Saman Vafadar

Laurent Gajny

Matthieu Boëssé

Wafa Skalli

Evaluation of CNN-based human pose estimation for body segment lengths assessment

Keywords: ergonomics, anthropometry, deep learning, stereo vision

Human pose estimation (HPE) methods based on convolutional neural

networks (CNN) have demonstrated significant progress and achieved state-of-theart results on human pose datasets. In this study, we aimed to assess the performance of CNN-based HPE methods for measuring anthropometric data. A Vicon motion analysis system as the reference system and a stereo vision system recorded ten asymptomatic subjects standing in front of the stereo vision system in a static posture. Eight HPE methods estimated the 2D poses which were transformed to the 3D poses by using the stereo vision system. Percentage of correct keypoints, 3D error, and absolute error of the body segment lengths are the evaluation measures which were used to assess the results. Percentage of correct keypointsthe standard metric for 2D pose estimationshowed that the HPE methods could estimate the 2D body joints with a minimum accuracy of 99%. Meanwhile, the average 3D error and absolute error for the body segment lengths are 5 cm.

Introduction

Work on Convolutional Neural Network (ConvNet, or CNN) as a neural network model to imitate the ability of human being for pattern recognition has already begun since the late seventies [START_REF] Fukushima | Neocognition: a self[END_REF], [START_REF] Fukushima | Cognitron: A self-organizing multilayered neural network[END_REF]. However, the computational costs of ConvNets had restricted its extensive use. Nowadays, the GPU-accelerated computing techniques have made the training procedure more efficient [3], resulting in the wide applications of CNNs in handwriting recognition [START_REF] Wu | Improving handwritten Chinese text recognition using neural network language models and convolutional neural network shape models[END_REF], behavior recognition [START_REF] Jain | Hybrid deep neural networks for face emotion recognition[END_REF], human pose estimation [START_REF] Gong | Human Pose Estimation from Monocular Images: A Comprehensive Survey[END_REF], and medical image analysis [START_REF] Litjens | A survey on deep learning in medical image analysis[END_REF].

Human Pose Estimation (HPE) methods are computer vision techniques to localize the human body joints. HPE methods, depending on the interpretation of the body structure are categorized into generative, discriminative and hybrid methods [START_REF] Sarafianos | 3D Human pose estimation: A review of the literature and analysis of covariates[END_REF]. Generative methods match the image observations -or image features which are the most representative information, e.g., edges, silhouettes -with the projection of the employed human body model to the image by adjusting the body model. On the other hand, discriminative methods model the relations between the image observations and human poses [START_REF] Gong | Human Pose Estimation from Monocular Images: A Comprehensive Survey[END_REF]. For the moment, the most popular method for feature extraction is ConvNet. HPE methods based on ConvNets have demonstrated significant progress on challenging benchmarks (e.g. MPII [START_REF] Andriluka | 2D Human Pose Estimation: New Benchmark and State of the Art Analysis[END_REF]). The success of HPE methods based on ConvNets justifies investigation for specific applications such as anthropometry measurement.

The current applications of anthropometry measurements can be found in ergonomics. For instance, for designing fitting materials, such as the workspace and clothing to improve the safety and comfortability [START_REF] Bonnechère | Determination of the precision and accuracy of morphological measurements using the Kinect TM sensor: Comparison with standard stereophotogrammetry[END_REF]. This study aimed to evaluate the CNN-based HPE methods for measuring anthropometric data. A stereo vision system combined with 2D HPE methods were used to recover the 3D body joint positions. Also, a marker-based motion capture system was used to assess the validity of the results.

Materials and Methods

Ten healthy subjects (5 males, 5 females) after informed consent participated in this study. The work has been approved by the relevant ethics committee (CPP 06036). Subjects were on average 24 years old (SD: 2, range: 21-27), mean height was 173 cm (SD: 9 cm, range: 160-187 cm), mean body mass was 64 kg (SD: 9 kg, range: 53-80 kg), and mean Body Mass Index (BMI) was 21 (SD: 2, range: [START_REF] Chu | Multi-Context Attention for Human Pose Estimation[END_REF][START_REF] Yang | Learning Feature Pyramids for Human Pose Estimation[END_REF][START_REF] Heikkilä | A Four-step Camera Calibration Procedure with Implicit Image Correction[END_REF][START_REF] Bell | A comparison of the accuracy of several hip center location prediction methods[END_REF][START_REF] Xu | The validity of the first and second generation Microsoft Kinect for identifying joint center locations during static postures[END_REF][24][25].

Two calibrated and synchronized devices, a Vicon motion capture system (Vicon Motion Systems Ltd, UK) equipped with twelve Vicon Vero cameras as the reference system and a stereo vision system, were used to capture the data with the frequency of 100 Hz. The stereo vision system consisted of two GoPro Hero 7 Black cameras (GoPro, Inc., US) which recorded videos with the resolution of 1080p and linear field of view. The relative distance and angle between the two cameras were 75 cm and 15 deg, respectively, mounted on a tripod with a height of 120 cm.

Forty-eight reflective markers, according to a designed marker-set compatible with [START_REF] Leardini | A new anatomically based protocol for gait analysis in children[END_REF], [START_REF]Nexus 2.6, Documentation, Full body modeling with Plug-in Gait[END_REF], were attached to the subject's body segments. As shown in Figure 1Erreur ! Source du renvoi introuvable., subjects were asked to stand in a static posture in front of the stereo vision system, approximately 3.5 m away from the device, for 3 seconds. Table 1Erreur ! Source du renvoi introuvable. shows the detail of the estimation of the morphological data using the reconstructed 3D positions of the reflective markers.

