Iad Abdul Raouf

Vincent Gay-Bellile

Steve Bourgeois

Cyril Joly

Alexis Paljic

MagHT: a Magnetic Hough Transform for Fast Indoor Place Recognition

This article proposes a novel indoor magnetic field-based place recognition algorithm that is accurate and fast to compute. For that, we modified the generalized "Hough Transform" to process magnetic data (MagHT). It takes as input a sequence of magnetic measures whose relative positions are recovered by an odometry system and recognizes the places in the magnetic map where they were acquired. It also returns the global transformation from the coordinate frame of the input magnetic data to the magnetic map reference frame. Experimental results on several real datasets in large indoor environments demonstrate that the obtained localization error, recall, and precision are similar to or are better than state-ofthe-art methods while improving the runtime by several orders of magnitude. Moreover, unlike magnetic sequence matchingbased solutions such as DTW, our approach is independent of the path taken during the magnetic map creation.

I. INTRODUCTION

Place recognition is a popular solution for indoor localization due to the absence of GNSS signals. Vision-based approaches [START_REF] Campos | ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial, and Multimap SLAM[END_REF] are the most common. However, they fail in low or repetitive textured environments and when visual cues change as time goes by [START_REF] Coulin | Tightly-Coupled Magneto-Visual-Inertial Fusion for Long Term Localization in Indoor Environment[END_REF]. Some work improves the robustness, for instance, by learning different recognition modules for various illumination conditions [START_REF] Labbé | Multi-Session Visual SLAM for Illumination-Invariant Re-Localization in Indoor Environments[END_REF]. However, it tackles only one of the problems and increases the computation time.

On the contrary, many works have shown that the ambient magnetic field spatial variability can be used reliably for indoor localization over long periods [START_REF] Coulin | Tightly-Coupled Magneto-Visual-Inertial Fusion for Long Term Localization in Indoor Environment[END_REF], [START_REF] Ouyang | A Survey of Magnetic-Field-Based Indoor Localization[END_REF]. Indoor, the magnetic field varies slowly because of the natural variation of the global earth's magnetic field over the years [START_REF] Ouyang | A Survey of Magnetic-Field-Based Indoor Localization[END_REF]. It is also tolerant of moving objects in the scene. Human crowd or non-ferromagnetic furniture does not significantly impact the magnetic field [START_REF] Ashraf | A Comprehensive Analysis of Magnetic Field Based Indoor Positioning With Smartphones: Opportunities, Challenges and Practical Limitations[END_REF]. In contrast, larger objects such as a car and an elevator cabin modify it for a few meters [START_REF] Shu | Magicol: Indoor Localization Using Pervasive Magnetic Field and Opportunistic WiFi Sensing[END_REF].

Magnetic field-based relocalization algorithms exploit several magnetic data collected along a trajectory (called "input trajectory" thereafter), a single measure not being sufficiently discriminating to differentiate between places. Most existing approaches assume that those magnetic data are acquired by following the path taken to build the magnetic map [START_REF] Antsfeld | Magnetic Field Sensing for Pedestrian and Robot Indoor Positioning[END_REF]- [START_REF] Yao | Robust Magnetic Field Loop Closure Detection for Low-Cost Robot's Localization and Mapping[END_REF]. Other probabilistic approaches [START_REF] Solin | Terrain navigation in the magnetic landscape: Particle filtering for indoor positioning[END_REF], [START_REF] Ma | Basmag: An Optimized HMM-Based Localization System Using Backward Sequences Matching Algorithm Exploiting Geomagnetic Information[END_REF] do not constraint the movement but require heavy computational resources to achieve good performances (recognition rate, false positive rate, etc.) or reduced runtime is achieved through performance sacrifices. 1 Authors are with Université Paris-Saclay, CEA, List, F-91120, Palaiseau, France iad.abdulraouf@cea.fr This paper describes a new magnetic place recognition algorithm for large indoor environments. Unlike previous work, it is both fast to compute and makes no assumptions about the path taken. Consequently, it is suitable for 3D navigation in any environment, including large open areas. It only assumes prior reconstruction of the input trajectory in a gravity frame by an odometry system that includes an inertial measurement unit (IMU). The proposed approach adapts the generalized Hough transform [START_REF] Ballard | Generalizing the Hough transform to detect arbitrary shapes[END_REF] to magnetic data. It results in several contributions, which are the following:

