area and the analyzed areas, d- in-site measurements on the top of the unstable rock</figcaption></figure>

<table><caption>Table 2 : Description of the point clouds acquisition</caption><thead><tr><td>Scan id</td><td>Acquisition time</td><td>Used scanner</td><td>Scan id</td><td>Acquisition time</td><td>Used scanner</td></tr></thead><tbody><tr><td>1</td><td>17/12/2019</td><td>TRIMBLE SX 10</td><td>6</td><td>05/10/2020</td><td>TRIMBLE SX 10</td></tr><tr><td>2</td><td>14/01/2020</td><td>TRIMBLE SX 10</td><td>7</td><td>14/12/2020</td><td>TRIMBLE SX 10</td></tr><tr><td>3</td><td>12/03/2020</td><td>TRIMBLE SX 10</td><td>8</td><td>19/03/2021</td><td>TRIMBLE SX 10</td></tr><tr><td>4</td><td>15/06/2020</td><td>TRIMBLE SX 10</td><td>9</td><td>21/06/2021</td><td>RIEGL VZ 2000i</td></tr><tr><td>5</td><td>07/08/2020</td><td>TRIMBLE SX 10</td><td>10</td><td>15/03/2022</td><td>RIEGL VZ 2000i</td></tr></tbody></table>

As the unstable mass is located above the most active part of the Séchilienne landslide, we could access field measurements set for the operational monitoring of the landslide. A radar target and a geodetic measurement point are located on the top of the unstable mass (Figure 3 b and d). A terrestrial ULB radar is indeed used to monitor the deformation of the landslide from the opposite side of the valley (Durville et al., 2009). The radar measurement provides the distance between the radar target and the radar itself, indicating the movement of the target towards the radar. The second field measurement is the manual measurement of the 3D positions of a geodetic point: distance measurement is accurate to ± 1mm and angle one to ± 0.00015 grad. The successive campaigns have been made at different
frequency in function of the velocity of the landslide. This measurement is not continuous and we
needed to make linear interpolation between the measurements. Figure 4 displays both radar and
geodetic measurements, showing that the values obtained from the radar measurements are lower than
those obtained from the geodetic measurements. This discrepancy highlights the fact that the radar
measurements underestimate the actual 3D movements. Because of the nature of what is measured by
radar and the frequency of geodetic measurement, these measurements helped us to assess the real
movements by providing an order of magnitude of movement.

<figure><img src="image_10.png" /><figcaption>Figure 4: Geodetic and radar measurements available at the top of the unstable mass</figcaption></figure>

4 Results

4.1 Synthetic data

In this section, only the results of the configurations $C_{1,\sigma}$ and $C_{2,\sigma}$ with $\sigma = 0.001, 0.002, 0.005, 0.01$ and $0.02 \, m$ are presented. The results for the configuration $C_{3,\sigma}$ are provided in Appendix. The values of $r_n, r_s$ and $d$ used to calculate 3D displacements with the local ICP registration method were set to 0.5 m, 0.2 m and 0.1 m respectively. The overlap ratio was chosen equal to 0.9. The choice of the parameters values is discussed in section 5. Only the displacement value of computation points with a score equal to 1 are shown in the rest of the paragraph.
We recap that in the configuration $C_{1,\sigma}$ (section 3.1), the imposed displacement of the moved area was perpendicular to the surface ($t_z = \|\vec{t}\|$) with a magnitude equal to 0.005 m. When the noise was low ($\sigma = 0.001$ or $0.002$ m), all three methods provided similar results in absolute value (Figure 5). Indeed, for the approach with M3C2 distance, the result was influenced by the computation of the normal with value both positive and negative but equal in value to 0.005m. As the noise increased (0.005 m), the M3C2 distance failed to detect the displacement whereas the local ICP registration method and the averaged C2M could still detect it. For $\sigma = 0.01$ m, it became challenging to detect the imposed movement with the averaged C2M but it remained very clear with the L-ICP method. For $\sigma = 0.02$ m, none of the methods could reproduce the real movement. The L-ICP method succeeds in providing the correct displacements in the moving zone, but these displacements were not significant given the noise level in the so-called stable area.

In the configuration $C_{2,\sigma}$, the imposed displacement of the moved area was in the plane of the surface ($t_x = \|\vec{t}\|$) with the same magnitude. In this case, M3C2 distance and the averaged C2M failed to detect the real movement even with low noise $\sigma = 0.001$ m (Figure 6). However, the local ICP registration could track the displacement up to a noise equal to 0.01 m similar to what was observed in the configuration $C_{1,\sigma}$.

This result was confirmed by the results obtained for the configuration $C_{3,\sigma}$ where $t_x = \frac{\|\vec{t}\|}{3}$, $t_y = \frac{\|\vec{t}\|}{3}$, $t_z = \frac{\|\vec{t}\|}{3}$. In this case (Figure 7), the local ICP registration method was able to detect the displacements of 0.005 m up to a level of noise equal to 0.01 m whereas the two others methods could only up to a lower level of noise (0.002 m) but with an underestimation of the real displacement.

Using these synthetic data, we demonstrated that the proposed L-ICP method is capable of accurately calculating the real 3D displacements regardless of the direction of the movement until a value of noise
equal to 0.01m for a displacement value of 0.005 m. This is not the case for the M3C2 distance or the average C2M.