The 3 seconds of the videos recorded by the stereo vision system resulted in 300 frames. For the first frame of each video, a bounding box was manually defined to crop the frame in which the subject was at the center. Then, for each next frame, a dynamic bounding box was determined based on the estimated pose of the previous frame so that the height of the subject was equal to 75% of the bounding box height. Then, the cropped frames were resized to the resolution of 256 × 256 pixels and 368 × 368 pixels which are compatible with the size of the input image of the selected HPE methods. The cropped and subsequently resized images were saved to be used as the input of HPE methods. Eight HPE methods [START_REF] Bulat | Binarized Convolutional Landmark Localizers for Human Pose Estimation and Face Alignment with Limited Resources[END_REF]- [START_REF] Yang | Learning Feature Pyramids for Human Pose Estimation[END_REF] based on convolutional neural networks for which codes were publicly available, achieving the state-of-theart results on challenging benchmarks (e.g., MPII [START_REF] Andriluka | 2D Human Pose Estimation: New Benchmark and State of the Art Analysis[END_REF]), have been selected to estimate the 2D poses. The 2D poses consist of 16 body keypoints including upper and lower head, neck, shoulders, elbows, wrists, torso, hips, knees and ankles (Wei et al., 2016 [17] estimate 14 keypoints; excluding lower head and torso). After 2D pose estimation for all the captured frames, since the subjects were standing in a static posture across the 300 frames, the mean values of the estimated body keypoints were computed. 2D to 3D pose lifting has been accomplished with the stereo vision system. After the intrinsic and extrinsic calibration of the stereo vision system, the 3D positions can be recovered using the perspective projection of the 3D point on the image planes. Herein, the retrieved 2D body keypoints were assumed to be the perspective projection of the corresponding 3D point on the left and right image plane; Thereby, the 3D positions of the body keypoints were obtained by using the linear triangulation method [START_REF] Heikkilä | A Four-step Camera Calibration Procedure with Implicit Image Correction[END_REF]. Hence, the morphological data were subsequently computed, as shown in Table 1Erreur ! Source du renvoi introuvable..Three metrics evaluate the accuracy of the HPE methods, PCKh, 3D error and absolute error of the body segments lengths. Percentage of Correct Keypoints normalized with the head segment length (PCKh) defines an estimated keypoint to Figure 1. One of the subjects standing in front of the stereo vision system (This image has been taken by the left camera of the stereo vision system).

be correct if the distance to the corresponding reference value is less than a threshold which is a function of the head segment length -for instance PCKh@0.5 considers the 50% of the head segment length as the threshold. 3D error measures the Euclidean distance between a reconstructed 3D keypoint and its reference value. Absolute error which have been used to compare the segment lengths consists of the absolute difference between the measured values by the Vicon and stereo vision system.

Table 1. The acronyms stand for: HLE = Humeral Lateral Epicondyle, HME = Humeral Medial Epicondyle, USP = Ulnar Styloid Process, RSP = Radial Styloid Process, HJC = Hip Joint Center (femoral head based on the method of Bell et al [START_REF] Bell | A comparison of the accuracy of several hip center location prediction methods[END_REF]), FLE = Femoral Lateral Epicondyle, FME = Femoral Medial Epicondyle, LM = Lateral Malleolus, MM = Medial Malleolus.

Body segment

Vicon system stereo vision system Forearm 0.5×(HLE+HME) -0.5×(USP+RSP) Elbow -Wrist Thigh HJC -0.5×(FLE+FME) Hip -Knee Leg 0.5× (FLE+FME) -0.5×(LM+MM) Knee -Ankle

Results

Figure 1Erreur ! Source du renvoi introuvable. shows the 2D pose estimation accuracy using the PCKh metric. The accuracy of all the selected HPE methods for 2D pose estimation was above 99% using the standard metric PCKh@0.5 [START_REF] Andriluka | 2D Human Pose Estimation: New Benchmark and State of the Art Analysis[END_REF]. Table 2 shows the 3D errors for body keypoints. The mean value of the 3D error is 5 cm. Table 3 shows the absolute error for the body segment lengths which were obtained based on the estimated 3D poses. The mean error for the lengths of the body segments, same as the 3D error, is 5 cm.

Discussion

In this study, with the goal of evaluation of CNN-based HPE methods for measuring body segment lengths, eight HPE methods were employed to estimate the 2D poses which were subsequently transformed to 3D poses using a stereo vision system. The body segment lengths were computed based on the estimated 3D poses. The results show the errors of 2D pose estimation, 3D reconstruction, and anthropometric data -following the selected hierarchy to compute the anthropometric data. Table 4 shows the accuracy of the HPE methods on the MPII dataset using the PCKh metric. These results showed that the most demanding body keypoints to estimate were the ankle, knee, and wrist. However, Figure 2, which shows the accuracy of the HPE methods on the dataset of this study, shows that the knee, hip, and elbow were the most difficult keypoints to locate accurately. Also, evaluation using PCKh@0.5 metric that measures the accuracy of all methods for all keypoints to be higher than 99% indicates that this value is comparably higher than the values reported in the literature. These two points highlight the role of the training and testing dataset. In the dataset of this study, there was no occlusion -neither selfocclusion nor occlusion by other entities -or challenging pose. Now, comparing all the HPE methods may underline that one method cannot outperform all other methods for all the body keypoints. For instance, Wei et al. 2016 [16] achieve the best performance for estimating the positions of the ankle, knee, elbow, and wrist, but its accuracy for the hip is significantly less than the other HPE methods -i.e., there is no universal method outperforming all the other methods.

The results showed that the main parameters influencing the accuracy of an HPE method based on CNNs can be, the architecture of the convolutional neural network, the training and testing dataset, and the training strategy. Size of the input image of Wei et al., 2016 [17], which is the most accurate methods for the estimation of wrist and ankle based on the results shown in Figure 2, is 368 × 368 while for the others is 256 × 256. Thus, it strengthens the hypothesis that the resolution of the input image could also be a prominent factor in determining the accuracy of the HPE methods. Also, there are minor parameters which affect the output of the HPE methods and thereby their accuracies, such as the noise of the input image, the position, and scale of the subject inside the cropped frames. Table 4. Quantitative results on the MPII dataset using the PCKh@0.5 metric.

ankle Knee hip elbow wrist Bulat et al., 2017 [13] 64.0 70.5 79.1 78.8 71. 5 Rafi et al., 2016 [14] 73.4 80.6 86.8 86.4 81. 3 Belagiannis et al., 2017 [15] 78.4 82.6 87.9 88.2 83.0 Wei et al., 2016 [16] 79.4 82.8 88.4 88.7 84.0 Bulat et al., 2016 [17] 81.9 85.7 89.4 89.9 85. 3 Newell et al., 2016 [18] 83.6 87.4 90.1 91.2 87. 1 Chu et al., 2017 [19] 85.0 88.0 90.6 91.9 88. 1 Yang et al., 2017 [20] 85.3 88.6 91.1 91.9 88.2

3D pose recovery has been made using the linear triangulation method by assuming that the estimated 2D poses are the perspective projection of the 3D pose. However, the deviation of the 2D poses from their reference value may be exacerbated through triangulation. Figure 3 shows an explicit example that the estimated ankle joints on the left and right images are not stereo correspondent -i.e., the estimated ankles (either left or right ankle) do not refer exactly to the same anatomical point.