1) A fast-matching method between input magnetic data and a magnetic map, robust to small spatial variations in the magnetic field. 2) A voting process that estimates the transformation candidates between the global reference frame of the map and the input trajectory frame. The voting and the matching treat input magnetic data independently to ensure our method is independent of the mapping path. 3) A pose estimation method to process all individual votes efficiently, robust to more than 99 % outliers, that yields a unique estimation of the frame transformation. 4) Overall, a place recognition algorithm that combines the previous contributions into a method several orders of magnitude faster than the state of the art while having similar or better recall, precision, and errors. To support our claims, we present experimental results of the proposed method inside open and closed multi-story indoor environments and an extensive comparison against a state-of-the-art method [START_REF] Solin | Terrain navigation in the magnetic landscape: Particle filtering for indoor positioning[END_REF].

II. RELATED WORK

Magnetic place recognition algorithms identify where a collection of magnetic measures have been acquired in a magnetic map of the environment.

The first family of approaches relies exclusively on a temporal series of magnetic measures provided by a magnetometer. To reduce the problem's complexity, they assume that the set of possible trajectories is countable. Consequently, the magnetic map is reduced to a collection of temporal series of magnetic measures, and the place recognition to a pattern matching problem between temporal series. While the first solutions relied on handmade algorithms such as DTW [START_REF] Wang | Keyframe based largescale indoor localisation using geomagnetic field and motion pattern[END_REF], [START_REF] Yao | Robust Magnetic Field Loop Closure Detection for Low-Cost Robot's Localization and Mapping[END_REF], their too-high false positive rate requires their use to be combined with additional inputs, such as WIFI [START_REF] Yao | Robust Magnetic Field Loop Closure Detection for Low-Cost Robot's Localization and Mapping[END_REF] or motion patterns [START_REF] Yao | Robust Magnetic Field Loop Closure Detection for Low-Cost Robot's Localization and Mapping[END_REF], to confirm the place recognition. This issue was solved more recently by deep-learning-based pattern matching [START_REF] Antsfeld | Magnetic Field Sensing for Pedestrian and Robot Indoor Positioning[END_REF], [START_REF] Lee | AMID: Accurate Magnetic Indoor Localization Using Deep Learning[END_REF]. However, all those solutions remain limited by their map representation. While the hypothesis of a limited number of trajectories is acceptable for corridor environments, such a hypothesis is no longer acceptable for open areas such as an atrium.

To tackle this limitation, the second family of approaches proposes to replace temporal pattern matching with spatial pattern matching. For that, an additional odometry system provides a spatial trajectory in addition to the magnetic measurements. The pattern matching is then achieved by exploring a spatial map of the magnetic field through particle filtering [START_REF] Solin | Terrain navigation in the magnetic landscape: Particle filtering for indoor positioning[END_REF] or Hidden Markov Model [START_REF] Ma | Basmag: An Optimized HMM-Based Localization System Using Backward Sequences Matching Algorithm Exploiting Geomagnetic Information[END_REF], the measurements being compared to the map prediction for the hypothesized locations. While those approaches are not limited to predetermined paths, they suffer from a computational time burden that increases with the size of the map.

To our knowledge, no algorithm can perform magnetic place recognition in large-scale environments independently from the mapping path and with a low computational cost. We designed a novel method described in section III that satisfies all these conditions.

III. MAGNETIC HOUGH TRANSFORM A. Overview

Our goal is to find the rigid 3D transformation T wa ∈ SE(3) from the reference frame a associated with a short input trajectory recovered by an odometry system (e.g., visual-inertial SLAM [START_REF] Campos | ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial, and Multimap SLAM[END_REF]) to a world reference frame w associated to a magnetic map. A rigid transformation model supposes that the odometry drift is neglected, a reasonable assumption for short trajectories of a few meters. Frames a and w are also assumed to be gravity frames, meaning their z-axis is upright. This vertical alignment is obtained from an IMU sensing the gravity vector. It constrains T wa to have only 4 degrees of freedom (x, y, z, ψ) ∈ R 4 with t = (x, y, z) the translation and ψ the yaw angle. The estimation of T wa is computed by linking a finite set of magnetic vectors m w j from the map with another finite set of measured magnetic vectors m a i along the input trajectory. For that, we used a generalized Hough transform. It is a method for converting data from an input space to a parameter space. Intuitively, instead of detecting the contour of an object in a 2D image by a visual Hough algorithm [START_REF] Ballard | Generalizing the Hough transform to detect arbitrary shapes[END_REF], our Magnetic Hough Transform (MagHT) detects any trajectory shape in a 3D magnetic map. It is composed of the following steps:

• Voting: For each measures m a i , all compatible magnetic vectors m w j are extracted to form several pairs. Then each pair leads to voting for one possible estimation Twa of the rigid transformation.