<table><thead><tr><th>σ (SNR)</th><th>L-ICP</th><th>M3C2</th><th>Averaged C2M</th></tr></thead><tbody><tr><td>0.001 m<br>(5)</td><td></td><td></td><td></td></tr><tr><td>0.002 m<br>(2.5)</td><td></td><td></td><td></td></tr><tr><td>0.005 m<br>(5)</td><td></td><td></td><td></td></tr><tr><td>0.01 m<br>(0.5)</td><td></td><td></td><td></td></tr><tr><td>0.02 m<br>(0.25)</td><td></td><td></td><td></td></tr></tbody></table>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>
<figure><img src="image_26.png" /><figcaption>Figure 5: Results of the three methods (L-ICP, M3C2 distance and averaged C2M) in the configuration $C_{1,\sigma}$ in function of $\sigma$</figcaption></figure>

<table><thead><tr><th>σ (SNR)</th><th>L-ICP</th><th>M3C2</th><th>Averaged C2M</th></tr></thead><tbody><tr><td>0.001 m<br>(5)</td><td></td><td></td><td></td></tr><tr><td>0.002 m<br>(2.5)</td><td></td><td></td><td></td></tr><tr><td>0.005 m<br>(5)</td><td></td><td></td><td></td></tr><tr><td>0.01 m<br>(0.5)</td><td></td><td></td><td></td></tr></tbody></table>

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /></figure>

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /></figure>
<figure><img src="image_39.png" /><figcaption>Figure 6: Results of the three methods (L-ICP, M3C2 distance and averaged C2M) in the configuration $C_{2,σ}$ in function of $σ$</figcaption></figure>

## 4.2 Unstable rock in a rocky cliff

The computation of the 3d displacements was performed using the first point cloud as reference. Canupo algorithm was used to remove vegetation. The values of $r_n$, $r_s$ and $d$ employed in the calculation of the 3D displacements with the L-ICP method were 1 m, 0.2 m and 0.1 m respectively. The overlap ratio was 0.9.

An example of the results obtained with the L-ICP method is illustrated in Figure 7: the figure displays the comparison of the cloud of 12/03/2020 with the reference cloud (17/12/2019). Above, the value of the 3D displacements is displayed and bottom panel indicates corresponding score. In the following paragraph, only the points with a score equal to 1 were considered.
<figure><img src="image_40.png" /></figure>

<figure><img src="image_41.png" /><figcaption>Figure 7: application of the L-ICP method between the cloud of 12/03/2020 and the reference cloud (17/12/2019): a- 3D displacements, b- score of the method</figcaption></figure>

We studied first the magnitude of displacements and then the direction. The results obtained by the L-ICP method and the two classical processing method (averaging C2M and M3C2 distances) were aggregated by averaging the values on the whole unstable rock $A_0$, on the specific areas $A_1$ and $A_2$ (see section 3.2). The level of detection LoD was deduced from the distribution of displacement values in the stable area with a 95% confidence level. These results were then compared with the available measurements data on this site. From Figure 4, measurements data were selected for the study period (December 2019 – March 2022). For the aim of comparison, the geodetic data were linearly interpolated. Radar data were sparse due to the device dysfunction during the study period. Available
data were plotted and it is noted that the radar data underestimates the real 3D displacements since it
measures the movement of the rock in the view direction only. Besides, we have to note that geodetic
measurements are made at the top of the mass whereas the analysis of the areas A₀, A₁ and A₂ report
respectively a global behaviour of the mass, the movement at the middle and ¾ height of the column.

Figure 8 and Table 3 show the displacement values derived from the L-ICP method. For the three
areas A₀, A₁ and A₂, significant displacements during the first period were observed, exceeding LoD.

For example, for the first period (December 2019-January 2020), the mean displacement of the area
A₀ was 0.0021 m while the LoD was 0.0014 m. It was to note that the displacement exhibited similar
values with seasonal variations (acceleration during winter and spring, slowdown during the summer
and autumn). The cumulative displacement over the first six months was equal to 0.0074 m (December
2019-June 2020) and reached 0.0099 m between December 2019 and December 2020. Additionnaly a
slight increase in LoD value was observed, possibly due to evolution of vegetation and change of the
device. The acquisition (or pre-processing) of the point cloud of June 2021 was not to be taken into
account because of the excessive LoD. The value of displacements provided by the L-ICP method
aligned well with the available measurement data. They were of the same order of magnitude as the
mean value of the geodetic data and were higher than the radar data. Consequently, the L-ICP method
demonstrated its ability to provide accurate values of 3D displacements.

The M3C2 distance exhibited a high LoD (Figure 13 and Table 5) more than 0.005 m from the start of
the acquisitions. As a result, the computed values were only significant after one year in December
2020. The average C2M produced a low LoD (Figure 14 and Table 6) between 0.0013 and 0.0025 m
until March 2021. The computed distances values were thus significant from the first period.

Figure 9 presents a comparison of the results between the three methods focusing only on one area (A₂)
for better readability. We can note that the LoDs of averaged C2M and local registration based method
were similar while the LoD of M3C2 distance was significantly higher. The displacement values
provided by M3C2 distance and averaged C2M were similar to and lower than values calculated with the L-ICP method (almost twice). The real movement of the rocky part may not be necessarily normal to its mean surface. As demonstrated by the synthetic data in section 4.1, the M3C2 distance and averaged C2M methods could underestimate the real 3D displacements in such cases.