Table 2 shows the 3D error for the body keypoints. The mean 3D error for the estimation of body keypoints is 5 cm. In a similar study [START_REF] Xu | The validity of the first and second generation Microsoft Kinect for identifying joint center locations during static postures[END_REF] which has used Microsoft Kinect ™ for 3D pose estimation in a static posture, the average 3D error in standing posture has been reported to be 8 cm and 9 cm for the first-and secondgeneration Kinect sensor, respectively.

The 3D error, reported in Table 2, shows that the maximum errors, for the elbow and wrist using the HPE method of Rafi et al., 2016 [14], are 60 cm and 67 cm, respectively. This occurrence is because of the false 2D detections of the HPE method for several frames of the static acquisition for one of the subjects. Table 3 shows the absolute error for the body segment lengths, while the mean error for the length of the body segments is 5 cm. A deeper look at this table shows that some methods cannot estimate the left and right body segment with the same accuracy. For instance, in the meanwhile that the 3D error for ankle and knee estimation, by Bulat et al., 2017 [13], is 4 cm, the absolute error for the left leg is 3 cm, and for the right leg is 6 cm. It also may highlight that post-processing could improve the uniformity of the results.

In conclusion, even though a stereo vision system combined with HPE methods can provide a cost-effective, easy to use, time efficient tool to measure the morphological data, the mean error is 5 cm that may not be adequate for applications in ergonomics. However, HPE methods may open new perspectives for measuring morphological data.

Figure 2 .

 2 Figure 2. Quantitative results on 2D estimated keypoints using PCKh metric.

Figure 3 .

 3 Figure 3. 2D estimation of the ankle joints for a single frame. The red, green, and blue dots, represent the estimation of the right ankle, left ankle, and the reference values, respectively.

Table 2 .

 2 Quantitative results on 3D reconstructed keypoints using 3D error. Mean (Min, Max) values are reported in millimeter.

	left ankle	left knee	left hip	left elbow	left wrist

Acknowledgments

The authors thank the ParisTech BiomecAM chair program, on subject-specific musculoskeletal modelling and in particular Société Générale and COVEA.


Pauline Letortu
email: pauline.letortu@univ-brest.fr

Roza Taouki
email: roza.taouki@univ-brest.fr

Marion Jaud
email: marion.jaud@univ-brest.fr

Stéphane Costa
email: stephane.costa@unicaen.fr

Olivier Maquaire
email: olivier.maquaire@unicaen.fr

Christophe Delacourt
email: christophe.delacourt@univ-brest.fr

Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline® (ASP®) and MicMac® processing chains

Keywords: Pléiades satellites, oblique images, 3D restitution, cliff face, coastal erosion

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Starting in the 2000s, the new generations of very high spatial resolution (less than 1 m in panchromatic mode) and agile satellites with short revisit time (QuickBird, WorldView, GeoEye, Pléiades, until around 40°) offer a greater scientific potential to combine large scale, high-resolution studies [START_REF] Poli | Radiometric and Geometric Evaluation of GeoEye-1, WorldView-2 and Pléiades-1A Stereo Images for 3D Information Extraction[END_REF][START_REF] Collin | High Resolution Topobathymetry Using a Pleiades-1 Triplet: Moorea Island in 3D[END_REF], and to do three-dimensional (3D) topographic reconstructions from pairs or triplets of images from different viewing angles. Some topics in geosciences have explored the potential of these new datasets. Elevation changes in glacier topography can be studied thanks to Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 3 Pléiades stereo imagery [START_REF] Berthier | Glacier Topography and Elevation Changes Derived from Pléiades Sub-Meter Stereo Images[END_REF], height changes due to earthquakes can be determined by stereo and tri-stereo reconstructions with a precision of a few decimetres [START_REF] Zhou | Assessing the Ability of Pleiades Stereo Imagery to Determine Height Changes in Earthquakes: A Case Study for the El Mayor-Cucapah Epicentral Area[END_REF], lava flow volume can be estimated with Digital Elevation Model (DEM) of Difference (DoD) computed from Pléiades triplet images [START_REF] Bagnardi | High-Resolution Digital Elevation Model from Tri-Stereo Pleiades-1 Satellite Imagery for Lava Flow Volume Estimates at Fogo Volcano[END_REF].