• Clustering: Depending on the size of the map, a few dozen input measurements can generate thousands of votes. The clustering step allows to identify a consensus around similar values. • Estimation: The final Twa estimate is taken equal to the centroid of the largest Twa cluster. Each step is detailed in the following sections and illustrated in Fig 1.

B. Pose Voting

The Hough transform first matches magnetic vectors from the input trajectory with similar magnetic vectors of the map to compute a vote Twa .

1) Feature matching: Because T wa is unknown, it is impossible to use the full magnetic vector whose expression depends on the orientation of its frame. However, both frames are gravity frames. Consequently, we use the following yaw invariant features ( m xy , m z ) ∈ R + × R, with m xy the norm of the horizontal component and m z the vertical component. Then each input's magnetic feature is associated with all map's magnetic features close enough (i.e., within a radius δ) in the feature space R + × R. At places where the field is relatively uniform, δ should be small not to match too many features and vice versa, so we made it adaptative based on local input magnetic field variations (details are given in section IV-B). Computing all possible couple's distances to find the ones close enough is too expensive. Thereby map features are indexed into a k-d tree, well known to enable fast range search in small dimensions.

2) Voting: Then, for each matched pair (m a i , m w j ), an estimation Twa is defined such that both magnetic vectors and their respective position are "aligned" while respecting the gravity constraint. Formally, this is done through magnetic frames h i and h j introduced in Fig. 1. Both are identified as the same frame h created from the same physical reality (independent of a or w in which h is defined). Thus a vote Twa is obtained by:

Twa = T whj T hia , (1)
where T whj and T hia are precomputed.

C. Pose Clustering

The vote set is usually big and very noisy (e.g., thousands of outlier votes for only a few dozen correct votes). Hence, votes are processed to find an accumulation somewhere, characterizing a convergence around a consensus value. Traditionally, in very low dimensions, the voting space is discretized into bins, each counting the number of votes received [START_REF] Ballard | Generalizing the Hough transform to detect arbitrary shapes[END_REF]. Then the result is smoothed, and the maximum is found. However, the more the dimension of the space increases, the more the bins are numerous (and mostly empty), making the method unusable in practice. An alternative that scales better [START_REF] Buch | Rotational Subgroup Voting and Pose Clustering for Robust 3D Object Recognition[END_REF] is to loop through votes and search for accumulation in their respective neighborhood. This idea is, for instance, the general idea used by DBSCAN clustering [START_REF] Ester | A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise[END_REF], which is well known to be fast and robust to outliers [START_REF] Schubert | DBSCAN Revisited, Revisited: Why and How You Should (Still) Use DBSCAN[END_REF].

Using such an algorithm implies introducing a distance function on votes (x, y, z, ψ) ∈ R 3 × [0, 2π] that defines what is a neighborhood of radius . In particular, we must consider the different scale and periodic nature of the yaw ψ. This vote space can be seen as a subset of SE(3) on which a frequent approach is to separate the contribution of the rotation from that of the translation and scale the rotation part by a factor r, often chosen experimentally [START_REF] Brégier | Defining the Pose of Any 3D Rigid Object and an Associated Distance[END_REF] :

d(T 1 , T 2 ) = (∆ψ) 2 + r t 2 -t 1 2 , (2)
Magnetic Map

Offline process

Input trajectory with magnetic data Iteration over the magnetic data w w w w w a w a a w a Fig. 1: Inputs are a discrete magnetic map in a gravity frame w (orange) and a trajectory with magnetic data expressed in another gravity frame a (red). Each blue and green vector represents a magnetic vector of the map and a magnetic vector of the input trajectory. Frames h i and h j are gravity frames defined for each magnetic vector m i and m j . Their (Ox) axis are aligned with m xy . Each measured magnetic vector m i matches multiples m j through the feature space. For each magnetic match, one vote is generated by the superimposition of their respective h frame. After all input magnetic data have been handled, clustering search accumulations among all votes. The biggest cluster is selected to estimate the transformation T wa from its centroid.

with T 1 and T 2 two gravity transform, t 1 and t 2 their translation part and ∆ψ the yaw angle difference in [-π, π).