<figure><img src="image_42.png" /><figcaption>Figure 8: Comparison of 3D displacements derived with the local ICP registration approach with reference measurements</figcaption></figure>
<figure><img src="image_43.png" /><figcaption>Figure 9: Comparison of the 3D displacements derived the three tested methods with reference measurements for the area A2</figcaption></figure>

<table><caption>Table 3: displacement values (m) in function of time obtained with the local-ICP registration based: LoD deduced from the stable area and study of the evolution of the three areas A₀, A₁ et A₂</caption><thead><tr><th>Identifiant</th><th>Period</th><th>LoD</th><th>A<sub>0</sub></th><th>A<sub>1</sub></th><th>A<sub>2</sub></th></tr></thead><tbody><tr><td>1</td><td>17/12/2019-14/01/2020</td><td>0,0014</td><td>0,0021</td><td>0,0023</td><td>0,0028</td></tr><tr><td>2</td><td>17/12/2019-12/03/2020</td><td>0,0020</td><td>0,0046</td><td>0,0046</td><td>0,0048</td></tr><tr><td>3</td><td>17/12/2019-15/06/2020</td><td>0,0028</td><td>0,0074</td><td>0,0068</td><td>0,0074</td></tr><tr><td>4</td><td>17/12/2019-07/08/2020</td><td>0,0031</td><td>0,0076</td><td>0,0071</td><td>0,0077</td></tr><tr><td>5</td><td>17/12/2019-05/10/2020</td><td>0,0026</td><td>0,0086</td><td>0,0084</td><td>0,0094</td></tr><tr><td>6</td><td>17/12/2019-14/12/2020</td><td>0,0028</td><td>0,0099</td><td>0,0098</td><td>0,0117</td></tr><tr><td>7</td><td>17/12/2019-19/03/2021</td><td>0,0029</td><td>0,0178</td><td>0,0175</td><td>0,0197</td></tr><tr><td>8</td><td>17/12/2019-21/06/2021</td><td>0,0138</td><td>0,0232</td><td>0,0242</td><td>0,0251</td></tr><tr><td>6</td><td>17/12/2019-15/03/2022</td><td>0,0056</td><td>0,0326</td><td>0,0327</td><td>0,0359</td></tr></tbody></table>

In addition to the magnitude of the 3D displacements, the L-ICP method can provide the movement direction. From the 3D components of the displacements, the dip and direction in relation to the x-axis of the computed displacements could be calculated. Figure 10 indicates that the range of the direction (dip and direction in relation to the x-axis) was less wide in the area A₁ than on the stable zone. A
preferential direction appeared on the A₁ area with small variations as a function of time for the dip (length of the box less than 11°) and a relative regularity for the direction. On the stable area, we can observe noise with the variability of direction of the very small displacements (higher length of the box, the minimum length is more than 70°). The same analysis using results derived from the M3C2 method shows the directions of the normals calculated in the algorithm rather than the direction of displacement (Figure 15). The dip values varied between -20° and -42° for the L-ICP method and was equal to -14° for M3C2 distances in the area A₁. The directions varied between -39° and -52° for the L-ICP method and was equal to -31° for M3C2 distances in the area A₁.

To conclude with the column deformation mechanism, we obtained that the 3D displacements values and directions are constant along the column, with no gradient from bottom to top. We also observe a rigid translational movement, allowing us to identify a sliding mechanism rather than a toppling deformation mechanism.

<figure><img src="image_44.png" /></figure>
# 5 Discussion

As previously demonstrated on two data sets, the L-ICP method provides the 3D displacements (both the value and the direction). Obtaining the direction of movement is indeed crucial for understanding the underlying mechanisms involved in the rockfall. While two recent papers (Williams et al., 2021; Zahs et al., 2022) had the same objective, our approach recent papers is more automatic and easier. Unlike the computations of the C2M or M3C2 distances, our method does not assume a specific direction for the comparison of point clouds. The direction of displacements is an output of the proposed method rather than an input as it is often the case in the distance computations.

The assumption of rigid local movement is a key assumption of the method, enabling the two subclouds to be registered. This assumption is acceptable in the case of precursory movements within rock slopes and cliffs, since rotation or translation are limited. On the other hand, it does not limit the need for a single rigid movement in the scene. With the local approach, it is possible to highlight differential movements between areas with different movements.

Furthermore, the proposed method exhibits robustness regarding the choice of the reference cloud. In section 4, the first cloud is always chosen as reference. In this part, we test the ability to track differential evolutions by regularly changing the reference. We selected three clouds acquired on 17/12/2019, 12/03/2020 and 05/10/2020. We applied the L-ICP method three times to investigate the evolution during the periods 17/12/2019-12/03/2020, 12/03/2020-05/10/2020 and 17/12/2019-05/10/2020. The results are shown in the Table 4. We compared the sum of the 3D displacement values on the two sub-periods (17/12/2019-12/03/2020 and 12/03/2020-05/10/2020) and the value obtained on the full period (17/12/2019-05/10/2020). We observed that for the area A₀, the values were the same (0.0085 m vs to 0.0086 m). As, the dip and dip direction remained globally constant throughout the study period, the displacement vectors were almost in line. The above equality demonstrates that the
results are independent of the reference cloud choice. It is still necessary to ensure that the result remains above the LoD. This was the case as the LoD max value was equal to 0.0026 m.