To observe all the changes of the coastal cliff, the entire cliff face (from the foot of the cliff to its top) should be observed. This means that the best point of view is horizontal. However, cliff face surveys are quite rare given that few datasets use this point of view. Until recently, most datasets had a vertical point of view (aerial photographs, aerial Light Detection And Ranging (LiDAR), satellite imagery, etc.), and therefore the most common proxy to determine the evolution of the cliff was the cliff top (e.g. [START_REF] Costa | Dynamique Littorale et Risques Naturels : L'impact Des Aménagements, Des Variations Du Niveau Marin et Des Modifications Climatiques Entre La Baie de Seine et La Baie de Somme[END_REF][START_REF] Zviely | Coastal Cliff Retreat Rates at Beit-Yannay, Israel, in the 20th Century[END_REF][START_REF] Foyle | Decade-Scale Coastal Bluff Retreat from LiDAR Data: Lake Erie Coast of NW Pennsylvania, USA[END_REF]. The arrival of agile (i.e. satellites able to observe the field from a high angle of incidence) and very high spatial resolution satellites, Terrestrial Laser Scanners (TLS), terrestrial photogrammetry, mobile laser scanners set up on a boat have made it easier to observe the cliff face and therefore to record its changes (e.g. [START_REF] Letortu | The Potential of Pléiades Images with High Angle of Incidence for Reconstructing the Coastal Cliff Face in Normandy (France)[END_REF][START_REF] Gulyaev | Terrestrial Methods for Monitoring Cliff Erosion in an Urban Environment[END_REF][START_REF] Letortu | Examining High-Resolution Survey Methods for Monitoring Cliff Erosion at an Operational Scale[END_REF]Michoud et al. 2014, respectively). Whereas i) coastal cliffs likely exist on roughly 52% of the global shoreline [START_REF] Young | Global Distribution of Coastal Cliffs[END_REF] ii) many people, houses, companies, infrastructure are/could be threatened by the risk of coastal erosion iii) there are high societal and political demands for reliable, homogeneous, perennial and low-cost data on long stretches of coastline in order to better understand erosion and protect inhabitants iv) various agile and very high spatial resolution satellites are available (e.g. QuickBird, GeoEye, WorldView and Pléiades), this research topic is still in its early stages with a unique paper [START_REF] Letortu | The Potential of Pléiades Images with High Angle of Incidence for Reconstructing the Coastal Cliff Face in Normandy (France)[END_REF]). Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 4 Pléiades-HR (High-Resolution Optical Imaging Constellation) is a twospacecraft constellation of CNES (the French Space Agency). The Pléiades 1A and 1B satellites were launched (16 December 2011, 02 December 2012, respectively) by the Soyuz launcher from the French Guiana Space in Kourou. The Pléiades satellites have six main qualities that are useful for coastal cliff studies (ASTRIUM 2012):

(1) The very high spatial resolution of their images (e.g. a ground sampling distance of 0.70 m at the nadir for panchromatic images);

(2) A high level of agility, with a theoretical viewing angle up to 47°;

(3) The daily revisit frequency;

(4) A swath width of 20 km at the nadir, in line with the coastal management scale, i.e. the hydro-sedimentary cell (from hundreds of metres to hundreds of kilometres);

(5) A mission lifetime of ten years and a continuity of measurements between the next versions of the satellites (Pléiades Neo constellation);

(6) Free access to the images under certain conditions for research institutes.

The EROFALITT (erosion of coastal cliffs) project was funded by CNES (2016CNES ( -2020) )  What is the best processing chain to obtain a 3D reconstitution of the cliff face between Ames Stereo Pipeline ® (ASP ® ) and MicMac ® from our image dataset?

Why?

 What are the key parameters that depend on the images or the processing chain per software in order to facilitate any transposition of our method to other sites or images (no need to test all the parameters, but only a few)?

A high angle of incidence and multi-date images acquired by a push broom sensor limit the number of software programmes that can be used to process images (e.g. ASP ® , ERDAS IMAGINE ® , Satellite Stereo Pipeline ® (S2P ® ), MicMac ® , Agisoft Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 6 Metashape ® ). Previously, we used ERDAS IMAGINE ® [START_REF] Letortu | The Potential of Pléiades Images with High Angle of Incidence for Reconstructing the Coastal Cliff Face in Normandy (France)[END_REF]; however open-source software and well-documented processing were important criteria in our choice of which software to test. Our goal is to understand why one software package or processing parameter works better than another, therefore we must avoid the 'black box' effect. Consistent with these requirements, we selected the ASP ® (https://ti.arc.nasa.gov/tech/asr/groups/intelligent-robotics/ngt/stereo/; [START_REF] Shean | An Automated, Open-Source Pipeline for Mass Production of Digital Elevation Models (DEMs) from Very-High-Resolution Commercial Stereo Satellite Imagery[END_REF]) and MicMac ® (https://micmac.ensg.eu/; Rupnik, Daakir, and Pierrot Deseilligny 2017) software programmes and the test will focus on the parameters used in stereo matching algorithms. The tests are based on the best images in our set acquired in June and July 2017 with pitch imaging angles of 40° and between 0° and 10° [START_REF] Letortu | The Potential of Pléiades Images with High Angle of Incidence for Reconstructing the Coastal Cliff Face in Normandy (France)[END_REF].

First, the material and methods including the study area will be described, then the results of our software and processing chain comparison will be presented and discussed.

Materials and methods

Study site

Located in Normandy (Seine-Maritime, NW France) along the English Channel, Varengeville-sur-Mer (1°00'27.34"E; 49°54'59.77"N) is characterized by sub-vertical coastal cliffs (70° to 90°) carved in Upper Cretaceous chalk with flints (part of the Paris Basin; [START_REF] Pomerol | Lithostratigraphy and Biostratigraphy of the Lewes and Seaford Chalks: A Link across the Anglo-Paris Basin at the Turonian-Senonian Boundary[END_REF][START_REF] Mortimore | Chalk Physical Properties and Cliff Instability[END_REF]). The study area stretches over 600 m, extending 300 m on both sides of the dry valley, called Petit Ailly (Figure 1). These cliffs are mainly white in colour (chalk), but are darkened (brown colour) by a bed comprised of clay and sand sediment from the Tertiary Period (Palaeogene). These cliffs are very prone to erosion (0.36 m year -1 between 2010 and 2017 (Letortu et al. Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 7 2019) whereas the average county retreat rate is 0.15 m year -1 (between Cap d'Antifer and Le Tréport, during the 1966-2008 period (Letortu et al. 2014)), with many rockfalls of several cubic metres to hundreds of thousands of cubic metres [START_REF] Letortu | Statistical and Empirical Analyses of the Triggers of Coastal Chalk Cliff Failure[END_REF].

A fatality occurred in August 2015 in Varengeville-sur-Mer due to falling rocks. Figure 1. Presentation of the study area of Varengeville-sur-Mer (Seine-Maritime, Normandy, France).