Besides, fully computing the distance matrix between each pair of (thousands of) votes to retrieve the neighborhoods would be intractable. Therefore efficient range search through spatial indexation (e.g., by a k-d tree) is needed. Such indexing is quickly built after the unfavorable periodic vote space is mapped into its 4-dimensional manifold image in R 5 : f : (x, y, z, ψ) → (x, y, z, r.cos(ψ), r.sin(ψ)) .

(

) 3
For small neighborhoods of size r, the SE(3) distance (2) defined on the vote manifold can be conveniently approximated by the Euclidean distance on R 5 .

D. Pose Estimation

After the clustering step, if no cluster is present, it implies that the Hough transform did not converge, which can mean that the input trajectory is outside the map. If there is at least one cluster, the best one is selected. For simplicity, it is defined as the cluster with the largest number of elements. Estimation is done by computing its centroid in R 5 , which is then projected back into vote space:

(x, y, z) = 1 |I| i∈I (x i , y i , z i ), (4)
ψ = arctan2 1 |I| i∈I sin(ψ i ), 1 |I| i∈I cos(ψ i ) , (5)
with I the index set of the selected votes, and |I| its cardinality.

IV. EXPERIMENTAL EVALUATIONS The proposed magnetic Hough transform algorithm is evaluated regarding pose error, recall, precision, and runtime in 2D and 3D environments, including large open areas, staircases, and narrow corridors. A comparison with a stateof-the-art magnetic place recognition algorithm based on particle filtering [START_REF] Solin | Terrain navigation in the magnetic landscape: Particle filtering for indoor positioning[END_REF] is also presented.

A. Datasets 1) Hardware and sequences:

To evaluate the performances of the MagHT algorithm in a challenging context, the test sequences (from which the input trajectories are extracted) have to not all follow the mapping path, and not all be acquired just after the mapping acquisition. Furthermore, different environments, such as open areas, staircases, and narrow corridors, must be covered. All sequences should also be associated with inertial data to compute the gravity constraint. To our knowledge, no public dataset combines all those characteristics. Hence we produced our own. Our acquisition platform is a helmet equipped with 4 FLIR Blackfly S cameras and an SBG-Ellipse-N containing an IMU and a magnetometer. All sensors are rigidly mounted and synchronized. Cameras and IMU are calibrated using Kalibr [START_REF] Rehder | Extending kalibr: Calibrating the extrinsics of multiple IMUs and of individual axes[END_REF]. The magnetometer is calibrated outdoors by spherical calibration [START_REF] V. Renaudin | Complete Triaxis Magnetometer Calibration in the Magnetic Domain[END_REF]. However, it could be calibrated indoors too [START_REF] Coulin | Online Magnetometer Calibration in Indoor Environments for Magnetic field-based SLAM[END_REF].

The first dataset called corridor covers 1400 m 3 of corridors and staircases in a three-story building. The test sequence is one kilometer long and was acquired one year after the mapping sequence. The second dataset called atrium covers 1200 m 2 of a ground floor. It includes a large atrium mapped with a trajectory deliberately different from the 240meter test trajectory (see Fig 2). There, mapping and test trajectories often cross at large angles (even perpendicularly), and the goal is to assert that relocalizations rely only upon the map of the atrium, independently from the path taken to map it. Several hours separate both acquisitions.

2) Ground truth: Ground truth poses are required for both building the magnetic map and quantitatively evaluating the accuracy of magHT. A visual-inertial graph SLAM [START_REF] Campos | ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial, and Multimap SLAM[END_REF] obtains them, with loop closure followed by a global bundle adjustment as a post-process. It also results in visual maps composed of 3d point clouds that can be used to express the ground truth poses of the test trajectories in the map coordinate frames. A visual relocalization algorithm is used to match 3D points between the two maps, and a 3D transformation is estimated from those 3D-3D correspondences by a Ransac algorithm. It typically yields a trajectory of poses located within a 10 centimeters error margin.