<table><caption>Table 4: Comparison of results provided by the L-ICP method in function of the chosen reference cloud</caption><thead><tr><th></th><th>17/12/2019-<br>12/03/2020</th><th>12/03/2020-<br>05/10/2020</th><th>17/12/2019-<br>05/10/2020</th></tr></thead><tbody><tr><td>LoD of 3D displacement (m)</td><td>0,0020</td><td>0.0024</td><td>0,0026</td></tr><tr><td>A<sub>0</sub> – 3D displacement (m)</td><td>0,0046</td><td>0.0039</td><td>0,0086</td></tr><tr><td>A<sub>0</sub> – dip (°)</td><td>-38,2</td><td>-37,5</td><td>-41,5</td></tr><tr><td>A<sub>0</sub> – dip direction (°)</td><td>-54,8</td><td>-51,9</td><td>-54,3</td></tr><tr><td>A<sub>1</sub> – 3D displacement (m)</td><td>0,0046</td><td>0.0036</td><td>0,0084</td></tr><tr><td>A<sub>1</sub> – dip (°)</td><td>-32,4</td><td>-36,8</td><td>-38,3</td></tr><tr><td>A<sub>1</sub> – dip direction (°)</td><td>-44,6</td><td>-50,9</td><td>-49,0</td></tr><tr><td>A<sub>2</sub> – 3D displacement (m)</td><td>0,0048</td><td>0.0045</td><td>0,0094</td></tr><tr><td>A<sub>2</sub> – dip (°)</td><td>-38,5</td><td>-24,0</td><td>-33,8</td></tr><tr><td>A<sub>2</sub> – dip direction (°)</td><td>-39,4</td><td>-61,4</td><td>-47,7</td></tr></tbody></table>

Besides, the defined score enables the assessment of the local ICP registration quality: a score of 1 indicates that the proposed method is able to track objects locally. On the contrary, on score of 0 can highlight a morphological change such as a rockfall. An additional test was performed with the synthetic data (see section 3.1). The moved area (in blue Figure 2) is not translated but globally rotated of 180°. At a local scale and in the range of the selected parameters of the method (values of $r_n$ and $d$), there is no resemblance simulating thus a rockfall. Results are shown on Figure 11. It can be observed in this case that that the score of the changed area is equal to 0. This demonstrates that the proposed method effectively identifies non-continuous rockfall-type changes using the method's score.
<figure><img src="image_45.png" /><figcaption>Figure 11: Score of the L-ICP method in case of simulated rockfall</figcaption></figure>

We would like to come back to the choice of values for the method parameters specifically $r_n$, $r_s$ and $d$:

* $r_n$ must be chosen in function of the density of the point clouds and the dimension of the expected moving area. Sufficient points are indeed required to perform point cloud registration, which is a limitation of the method that's why it may not be able to detect and track the movement of stones or very small areas. Moreover, at the transition zone between the moving and stable areas, provided displacement values are not relevant resulting a score of 0. So $r_n$ must be small enough to detect small moving areas while being large to carry out the registration.

* The value of $r_s$ should be smaller than $r_n$ and is directed linked to the computation time. It determines the neighborhood of the registered point clouds where the distance is computed. With a value equal to $r_n$, the computation time will be longer but the quality of the registration would be better assessed.

* $d$ must be defined in function of the expected movements. For example, when tracking precursory displacements in a rock cliff, the expected magnitudes are typically a few millimeters or centimeters. This value depends on the frequency of acquisitions and is also connected to the computation time. The higher the $d$, the longer the computation time.
Directly related to the value of *d*, the question of the maximal detectable displacement arises.
Originally, the L-ICP method was developed to track precursory movements in a series of point clouds.
The magnitude of these movements is expected to be small (a few millimeters or centimeters in
translation and a few degrees in rotation). In this case, the L-ICP approach between the two
neighborhoods works well since the point clouds are close. There is thus a limit to the block rotation.
If the rotation of the unstable part is too great, the area seen during the two acquisitions will be different,
and the local registration will not work. In this case, we need to increase the frequency of acquisitions
to track the existing rotation. For translational movement, as its component increases, registrating two
local point clouds becomes more challenging. First, it is necessary to increase the value of *d* to be sure
that the area fitting with N₂ is available in N₁ (notations used in Figure 1). In case of large deformations
in landslides (Chanut et al., 2021), a high value of *d* needs to be chosen. In this configuration, the
algorithm may converge on a local minimum that does not correspond to the zone's registration with
its counterpart at time 2, as the displacement was large. The method cannot be applied as is and requires
adaptation. One possible solution is to perform the local registration in two stages: a coarse registration
with a high value *r*<sub>n</sub> and a low overlap between zones, followed by a fine registration because similar
areas would now be close together, as is the case for precursors monitoring.

To further improve the method, limiting the number of hidden zones during acquisition could enable
better accuracy in the local registration. Stereo-acquisitions of the same cliff area would provide a more
complete geometry.

Finally, the calculation time for a point with the code developed in python is about 1 s. It is therefore
not possible to apply it to all points sequentially as it stands. For a million points, the calculation time
would be 11.5 days. Several strategies can be deployed: parallelization and optimization of the code,
or a multi-scale approach by refining the calculation on potentially unstable zones.
## 6 Conclusion

The L-ICP method has been proposed for tracking precursory movements in rockfalls through the comparison of point clouds. The method is based on a local ICP registration of point clouds neighborhoods to determine the 3D displacement, including both the value and direction of the movement. This information is crucial for understanding underlying mechanisms involved during the instability. Additionally, a LoD is derived from stable zone analysis, providing further insights into the results.