Climatically, the study area belongs to the western part of Europe, which is particularly exposed to the influences of low oceanic pressures, and thus, to the types of disturbed weather that dominate approximately 2/3 of the year [START_REF] Pédelaborde | Le Climat Du Bassin Parisien : Essai d'une Méthode Rationnelle de Climatologie Physique[END_REF][START_REF] Trzpit | Climat[END_REF]). Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 8

The average tidal range is 8 m (macrotidal environment). At low tide, the foreshore is characterized by a wide shore platform slightly inclined to the sea covered by sand and with a gravel barrier near the contact with the cliff foot. The average altitude of the Varengeville-sur-Mer cliffs is approximately 30 m and the coastline is relatively jagged due to rockfall scars that exploit pre-existing fracturing. The cliff face is oriented toward the NNE (Figure 1). This site, found on both sides of the dry valley of Petit Ailly, was chosen because the cliff dynamics are frequently monitored (e.g. [START_REF] Costa | Sedimentary Coastal Cliffs of Normandy: Modalities and Quantification of Retreat[END_REF]Letortu et al. 2019). Since 2010, it is surveyed by terrestrial laser scanners (3 to 4 times a year), Unmanned Aerial Vehicle (UAV) (up to once a year), and aerial topo-bathymetric LiDAR (every 3 years). Since 2014, it belongs to the French Observation National Service DYNALIT (coastal dynamics), which encompasses various coastal sites of scientific interest to better understand the coastal dynamics.

The acquisition of oblique and multi-date images from satellites in this study area is challenging for four reasons:

(1) cloudy and rainy weather is frequent because it is located in mid-latitudes where disturbed weather dominates, and therefore it can be rare to have good conditions for image acquisition;

(2) while the Pléiades satellites have a meridian orbit, the NNE orientation of the cliff face makes it difficult to acquire the image;

(3) the cliff face is sub-vertical (70° to 90°) and, due to its orientation, it is in the shadow cast by the cliff at the time the satellite passes over, even during summer (Figures 2 and3);

(4) a high tidal range may hide the cliff foot whereas the whole cliff face is needed. Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 9

Data

Images were acquired in autumn 2016 (four stereoscopic pairs), in summer 2017 (five stereoscopic pairs) and in winter 2017/2018 (five stereoscopic pairs), covering the 20 kmlong cliff line from Quiberville to Berneval-le-Grand (Figure 1). Out of these 28 images, the most relevant stereoscopic pairs for the 3D reconstitution are from June to July 2017 as the weather was sunny and there were few shadows on the cliff face [START_REF] Letortu | The Potential of Pléiades Images with High Angle of Incidence for Reconstructing the Coastal Cliff Face in Normandy (France)[END_REF].

We decided to focus on six relevant images (10 June 2017, 15 June 2017, 06

July 2017 with incidence angles of 0° to 10° and 40°) and therefore we reduced the study area to only around the dry valley of Petit Ailly at Varengeville-sur-Mer (600 m long), where validation data are available. Over this spatially limited area, a large number of tests on the image processing workflow can be considered in terms of computing resources and computing time (Figures 2 and3). Both methods proved to be relevant in coastal cliff erosion studies thanks to their high resolution and their centimetre precision [START_REF] Letortu | Examining High-Resolution Survey Methods for Monitoring Cliff Erosion at an Operational Scale[END_REF]. Since the images are taken from different viewpoints, the apparent motion of the scene between the views is computed (called "disparity" in the case of stereo-rectified image pairs) [START_REF] Hartley | Multiple View Geometry in Computer Vision[END_REF]. Stereo matching in the correlation step is the core of the image processing workflow (Figure 4). It involves identifying pixel correspondences between the left and right epipolar images. Our tests focused on this correlation step, which is different between ASP ® and MicMac ® . A disparity value is computed by correlation for each valid pixel identified in the input image. As the search window size is a key parameter of the correlation step and in order to be efficient in larger search ranges, a Gaussian pyramid approach is applied, that is to say disparities are first estimated using sub-sampled images, and are gradually refined at higher resolution.

Methods

Software packages

 Semi-Global Matching (SGM), introduced in Hirschmuller (2008). The "classical" SGM algorithm has undergone two important changes in ASP ® in order to include unrectified, larger images (NASA 2019): i) two-dimensional (2D) disparity search is performed, similarly to what is done in the Neighbor-Guided Semi-Global Matching algorithm [START_REF] Xiang | Low Complexity Optical Flow Using Neighbor-Guided Semi-Global Matching[END_REF]) and ii) ASP ® uses a multi-resolution hierarchical search combined with a compressed memory scheme similar to what is used in the SGM algorithm [START_REF] Rothermel | SURE: Photogrammetric Surface Reconstruction from Imagery[END_REF].

This SGM algorithm is based on multi-directional dynamic approaches. Even if it can be time-consuming because of significant memory requirements, SGM algorithm appears to be more effective in images with less texture and can discern finer resolution features than LSW since it tends to use much smaller matching kernels. However, SGM is prone to generate artefacts at tile boundaries and to produce inaccurate results in textureless regions. The ASP developers recommend using it cautiously in order to minimize these drawbacks (NASA In ASP ® , the cost-mode variable (Figure 5) allows the user to choose the cost function used during the correlation step:

 Normalized Correlation Coefficient (NCC) (cost mode 2): the traditional areabased matching cost is the square difference of the pixel intensities. NCC often accomplishes the matching cost aggregation. This is a window-based matching technique that accounts for compensating gain changes. The disparity is then determined by a local winner-take-all operation in a small search window and checking with a simple threshold. The last step is characterized by sub-pixel interpolation and other post processing [START_REF] Hu | Texture-Aware Dense Image Matching Using Ternary Census Transform[END_REF].

 Census Transform (cost mode 3): it associates a binary string to each pixel that encodes whether or not the pixel has a smaller intensity than each of its neighbours. Not only does it store the intensity ordering but also the spatial structure of the local neighbourhood [START_REF] Hirschmuller | Evaluation of Stereo Matching Costs on Images with Radiometric Differences[END_REF]. It performs well for outdoor environments with uncontrolled lighting. ASP ® allows the application of census transform only with the SGM correlator (NASA, 2019).

 Ternary Census Transform (cost mode 4): A modification of the census transform, which is more stable on low contrast terrain. The difference of the two census transform matching costs lies in the encoding of the results. For any given Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 16 rectangular window, a pixel will be encoded into a bit string in the Census Transform and into two bits in the Ternary Census Transform [START_REF] Hu | Texture-Aware Dense Image Matching Using Ternary Census Transform[END_REF].