3) Magnetic map: For a fair comparison, we used the same reduced rank Gaussian process extrapolation model [START_REF] Solin | Modeling and Interpolation of the Ambient Magnetic Field by Gaussian Processes[END_REF] for MagHT and the concurrent particle filtering algo- rithm [START_REF] Solin | Terrain navigation in the magnetic landscape: Particle filtering for indoor positioning[END_REF]. It is a continuous model that allows requests everywhere around the mapping sequence. However, our method is neither restricted to Gaussian processes nor continuous models and does not requires probabilistic values. Maps parameters defined in [START_REF] Solin | Modeling and Interpolation of the Ambient Magnetic Field by Gaussian Processes[END_REF] are fixed experimentally to sensible values describing typical variations: σ 2 lin , σ 2 SE , σ 2 noise = 650, 200, 2 µT 2 and l 2 SE = 1.69 m 2 with 512 basis functions by domain of size 5 × 5 × 2 m 3 .

4) Input trajectories: They are extracted from the test sequences. Using ground truth odometry (from the section IV-A.2) would be unrealistic for many applications. Thus the test sequences are also processed with monocular visualinertial SLAM [START_REF] Campos | ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial, and Multimap SLAM[END_REF] without loop closure or any post-process. For the "corridor" dataset, 460 input trajectories of length 12 meters are extracted from a sliding window on the complete sequence. For the "atrium" dataset, roughly 120 input trajectories of each length 3, 6, 9, 12, 15, and 18 meters are extracted. All of them are first expressed in an arbitrary gravity frame before being processed by the proposed algorithm. In total, MagHT is tested on more than a thousand input trajectories.

B. MagHT setup

1) Map preprocessing: Offline, the continuous map described in section IV-A is discretized on a grid using steps of size λ = 0.5 m. However, in the 3D case, this grid is not cubic, as it would harm the clustering results. Indeed, because of the gravity assumption and because the input path is often at a constant walking altitude, a grid discretization in z yields the same discretization in z inside the voting space. This voting artifact can break one big cluster into multiple smaller ones for each z layer. To reduce two fold the discretization step while keeping the number of element constant, half the column of a cubic grid are shifted upward by λ 2 , resulting in a body-centered orthorhombic Bravais lattice of parameter (λ √ 2, λ √ 2, λ).

2) Input trajectories preprocessing:

To not generate too many votes that would merge clusters, and because the magnetic field variations are low enough, measurements are smoothed to reduce noise and then downsampled using the same step length λ as for the map sampling. Unlike a temporal one, spatial sampling is robust when the carrier is not moving. The origin of a is translated at the barycenter of each input trajectory (not necessarily on the trajectory) to reduce voting errors induced by the lever-arm effect.

3) Parameters: To illustrate MagHT's ease of use, we set the same parameter values on all datasets. Following DBSCAN parameter guidelines [START_REF] Schubert | DBSCAN Revisited, Revisited: Why and How You Should (Still) Use DBSCAN[END_REF], minpts = 8, which is twice the vote DoF. Its range query size in the voting space should be as small as possible to reduce runtime, but it should be larger than the vertical λ 2 discretization. = λ gave good results. The distance function scaling factor r is set to 5 m such that the final translation error is approximately equal to the scaled yaw error. Matching in the feature space is done through the adaptative range:

δ = min(α|m a i -m a i-1 |, α|m a i+1 -m a i |, δ max ), α ∈ [0, 1]
, with i the index of the current input measure to match. Experimentally, δ max = 3.0 µT and α = 0.67. Notice that δ tends toward zero in uniform fields, which should avoid meaningless associations in outdoor environments.