The method was validated using synthetic data with an imposed known displacement and a variable noise level. The results demonstrated that the method is able to detect the “real” 3D displacements in any direction up to a signal to noise ratio equal to 0.5. Compared to the conventional methods such as M3C2 and C2M distances, the proposed method exhibited superior performance, especially in detecting in-plane movement whereas conventional are not able to detect it.

The application on an unstable rock (500 m³ column) in a rocky cliff confirmed its effectiveness to detect precursory movements and identify the deformation mechanism which is a sliding mechanism. The obtained 3D displacements have the same order of magnitude as the field measurements. In addition, the results do not depend on the point cloud chosen as reference. The proposed method tracks actually the deformation of the mass before failure. Moreover, the method demonstrated the ability to identify rockfall zones by detecting points with a zero correlation score.

To take things a step further, a few perspectives can be formulated. Firstly, the method could be adapted to quantify larger displacements, in addition to precursory movements. This requires the development of either coarse pre-registration or a multi-scale approach. Secondly, optimizing the code to handle larger point clouds containing millions of points would enhance the applicability of the method.

## 7 Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
8 Formatting of funding sources and acknowledgments

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors

9 Appendice

<table><thead><tr><th>σ (SNR)</th><th>L-ICP registration</th><th>M3C2</th><th>Averaged C2M</th></tr></thead><tbody><tr><td>0.001 m<br>(5)</td><td></td><td></td><td></td></tr><tr><td>0.002 m<br>(2.5)</td><td></td><td></td><td></td></tr><tr><td>0.005 m<br>(5)</td><td></td><td></td><td></td></tr><tr><td>0.01 m<br>(0.5)</td><td></td><td></td><td></td></tr></tbody></table>
<figure><img src="image_46.png" /><figcaption>Figure 12: Results of the three methods (L-ICP registration, M3C2 distance and averaged C2M) in the configuration $C_{3,\sigma}$ in function of $\sigma$</figcaption></figure>

<figure><img src="image_47.png" /><figcaption>Figure 13: comparison of 3D displacements derived with the M3C2 with reference measurements</figcaption></figure>
<figure><img src="image_48.png" /><figcaption>Figure 14 : comparison of 3D displacements derived with the averaged C2M distance with reference measurements</figcaption></figure>

<table><caption>Table 5 : displacement values (m) in function of time obtained with M3C2 distance: LoD deduced from the stable area and study of the evolution of the three areas A₀, A₁ et A₂ (Figure 3)</caption><thead><tr><th>Period</th><th>LoD</th><th>A<sub>0</sub></th><th>A<sub>1</sub></th><th>A<sub>2</sub></th></tr></thead><tbody><tr><td>17/12/2019-14/01/2020</td><td>0,0065</td><td>0,0020</td><td>0,0023</td><td>0,0039</td></tr><tr><td>17/12/2019-12/03/2020</td><td>0,0056</td><td>0,0033</td><td>0,0041</td><td>0,0035</td></tr><tr><td>17/12/2019-15/06/2020</td><td>0,0089</td><td>0,0053</td><td>0,0056</td><td>0,0056</td></tr><tr><td>17/12/2019-07/08/2020</td><td>0,0081</td><td>0,0052</td><td>0,0059</td><td>0,0058</td></tr><tr><td>17/12/2019-05/10/2020</td><td>0,0082</td><td>0,0065</td><td>0,0071</td><td>0,0090</td></tr><tr><td>17/12/2019-14/12/2020</td><td>0,0090</td><td>0,0081</td><td>0,0090</td><td>0,0115</td></tr><tr><td>17/12/2019-19/03/2021</td><td>0,0094</td><td>0,0132</td><td>0,0159</td><td>0,0158</td></tr><tr><td>17/12/2019-21/06/2021</td><td>0,0395</td><td>0,0163</td><td>0,0204</td><td>0,0158</td></tr><tr><td>17/12/2019-15/03/2022</td><td>0,0148</td><td>0,0228</td><td>0,0295</td><td>0,0235</td></tr></tbody></table>

<table><thead><tr><th>Period</th><th>LoD</th><th>A<sub>0</sub></th><th>A<sub>1</sub></th><th>A<sub>2</sub></th></tr></thead><tbody><tr><td>17/12/2019-14/01/2020</td><td>0,0013</td><td>0,0015</td><td>0,0021</td><td>0,0021</td></tr><tr><td>17/12/2019-12/03/2020</td><td>0,0014</td><td>0,0029</td><td>0,0038</td><td>0,0024</td></tr></tbody></table>
<table><caption>Table 6: displacement values (m) in function of time obtained with averaged C2M distance: LoD deduced from the stable area and study of the evolution of the three areas A₀, A₁ et A₂ (Figure 3)</caption><tr><td>17/12/2019-15/06/2020</td><td>0,0018</td><td>0,0042</td><td>0,0052</td><td>0,0036</td></tr><tr><td>17/12/2019-07/08/2020</td><td>0,0016</td><td>0,0043</td><td>0,0055</td><td>0,0036</td></tr><tr><td>17/12/2019-05/10/2020</td><td>0,0018</td><td>0,0053</td><td>0,0066</td><td>0,0058</td></tr><tr><td>17/12/2019-14/12/2020</td><td>0,0023</td><td>0,0067</td><td>0,0084</td><td>0,0082</td></tr><tr><td>17/12/2019-19/03/2021</td><td>0,0025</td><td>0,0114</td><td>0,0148</td><td>0,0121</td></tr><tr><td>17/12/2019-21/06/2021</td><td>0,0173</td><td>0,0135</td><td>0,0190</td><td>0,0142</td></tr><tr><td>17/12/2019-15/03/2022</td><td>0,0039</td><td>0,0200</td><td>0,0275</td><td>0,0204</td></tr></table>