In MicMac ® , the Malt tool proposes two semi-global matching algorithms, where the choice of the cost function is included in the step performed to choose a matching algorithm [START_REF] Rupnik | MicMac, Apero, Pastis and Other Beverages in a Nutshell![END_REF]) (Figures 4 and5):

 UrbanMNE is for a matching adapted to the urban digital elevation model. It handles matching in ground geometry, adapted to a scene that can be described by a single function Z = f(X,Y) (where X, Y, Z are Euclidean coordinates).

Having the output geometry equal to the input geometry, UrbanMNE is perfectly adequate for modelling quasi-planar objects.

 GeomImage is for matching in ground image geometry [START_REF] Rupnik | 3D Reconstruction from Multi-View VHR-Satellite Images in MicMac[END_REF]. In this case, matching is performed by using the 'ground image geometry', which is more flexible and better suited for the modelling of fully 3D objects. With this mode, the geometry of the modelling is adapted to a selected point of view, consistent with the acquisition. In addition, Malt GeomImage handles a 'One-Two-Pixel multi-view image matching' (1-2 pixel matching) method, which is a new matching cost function that produces surfaces with enhanced resolution compared to the window-based semi-global matching technique, where the data term is replaced by a multi-view single pixel similarity measure, and a two-pixel window [START_REF] Rupnik | More Surface Detail with One-Two-Pixel Matching[END_REF][START_REF] Rupnik | MicMac, Apero, Pastis and Other Beverages in a Nutshell![END_REF].

Because of different processing workflows, it could be difficult to standardize the processing parameters within the software itself and between software packages. We tried to optimize the consistency of the comparison (Figure 5). As the area of interest corresponds to steep slopes, we used small correlation windows (5 × 5 pixels, 7 × 7 pixels, 9 × 9 pixels), but the small size of the windows may introduce more false matches or noise (NASA 2019). For LSW, a larger correlation kernel is used (15 × 15) due to its difficulty to find tie points on the cliff face. The regularization factor adds a constraint on the a priori position of the reconstructed points. The higher the factor, the more regular the result. 2012). Bundle adjustment without GCPs ensure good results and do not introduce Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 18 undesirable deformations [START_REF] Rupnik | Refined Satellite Image Orientation in the Free Open-Source Photogrammetric Tools APERO/MICMAC[END_REF]. Because of frequent georeferenced point clouds (coming from UAV or TLS) as ground truth data, the roughly georeferenced satellite point clouds are then realigned by Iterative Closest Point (ICP) co-registration algorithm (CloudCompare ® ).

Quality Assessment

A relative precision criterion is compulsory in order be able to assess the 3D reconstruction quality and therefore the relevance of our data to make single-source or multi-source comparisons (TLS data or UAV data). Thus, 3D reconstructions from the Pléiades images were filtered (artefact removal), georeferenced and compared to ground truth data at Varengeville-sur-Mer, acquired on 26 June 2017 using UAV. These synchronous surveys (UAV and satellites) allow to limit errors due to erosion events.

The UAV and Pléiades point clouds were cut in order to have the same spatial extent (53700 m²) and the UAV point cloud was subsampled at 5 cm. A semi-automatic coregistration (ICP in CloudCompare ® ) using a rigid-body transform was performed to georeference the Pléiades point clouds by fitting on the UAV mesh (considered as the reference). This co-registration is efficiently constrained vertically (shore platform, plateau) and alongshore. Thus, the precision error of the Pléiades 3D reconstructions is assessed in comparison with Root Mean Square Error (RMSE in m) of the coregistration. Precision error is assessed in the cross-shore direction (which is the direction of erosion on the cliff face), based on the relative distance (normal of the cliff face) after fitting.

The georeferencing error (absolute error) is of lesser importance because we have frequent perfectly georeferenced and very high resolution surveys (TLS or UAV) that allow to align the point clouds coming from the Pléiades images. Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 Unsurprisingly, and regardless of the software used, satisfactory reconstructions (48/146) have a minimum of one image with an incidence angle of 40°. When the 3D reconstruction uses two images with angles of 0° to 10°, the cliff face reconstruction is, at best, assessed as 'few satisfactory', i.e. with noise, artefacts or holes (Table 1) due to the acquisition geometry which is not adapted to the sub-vertical cliff face [START_REF] Jaud | UAV Survey of a Coastal Cliff Face -Selection of the Best Imaging Angle[END_REF][START_REF] Letortu | The Potential of Pléiades Images with High Angle of Incidence for Reconstructing the Coastal Cliff Face in Normandy (France)[END_REF]. There are more satisfactory reconstructions of the cliff face when the stereo restitution uses two images with an angle of 40°. Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 21 Among the 146 tests, the best 3D reconstruction per image pair was selected based on the three parameters described below. The objective was to select a satisfactory 3D reconstruction, with the best compromise between low mean distance and standard deviation values, and a high point density value (Table 1). The best reconstructions were selected and there are ten (Table 2). Taking only the mean error and standard deviation values into account, the reconstructions from the 0° to 10° datasets may seem more precise than the 40° stereo pairs, but in reality, this is weighted by the fact that most of the points reconstructed at 0° to 10° are located on the top of the cliff and less on the cliff face.

Results

Criteria for 3D reconstruction ranking

Identification of the best image processing chain for the 3D cliff face reconstruction

The comparison is made on the satisfactory results obtained with ASP ® and with MicMac ® (Table 2). The precision of the cliff face reconstruction is slightly better with MicMac ® than with ASP ® (average relative distance of 0.04 m and -0.05 m, respectively) along with the standard deviation, which is lower with MicMac ® than with ASP ® (average standard deviation of 1.72 m and 2.46 m, respectively). Furthermore, point clouds with MicMac ® present a higher density (1.57 point m -² on average) than with ASP ® (0.75 point m -² on average). With a better average precision associated with a lower error dispersion on the cliff face and a higher point density, the 3D reconstruction with MicMac ® provides the most reliable dataset. The relative differences in the 3D restitution from the image sets at 40° are distributed randomly over the entire cliff face (Figure 7). These are mainly artefacts or noise that have not been removed during manual filtering. Per software programme, the best processing chain is (Table 2, Figure 8):  In ASP ® : MGM/SSGM matching algorithm, with a cost mode 3 or 4 and a correlation kernel of 7 × 7.