C. Particle filter setup

We compared MagHT against a bootstrap particle filter [START_REF] Solin | Terrain navigation in the magnetic landscape: Particle filtering for indoor positioning[END_REF] as it is one of the only state-of-the-art methods to perform magnetic relocalization on trajectories that do not follow the mapping path. Hence its performances are used as a baseline. Because no open source code is available, we made our best effort C++ implementation, following as closely as possible their algorithm description, which is tailored for 2D navigation. In detail, the state is defined as X = (x, y, ψ). At each timestep, the monocular visualinertial odometry (VIO) projected in 2D replaces their pedestrian dead reckoning model in the dynamic equation. A stratified resampling is used jointly with an Effective Sample Size resampling criteria set to a standard value of 0.5. Particle initialization is performed using the first magnetic vector to align the yaw angle ψ 0 . As in [START_REF] Solin | Terrain navigation in the magnetic landscape: Particle filtering for indoor positioning[END_REF], their likelihood is based on the yaw invariant features described in section III-B. Convergence is decided by setting a one-meter threshold on the particle x and y standard deviation. It is 2 to 3 times smaller than the equivalent criterion used in [START_REF] Solin | Terrain navigation in the magnetic landscape: Particle filtering for indoor positioning[END_REF]. The more accurate VIO allows it and avoids ambiguity from multimodal estimation.

D. Metrics

Five criteria are used to evaluate both methods: The translation error twa -t wa 2 , the rotation error | ψwa -ψ wa |, the precision, the recall, and the runtime. The precision is defined from the number of correct convergences (below onemeter error) over the total number of convergences, and the recall is defined from the number of correct convergences over all possible ones (i.e., the number of trajectories in the mapped area). The particle filter is indeed a filtering algorithm, so the best performances are obtained at the last measurement. Hence, for a fair comparison, the particle filter metrics are computed using directly the transformation from the last sensor frame to the world frame instead of T wa .

E. Experiments

Several experiments are conducted to assess several aspects of MagHT. All runtimes are achieved on one core of an 11th Gen Intel® Core™ i7-11800H with 16 GB of ram and no GPU. First, our method is compared against the particle filtering (PF) approach in paragraph IV-E.1. Particle filtering is about choosing the suitable trade-off between runtime and estimation quality. In our experiment, it is run with either 1600 or 6400 particles which will be abbreviated as pf1600 and pf6400. The second experiment described in paragraph IV-E.2 evaluate MagHT 3D relocalization capabilities and the magnetic field stability over time. Our proposed method performances in open and closed areas are compared in paragraph IV-E.3. The fourth experiment evaluates MagHT Robustness against false positives in unmapped areas in paragraph IV-E.4. Finally, we assess the no drift hypothesis in paragraph IV-E.5.

1) MagHT versus particle filtering: In this section, we only compare MagHT against a particle filter on the atrium dataset, using input trajectory of variable lengths 3, 6, 9, 12, 15, and 18 meters. The 3D dataset corridor is not used because the concurrent particle filter was initially proposed in 2D only. Besides, increasing the dimension state implies increasing the number of particles accordingly. One would expect similar results to the ones presented here but with worse computation time. Our method performances on corridor are studied in paragraph IV-E.2. For this experiment on atrium, all metrics are displayed in Fig. 4. MagHT recall is superior on trajectories shorter than 9 meters. It stems from the fact that we had to increase the measurement noise of the filter to preserve the particle diversity and, therefore, reduce false positives. Indeed, filtering algorithms that process measures one by one are more sensitive to outliers, especially at the beginning of the trajectory. However, higher noise values also increase the convergence time, thus reducing recall on shorter sequences. On the contrary, our algorithm processes all measures independently from their acquisition order, which increases its robustness. From this perspective, it is closer to the smoothing algorithm family. Particle smoothing also exists [START_REF] Sarkka | Bayesian Filtering and Smoothing[END_REF] but suffers from even higher runtimes. For trajectories above 12 meters, MagHT recall is between pf1600 and pf6400. Fig. 4b shows that the three algorithms have good precision, particularly pf6400, which has near zero false positives on all trajectory lengths. On the contrary, pf1600 precision is slightly lower than our proposed method. Sometimes no particles are near the correct solution, so it might converge toward a place where the magnetic field is similar. One can expect this effect to be magnified for larger environments. As visible in Fig. 4c, MagHT errors are almost as good as the particle filtering ones. On 12 meter trajectory, median errors for our method, pf1600 and pf6400, are respectively 0.21, 0.18, and 0.12 meters. When the thousands of particles converged correctly, the sampling was dense around the true pose, which approximate almost perfectly its distribution. On the contrary, magHT usually has between ten and one hundred votes inside the most significant cluster. Nevertheless, it stills allows to average singular votes Twa by computing the cluster centroid Twa . The accuracy of Twa might be improved by nonlinear refinement post-processing since our method efficiency leaves enough computational power.