<figure><img src="image_49.png" /><figcaption>Figure 15: direction of computation of M3C2 distances</figcaption></figure>

References

Abellán, A., Calvet, J., Vilaplana, J.M., Blanchard, J., 2010. Detection and spatial prediction of rockfalls by means of terrestrial laser scanner monitoring. Geomorphology 119, 162–171.

https://doi.org/10.1016/j geomorph.2010.03.016
528 Abellán, A., Jaboyedoff, M., Oppikofer, T., Vilaplana, J.M., 2009. Detection of millimetric deformation using a terrestrial laser scanner: experiment and application to a rockfall event. Nat. Hazards Earth Syst. Sci. 9, 365–372.
529 https://doi.org/10.5194/nhess-9-365-2009

531 Abellán, A., Oppikofer, T., Jaboyedoff, M., Rosser, N.J., Lim, M., Lato, M.J., 2014. Terrestrial laser scanning of rock slope instabilities: STATE-OF-SCIENCE (TERRESTRIAL LiDAR VS. ROCK SLOPE INSTABILITIES). Earth Surf. Process. Landf. 39, 80–97. https://doi.org/10.1002/esp.3493

534 Barbarella, M., Fiani, M., 2013. Monitoring of large landslides by Terrestrial Laser Scanning techniques: field data collection and processing. Eur. J. Remote Sens. 46, 126–151. https://doi.org/10.5721/EuJRS20134608

536 Besl, P.J., McKay, N.D., 1992. A method for registration of 3-D shapes. IEEE Trans. Pattern Anal. Mach. Intell. 14, 239–256. https://doi.org/10.1109/34.121791

538 Bitelli, G., Dubbini, M., Zanutta, A., 2004. Terrestrial Laser Scanning and digital photogrammetry techniques to monitor landslide bodies. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 35 (B5), 246–251.

540 Blanch, X., Abellan, A., Guinau, M., 2020. Point Cloud Stacking: A Workflow to Enhance 3D Monitoring Capabilities Using Time-Lapse Cameras. Remote Sens. 12, 1240. https://doi.org/10.3390/rs12081240

542 Blanch, X., Eltner, A., Guinau, M., Abellan, A., 2021. Multi-Epoch and Multi-Imagery (MEMI) Photogrammetric Workflow for Enhanced Change Detection Using Time-Lapse Cameras. Remote Sens. 13, 1460. https://doi.org/10.3390/rs13081460

545 Brodu, N., Lague, D., 2012. 3D terrestrial lidar data classification of complex natural scenes using a multi-scale dimensionality criterion: Applications in geomorphology. ISPRS J. Photogramm. Remote Sens. 68, 121–134. https://doi.org/10.1016/j.isprsjprs.2012.01.006

548 Casagli, N., Catani, F., Del Ventisette, C., Luzi, G., 2010. Monitoring, prediction, and early warning using ground-based radar interferometry. Landslides 7, 291–301. https://doi.org/10.1007/s10346-010-0215-y

550 Casagli, N., Frodella, W., Morelli, S., Tofani, V., Ciampalini, A., Intrieri, E., Raspini, F., Rossi, G., Tanteri, L., Lu, P., 2017. Spaceborne, UAV and ground-based remote sensing techniques for landslide mapping, monitoring and early warning. Geoenvironmental Disasters 4, 9. https://doi.org/10.1186/s40677-017-0073-1

553 Chanut, M.-A., Gasc-Barbier, M., Dubois, L., Carotte, A., 2021. Automatic identification of continuous or non-continuous evolution of landslides and quantification of deformations. Landslides. https://doi.org/10.1007/s10346-021-01709-2
556 Chanut, M.-A., Kasperski, J., Dubois, L., Dauphin, S., Duranthon, J.-P., 2017. Quantification des déplacements 3D par la
557 méthode PLAS – application au glissement du Chambon (Isère). Rev. Fr. Géotechnique 4.

558 https://doi.org/10.1051/geotech/2017009

559 Crosta, G.B., Agliardi, F., Rivolta, C., Alberti, S., Dei Cas, L., 2017. Long-term evolution and early warning strategies for
560 complex rockslides by real-time monitoring. Landslides 14, 1615–1632. https://doi.org/10.1007/s10346-017-0817-8

562 Day, S.S., Gran, K.B., Belmont, P., Wawrzyniec, T., 2013. Measuring bluff erosion part 1: terrestrial laser scanning
563 methods for change detection: MEASURING BLUFF EROSION PART 1. Earth Surf. Process. Landf. 38,
564 1055–1067. https://doi.org/10.1002/esp.3353

565 Delacourt, C., 2004. Velocity field of the “La Clapière” landslide measured by the correlation of aerial and QuickBird
566 satellite images. Geophys. Res. Lett. 31, L15619. https://doi.org/10.1029/2004GL020193

567 Dubois, L., Chanut, M.-A., Duranthon, J.-P., 2014. Amélioration continue des dispositifs d'auscultation et de surveillance
568 intégrés dans le suivi du versant instable des Ruines de Sechilienne. Géologues 182, 50–55.

569 Durville, J.-L., Kasperski, J., Duranthon, J.-P., 2009. The Séchilienne landslide : monitoring and kinematics., in: Rainfall
570 Induced Landslides. Presented at the 1st Italian Workshop on Landslides, Napoli, pp. 174–180.