 In MicMac ® : GeomImage (1-2 pixel matching) matching algorithm with a correlation window size of 3 × 3 or 7 × 7, associated with a regularization parameter of 0.10. In MicMac ® , GeomImage matching algorithm has better results than UrbanMNE one due to the topography of the cliff face and the acquisition geometry. As illustrated in Figure 8, the SGM methods provide better results as they are solved with multi-directional dynamic programming techniques, and thereby do not impose any constraints on the regularity term. The optimization is thus resolved along independent lines of pixels. These approaches provide robust reconstructions within a reasonable processing time (around 30 min for images of 1 million pixels). The reconstructed surfaces are morphologically preserved because the template windows chosen are small (3 × 3, 7 × 7) in the optimization process. In the SGM approach, occlusions are typically predicted by performing a symmetric consistency check in a stereo pair. Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857

Discussion

Potential of this approach for diachronic monitoring

The presented dataset is rather original and challenging given its unusual configuration (high imaging angle, multiple dates) and the fact that the images present shadows over the area of interest. Thus, this study highlights the flexibility of the tested processing chains.

At this stage, a first quantification of the eroded volume can be estimated by using a 'satisfactory' cliff face reconstruction and an older dataset collected in 2015 using TLS. A difference was calculated between the point cloud of the stereoscopic pair on 10 June 2017 and 15 June 2017 at 40° and the TLS mesh collected on 25 September 2015. On the eastern part of the cliff face, where there is an erosion area, the Pléiades-TLS comparison calculates an eroded volume of 796.5 m 3 for a surface area spanning 4752.5 m². This calculation is then compared with the result of the differences between the TLS mesh (25 September 2015) and the UAV point cloud (26 June 2017) which leads to an eroded volume of 1134.4 m 3 (over the same surface, knowing that the surface affected by the rockfall is of 543 m²) (Figure 9). The difference in the two volumetric estimations demonstrates that it is possible to quantify erosion by using Pléiades satellite photogrammetry within a margin of error of approximately 0.071 m 3 m -2 . Figure 9 For highly erosive areas, high angle of incidence images from the Pléiades satellites provide a new approach for a first order quantification of erosion on large portions of cliff lines (in line with the hydro-sedimentary cell), with high repeatability, satisfactory resolution and precision, and at low cost. This method therefore provides major opportunities for improving the knowledge about coastal cliff dynamics thanks to the rockfall detection threshold assessed at 100 m 3 , which corresponds to 69% of rockfalls censed around the study area [START_REF] Letortu | Statistical and Empirical Analyses of the Triggers of Coastal Chalk Cliff Failure[END_REF]. The creation of a considerable rockfall database on large stretches of coasts is thus possible, which could help to better understand rockfall triggers and, ultimately, to protect people [START_REF] Naylor | Rock Coast Geomorphology: Recent Advances and Future Research Directions[END_REF]. Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 28

Contribution of tri-stereo reconstruction

MicMac ® gives the best results in stereoscopic reconstruction and, unlike ASP ® , it can also be used to perform tri-stereoscopic reconstructions. Eighteen tri-stereo tests were carried out with MicMac ® from images with an incidence angle of 40° (10 June 2017, 15 June 2017 and 18 June 2017, Table 3), they are mostly satisfactory (11/18).

Compared with stereoscopic pairs, the point density is slightly higher with a stereoscopic triplet (1.82 point m -² versus 1.70 point m -²), the mean distance is lower (0.01 m versus 0.04 m) but has a higher data dispersion (standard deviation of 2.14 m versus 1.72 m) due to the presence of a higher number of artefacts.

Conclusions

As previously mentioned [START_REF] Jaud | UAV Survey of a Coastal Cliff Face -Selection of the Best Imaging Angle[END_REF][START_REF] Letortu | The Potential of Pléiades Images with High Angle of Incidence for Reconstructing the Coastal Cliff Face in Normandy (France)[END_REF], a stereo restitution of the cliff face based on images with an angle of incidence of 0° to 10° appears not adapted to the sub-vertical slope (70° to 90°) whereas images with an angle of incidence Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 29 of 40° allow satisfactory results to be achieved. Between ASP ® and MicMac ® , the best open-source stereo restitution software to use high angle incidence and multi-date images is MicMac ® and the best performance is obtained using GeomImage (1-2 pixel matching) with a size of correlation window of 3 × 3 or 7 × 7 associated with a regularization parameter of 0.10. With these parameters, 3D cliff face reconstructions have an average point density of 1.70 point m -², a mean distance from UAV ground truth data of 0.04 m and a standard deviation of 1.72 m. The ASP ® software with the MGM/SSGM stereo matching algorithm is the second-best option, with cost mode 3 or 4 and a correlation kernel of 7 × 7. These parameters provide point clouds with an average point density of 0.79 point m -², a mean distance of -0.06 m and a standard deviation of 2.46 m. These point cloud characteristics used in a diachronic approach can detect rockfalls above 100 m 3 , which includes the large majority of rockfalls (69%) around the study area [START_REF] Letortu | Statistical and Empirical Analyses of the Triggers of Coastal Chalk Cliff Failure[END_REF]. Pléiades oblique images appear to be a great opportunity for monitoring cliff faces, for quantifying erosion over large spans of coastline and for creating a rockfall database which could help to better understand rockfall triggers (in order to people prevention/protection).