Overall, MagHT performances are similar to the particle filtering ones, but it is ten thousand times faster (see fig 4d). The main difference is that input and map data are associated with the feature space. Consequently, all magnetic fieldrelated variables can be precomputed (e.g., the feature tree). Additionally, several online steps of our method are suitable for optimization through proper indexation trees. Conversely, the particle filter requires position and orientation hypothesis (particles) to compare a magnetic measure with the map. The larger the environment is, the more numerous the particles should be. Furthermore, each comparison implies a map call. For 6400 particles on a 12-meter trajectory, it causes about 80 000 calls (16 times what MagHT needs). None of them can be precomputed as particles' positions are unpredictable beforehand. For all these reasons, MagHT runtimes outperform particle filtering ones by far.

2) 3D relocalization and map stability: MagHT relocalization capability in a 3D environment as well as the magnetic field stability over time, are studied inside the corridor dataset (see Fig 3). MagHT is executed on 460 input trajectories of length twelve meters 1 . There is no false positive, and the recall is 89%. Hence, it allows frequent and reliable relocalization. The error histograms are shown in Fig. 5a and5b. Translation and yaw median errors equal 0.16 m and 1.08 • , respectively. These results confirm the magnetic field stability over time since the test sequence is acquired one year after the mapping acquisition. In addition to being accurate, the relocalization is lightweight, taking only 4.6 ms. The offline 11000 features indexation in the kd tree is also instantaneous (1.7 ms), which is promising for an extension to online magnetic Simultaneous Localization And Mapping (SLAM).

3) Open area versus narrow corridors: In this section, we compare MagHT performances on the atrium dataset with its performances on the corridor dataset. Respectively 120 and 460 inputs trajectories of length 12 meters are extracted from both test sequences. Error histograms on those inputs are visible in Fig. 5. Taking the corridor dataset as a reference, recall increased from 89% to 97%, but the precision lowered from 100% to 97%. Errors also increased from 0.16 to 0.21 meters and from 1.08 to 1.6 degrees. It stems from environment differences. First of all, in corridors, the distance to the closest ferromagnetic material is smaller than an atrium. Therefore, the field variations are higher in corridor. Consequently, spatially close features might still be too different to be associated. It leads to a lower vote density and, therefore, to fewer clusters. Hence the recall is lower. On the contrary, the less variation the field has, the less observable the position is, which is not specific to our proposed solution. It partially explains the worse precision and errors in the atrium. Moreover, in open environments, the map is full. It further increases the vote density and, therefore, the risk of having large wrong clusters. The adaptive feature matching strategy still gave us good performances in both environments. Finally, notice that the high recall on atrium demonstrates that MagHT is indeed able to perform relocalization even if the test trajectory crosses the mapping trajectory at high angles (see Fig. 2). Such angles would not be possible with sequence-based pattern-matching relocalization such as DTW.

4) Robustness in unmapped area: This experiment assesses MagHT's robustness to relocalization attempts when the true pose is outside the map. Such a situation can appear when the environment is subject to change or when a robot may achieve exploration phases out of the previously mapped area. Hence we used the map of the corridor dataset restricted to the second floor only, jointly with the input trajectories restricted to the third level. This way, over 250 input trajectories of 12 meters are in an unmapped area, and the map size is 400 m 3 . MagHT yields only three false positives (1.2%). Each of the three false clusters contains exactly eight votes, the bare minimum given our DBSCAN parameters.

5) Robustness to odometry inaccuracy: Our algorithm does not model odometry errors which are unavoidable in real systems. Hence MagHT's sensibility to it should be characterized. To this end, the visual-inertial odometry on the atrium dataset is computed using 1, 2, or 4 cameras without either loop closure or global bundle adjustment postprocessing. After 12 meters, these three odometry systems yield median relative pose error (RPE) [START_REF] Grupp | evo: Python package for the evaluation of odometry and slam[END_REF] of (0.09 m, 0.3°), (0.05 m, 0.2°) and (0.04 m, 0.2°). Maght performances are not affected. The respective relocalization median errors are (0.21 m, 1.6°), (0.20 m, 1.6°), and (0.21 m, 1.5°) for the translation and yaw estimates. It confirms our hypothesis that the drift may be neglected on short input trajectories.