571 Fanti, R., Gigli, G., Lombardi, L., Tapete, D., Canuti, P., 2013. Terrestrial laser scanning for rockfall stability analysis in
572 the cultural heritage site of Pitigliano (Italy). Landslides 10, 409–420. https://doi.org/10.1007/s10346-012-0329-5

574 Franceschi, M., Teza, G., Preto, N., Pesci, A., Galgaro, A., Girardi, S., 2009. Discrimination between marls and
575 limestones using intensity data from terrestrial laser scanner. ISPRS J. Photogramm. Remote Sens. 64, 522–528.
576 https://doi.org/10.1016/j.isprsjprs.2009.03.003

577 Giacomini, A., Thoeni, K., Santise, M., Diotri, F., Booth, S., Fityus, S., Roncella, R., 2020. Temporal-Spatial Frequency
578 Rockfall Data from Open-Pit Highwalls Using a Low-Cost Monitoring System. Remote Sens. 12, 2459.
579 https://doi.org/10.3390/rs12152459

580 Girardeau-Montaut, D., 2022. Cloud Compare Version 2.6.1 User Manual.

581 Giraudot, S., Lafarge, F., 2023. Classification. In CGAL User and Reference Manual. CGAL Editorial Board, 5.5.2
582 edition, 2023.

583 Jaboyedoff, M., Oppikofer, T., Abellán, A., Derron, M.-H., Loye, A., Metzger, R., Pedrazzini, A., 2012. Use of LIDAR in
584 landslide investigations: a review. Nat. Hazards 61, 5–28. https://doi.org/10.1007/s11069-010-9634-2
585 Kaab, A., 2000. Photogrammetry for early recognition of high mountain hazards: New techniques and applications. Phys.

586 Chem. Earth Part B Hydrol. Oceans Atmosphere 25, 765-770. https://doi.org/10.1016/S1464-1909(00)00099-X

587 Kasperski, J., Delacourt, C., Allemand, P., Potherat, P., Jaud, M., Varrel, E., 2010. Application of a Terrestrial Laser
Scanner (TLS) to the Study of the Séchilienne Landslide (Isère, France). Remote Sens. 2, 2785-2802.

589 https://doi.org/10.3390/rs122785

590 Kromer, R., Abellán, A., Hutchinson, D., Lato, M., Edwards, T., Jaboyedoff, M., 2015. A 4D Filtering and Calibration

591 Technique for Small-Scale Point Cloud Change Detection with a Terrestrial Laser Scanner. Remote Sens. 7,

592 13029-13052. https://doi.org/10.3390/rs71013029

593 Kromer, R.A., Abellán, A., Hutchinson, D.J., Lato, M.,nut, M.-A., Dubois, L., Jaboyedoff, M., 2017. Automated
594 terrestrial laser scanning with near-real-time change detection – monitoring of the Séchilienne landslide. Earth

595 Surf. Dyn. 5, 293-310. https://doi.org/10.5194/esurf-5-293-2017

596 Kromer, R.A., Hutchinson, D.J., Lato, M.J., Gauthier, D., Edwards, T., 2015. Identifying rock slope failure precursors
597 using LiDAR for transportation corridor hazard management. Eng. Geol. 195, 93-103.

598 https://doi.org/10.1016/j.enggeo.2015.05.012

599 Lague, D., Brodu, N., Leroux, J., 2013. Accurate 3D comparison of complex topography with terrestrial laser scanner:
600 Application to the Rangitikei canyon (N-Z). ISPRS J. Photogramm. Remote Sens. 82, 10-26.

601 https://doi.org/10.1016/j.isprsjprs.2013.04.009

602 Leprince, S., Ayoub, F., Klinger, Y., Avouac, J.P., 2007. Co-Registration of Optically Sensed Images and Correlation
603 (COSICorr): An operational methodology for ground deformation measurements. Presented at the IEEE

604 International Geoscience and Remote Sensing Symposium (IGARSS 2007), Barcelona.

605 Lowe, D.G., 1999. Object recognition from local scale-invariant features, in: Proceedings of the Seventh IEEE
606 International Conference on Computer Vision. Presented at the Proceedings of the Seventh IEEE International
607 Conference on Computer Vision, IEEE, Kerkyra, Greece, pp. 1150-1157 vol.2.

608 https://doi.org/10.1109/ICCV.1999.790410

609 Mayr, A., Bremer, M., Rutzinger, M., 2020. 3D POINT ERRORS AND CHANGE DETECTION ACCURACY OF
610 UNMANNED AERIAL VEHICLE LASER SCANNING DATA. ISPRS Ann. Photogramm. Remote Sens. Spat.
611 Inf. Sci. V-2-2020, 765-772. https://doi.org/10.5194/isprs-annals-V-2-2020-765-2020

612 Michoud, C., Carrea, D., Costa, S., Derron, M.-H., Jaboyedoff, M., Delacourt, C., Maquaire, O., Letortu, P., Davidson,
613 R., 2015. Landslide detection and monitoring capability of boat-based mobile laser scanning along Dieppe
614 coastal cliffs, Normandy. Landslides 12, 403-418. https://doi.org/10.1007/s10346-014-0542-5
615 Monserrat, O., Crosetto, M., 2008. Deformation measurement using terrestrial laser scanning data and least squares 3D surface matching. ISPRS J. Photogramm. Remote Sens. 63, 142–154.