Future projects aim at developing new approaches to optimize the detection and quantification of cliff face erosion using Pléiades images (including the Pléiades Neo constellation that will be launched in 2021 and 2022, with a spatial resolution of panchromatic images of 0.30 m at the nadir). To achieve this goal, images should have an angle of incidence from 20° to 30° (the best imaging angles for cliff face survey [START_REF] Jaud | UAV Survey of a Coastal Cliff Face -Selection of the Best Imaging Angle[END_REF] when cliffs have a sub-vertical slope (70° to 90°) as in Varengevillesur-Mer) and should be acquired in a favourable environment (few cloud cover and cliff face orientation parallel to the Pléiades orbit). About the method, instead of relying on a 3D reconstruction of the entire cliff face by stereo-and tri-stereo restitution, new

  in order to explore the potential of Pléiades images to monitor the evolution of coastal cliffs by observing the cliff face proxy. With Pléiades images with a high angle incidence, 3D reconstitutions of cliff faces along the coast of Normandy (NW France) were performed. This project was challenging because:  It is located in Varengeville-sur-Mer (Seine-Maritime), where disturbed weather and the NNE orientation of the cliff face can alter the image quality (due to clouds and shadows, respectively);  It has uncommon image acquisition modalities: because of the NNE orientation of the cliff face, it was shown that the standard stereo or tri-stereo acquisition was unsuitable. Another acquisition modality was proposed: a multi-date survey over several consecutive days. As the orbital pass position of the Pléiades satellites changes daily, a mono-acquisition up to an incidence angle of 40° (across-track) acquired on successive days (around 13:20 in local time, Universal Time Coordinated (UTC) + 2) can be used to observe the cliff face at various viewing angles to reconstruct it in 3D via stereo restitution. To assess the impact of the angle of incidence, two sets of images were simultaneously requested each day: one with a pitch imaging angle of 40° and a second one with a pitch imaging angle between 0° and 10° (more details in Letortu et al. 2020);  There is a limited choice of image processing software programmes as this is an unusual image dataset.The objectives of this paper are to answer two main questions:

  Figure 2. Date, local time of satellite pass, solar zenith angle, and incidence angle of the images selected for the tests.

  Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 13The image processing workflow of each software mainly follows the traditional stereo restitution steps for 3D reconstructions (Figure4): input data, cropped data, image alignment, correlation and 3D point cloud generation(NASA 2019;[START_REF] Rupnik | MicMac, Apero, Pastis and Other Beverages in a Nutshell![END_REF]).

Figure 4 .

 4 Figure 4. Image processing workflow of ASP ® and MicMac ® to obtain a 3D point cloud (NASA 2019; Rupnik et al. 2020).

  Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 14 In ASP ® , three matching algorithms are possible (Figures4 and 5): Local Search Window (LSW), which is the default ASP ® correlation algorithm.



  More Global Matching/Smooth Semi-Global Matching (MGM/SSGM): introduced in[START_REF] Facciolo | MGM: A Significantly More Global Matching for Stereovision[END_REF], the MGM algorithmLetortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857 15 (also called SSGM algorithm) reduces the amount of high-frequency artefacts in textureless regions in the output image but at the expense of a longer computing time. A hybrid SGM/MGM mode is also proposed in ASP ® where MGM only is used for the final resolution level which obtains results somewhere between the pure SGM and MGM options (NASA 2019).

Figure 5 .

 5 Figure 5. Parameters for the matching algorithms tested in (a) ASP ® and (b) MicMac ® .

  Figure 6. Cliff face reconstructed from UAV data (RICOCHET project, 26 June 2017) (a) and quality ranking of the 3D reconstructions from Pléiades images at Varengevillesur-Mer: (b) not satisfactory result (10 June 2017 and 15 June 2017 at 40°, MicMac ® , UrbanMNE, size of correlation window: 5 × 5, regularization factor: 0.20), (c) few satisfactory result (10 June 2017 and 15 June 2017 at 40°, ASP ® , Local Search Window, cost mode: 2, correlation kernel: 15 × 15, subpixel kernel: 41 × 41), (d) satisfactory result (10 June 2017 and 15 June 2017 at 40°, MicMac ® , GeomImage, multi scale correlation: 1, size of correlation window: 3 × 3, regularization factor: 0.05).

Figure 7 .

 7 Figure 7. Relative distance of the cliff face normals (in m) at Varengeville-sur-Mer between the 3D reconstructions (stereoscopic pair on 15 June 2017 and (a) 06 July 2017 at 40°) with (b) ASP ® (More Global Matching, cost mode: 3, correlation kernel: 7 × 7) and (c) MicMac ® (GeomImage, size of correlation window: 3 × 3, regularization parameter: 0.10) compared with (d) UAV 3D reconstruction (26 June 2017).

Figure 8 .

 8 Figure 8. Best parameters (in bold) for satisfactory 3D reconstructions of the cliff face at Varengeville-sur-Mer with (a) ASP ® and (b) MicMac ® .

  Figure 9. (a) Relative distance (m) of the cliff face between the TLS mesh (25 September 2015) and (b) the UAV data (26 June 2017) with detected erosion at Varengeville-sur-Mer.

  Table 3. 3D reconstruction tests based on tri-stereo matching in MicMac ® (triplet images: 10 June 2017-15 June 2017-18 June 2017).

Table 1 .

 1 Extract of the original table of the 146 tests with the selection of the best 3D reconstruction per pair (e.g. 10 June 2017 and 15 June 2017 at 40° using MicMac ® ).

Table 2 .

 2 The best cliff face 3D reconstructions per image pair based on 146 tests.

Acknowledgments

This work is also part of the Service National d'Observation DYNALIT, via the research infrastructure ILICO. The Pléiades images are subject to copyright: Pléiades © CNES, Distribution Astrium Services. Letortu P., Jaud M., Taouki M, Costa S., Maquaire O., Delacourt C., 2021. Three-dimensional (3D) reconstructions of the coastal cliff face in Normandy (France) based on oblique Pléiades imagery: assessment of Ames Stereo Pipeline ® (ASP ® ) and MicMac ® processing chains. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2021.1892857

Funding

This research was supported by the CNES (EROFALITT project). It is based on observations with the Pléiades satellites. This work was also funded by the ISblue project, the Interdisciplinary graduate school for the blue planet (ANR-17-EURE-0015), and was co-funded via a grant from the French government under the 'Investissements d'Avenir' programme. This work was also supported by the ANR project 'RICOCHET: multi-risk assessment on coastal territory in a global change context' funded by the French Research National Agency [ANR-16-CE03-0008].

methods will be based on a prior change detection on the cliff face in order to identify erosion areas. A diachronic 3D reconstruction of these areas should improve the quantification of the cliff erosion.