617 https://doi.org/10.1016/j.isprsjprs.2007.07.008

618 Nagler, T., Rott, H., Kamelger, A., 2002. Analysis of Landslides in Alpine Areas by Means of SAR Interferometry, in: Proceedings of IEEE International Geoscience and Remote Sensing Symposium. Presented at the Proceedings of IEEE International Geoscience and Remote Sensing Symposium, Toronto, Canada.

621 Oppikofer, T., Jaboyedoff, M., Blikra, L., Derron, M.-H., Metzger, R., 2009. Characterization and monitoring of the Åknes rockslide using terrestrial laser scanning. Nat. Hazards Earth Syst. Sci. 9, 1003–1019.

623 https://doi.org/10.5194/nhess-9-1003-2009

624 Rascle, P., 2023. CloudComPy.

625 Remondino, F., Guarnieri, A., Vettore, A., 2005. 3D modeling of close-range objects: photogrammetry or laser scanning?, in: Beraldin, J.-A., El-Hakim, S.F., Gruen, A., Walton, J.S. (Eds.), Presented at the Electronic Imaging 2005, San Jose, CA, p. 216. https://doi.org/10.1117/12.586294

628 Rosser, N.J., Petley, D.N., Lim, M., Dunning, S.A., Allison, R.J., 2005. Terrestrial laser scanning for monitoring the process of hard rock coastal cliff erosion. Q. J. Eng. Geol. Hydrogeol. 38, 363–375.

630 https://doi.org/10.1144/1470-9236/05-008

631 Royán, M.J., Abellán, A., Jaboyedoff, M., Vilaplana, J.M., Calvet, J., 2014. Spatio-temporal analysis of rockfall pre-failure deformation using Terrestrial LiDAR. Landslides 11, 697–709. https://doi.org/10.1007/s10346-013-0442-0

634 Samodra, G., Ramadhan, M.F., Sartohadi, J., Setiawan, M.A., Christanto, N., Sukmawijaya, A., 2020. Characterization of displacement and internal structure of landslides from multitemporal UAV and ERT imaging. Landslides 17, 2455–2468. https://doi.org/10.1007/s10346-020-01428-0

637 Spreafico, M.C., Perotti, L., Cervi, F., Bacenetti, M., Bitelli, G., Girelli, V.A., Mandanici, E., Tini, M.A., Borgatti, L., 2015. Terrestrial Remote Sensing techniques to complement conventional geomechanical surveys for the assessment of landslide hazard: The San Leo case study (Italy). Eur. J. Remote Sens. 48, 639–660. https://doi.org/10.5721/EuJRS20154835

641 Stumpf, A., Malet, J.-P., Allemand, P., Pierrot-Deseilligny, M., Skupinski, G., 2015. Ground-based multi-view photogrammetry for the monitoring of landslide deformation and erosion. Geomorphology 231, 130–145. https://doi.org/10.1016/j.geomorph.2014.10.039
644 Tantianuparp, P., Shi, X., Zhang, L., Balz, T., Liao, M., 2013. Characterization of Landslide Deformations in Three Gorges Area Using Multiple InSAR Data Stacks. Remote Sens. 5, 2704–2719.

646 https://doi.org/10.3390/rs5062704

647 Travelletti, J., Malet, J.-P., Delacourt, C., 2014. Image-based correlation of Laser Scanning point cloud time series for landslide monitoring. Int. J. Appl. Earth Obs. Geoinformation 32, 1–18.

649 https://doi.org/10.1016/j.jag.2014.03.022

650 Wang, G., Joyce, J., Phillips, D., Shrestha, R., Carter, W., 2013. Delineating and defining the boundaries of an active landslide in the rainforest of Puerto Rico using a combination of airborne and terrestrial LIDAR data. Landslides 10, 503–513. https://doi.org/10.1007/s10346-013-0400-x

653 Wheaton, J.M., Brasington, J., Darby, S.E., Sear, D.A., 2009. Accounting for uncertainty in DEMs from repeat topographic surveys: improved sediment budgets. Earth Surf. Process. Landf. n/a-n/a.

655 https://doi.org/10.1002/esp.1886

656 Williams, J.G., Anders, K., Winiwarter, L., Zahs, V., Höfle, B., 2021. Multi-directional change detection between point clouds. ISPRS J. Photogramm. Remote Sens. 172, 95–113. https://doi.org/10.1016/j.isprsjprs.2020.12.002

658 Williams, J.G., Rosser, N.J., Hardy, R.J., Brain, M.J., Afana, A.A., 2018. Optimising 4-D surface change detection: an approach for capturing rockfall magnitude-frequency. Earth Surf. Dyn. 6, 101–119.

660 https://doi.org/10.5194/esurf-6-101-2018

661 Zahs, V., Winiwarter, L., Anders, K., Williams, J.G., Rutzinger, M., Höfle, B., 2022. Correspondence-driven plane-based M3C2 for lower uncertainty in 3D topographic change quantification. ISPRS J. Photogramm. Remote Sens. 183, 541–559. https://doi.org/10.1016/j.isprsjprs.2021.11.018

664 Zhang, W., Qi, J., Wan, P., Wang, H., Xie, D., Wang, X., Yan, G., 2016. An Easy-to-Use Airborne LiDAR Data Filtering Method Based on Cloth Simulation. Remote Sens. 8, 501. https://doi.org/10.3390/rs8060501

666 Zhou, Q.-Y., Park, J., Koltun, V., 2018. Open3D: A Modern Library for 3D Data Processing. https://doi.org/10.48550/ARXIV.1801.09847

668