V. CONCLUSION

In this article, we introduced MagHT: a novel efficient, and accurate 3D relocalization algorithm based on the indoor magnetic field. To this date, other magnetic relocalization methods adapted to open areas are computationally expensive. On the contrary, our results demonstrate that MagHT execution time is several orders of magnitude faster than the concurrent particle filter while having comparable errors, recall, and precision. MagHT also performs fast relocalization in large 3D maps, which would require even more computational power for the filter-based method.

MagHT opens several directions for research. In future work, we intend to integrate it in a graph SLAM framework, thus upgrading the current state-of-the-art, primarily based on DTW. Superior recall in open areas would allow for more loop closure and therefore reduced errors. Furthermore, MagHT's low false positive rate outside the mapped area would benefit most SLAM backends. Having no false positive at all is desirable and would require improving our method using additional rejection criteria, such as a ratio test on cluster sizes. The extension of MagHT to online magnetic mapping is possible since our experiment demonstrates that the precomputed feature tree is fast to build. Such trees are also editable efficiently. For this study, we collected the magnetic field by wearing our helmet system on our heads. Additional difficulties due to dynamic magnetic perturbations induced by a robot might be expected. We will better characterize its impact. Finally, building a coherent map from several maps can be challenging in a multi-agent SLAM context. Therefore, we will also extend MagHT to perform multi-magnetic map alignment. Generally speaking, MagHT efficiency makes it a good option for the localization of various embedded systems, evolving in large environments encompassed in non-uniform magnetic fields.

ACKNOWLEDGMENT

The author wishes to thank Fabrice MAYRAN DE CHAMISSO and Richard GUILLEMARD for their valuable feedback on early versions of the technique.

Fig. 2 :

 2 Fig. 2: Top view of the atrium dataset showing the mapping trajectory (black) and the test trajectory ground truth (orange). Note that the test trajectory does not follow the mapping path. Map is displayed using the magnetic field norm.

Fig. 3 :

 3 Fig. 3: Visualization of corridor dataset showing the 3d map of the building magnetic field magnitude and the test trajectory.

Fig. 4 :

 4 Fig. 4: MagHT against particle filtering using 1600 and 6400 particles on variable trajectory lengths. In (d), odometry runtimes are not included.

Fig. 5 :

 5 Fig. 5: Error histograms were computed using corridor and atrium on 460 and 120 input trajectories of length 12 m, respectively. A threshold of 12 • defines false positives based on yaw errors. When scaled by the distance coefficient r, it is approximately equal to the one-meter threshold used for translation errors.

The previous experiment, in section IV-E.1, showed that twelve meters is the shortest length for best performances


Charlotte Emlinger

Karine Latouche

Cepii

Motivation Data Empirical specification Results Conclusion When Quality Management Helps Agri-food Firms to Export

Results Conclusion Empirical specification Results

Conclusion

Motivation

This paper

Investigates the impact of firms' commitment to traceability and food safety on export performance

Relies on the presence of quality management and control personnel to proxy this commitment

Conclusion

We show that quality management employees:

  Increasing demand for traceability and safety for food products : Public regulation (EC regulation 178/2002 of food traceability) Sanitary and Phytosanitary Standards (SPS) and Technical Barrier to trade (TBT) at the border Private certifications (HACCP, ISO, IFS, BRC...) → The ability to produce safe products, ensure their traceability and have it recognized through certification is an important component

  impacts on the duration of trade Kaplan-Meier survival functions of each length of spell → Different survival probability for firms with and without quality management on market with NTM Emlinger Latouche EAAE congress, Rennes, August 2023

  Exp fjkt = αQuality ft + βΠ ft + υ f + ξ jkt + ε All continuous variables are in logarithm. Robust standard errors clustered by firm-year in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01 p < 0.10, ** p < 0.05, *** p < 0.01

	Motivation Motivation Motivation Motivation Motivation Motivation Motivation	Data Data Data Data Data Data Data Data Data	Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification	Results Results Results Results Results Results Results Results Results	Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion
		Quality management and control personnel Literature Data sources Sample Specification Endogeneity Results : intensive margin of trade Results : extensive margin of trade Results : markets with NTM
			ln vfjkt Xfjkt
	Uses firm-level data from 2009 to 2019 Estimates the impact of quality management on the intensive and extensive margin of trade, on trade unit values Explores the heterogeneity of the effect by product-destination (presence of Non Tariff Measures) Staff in charge of the firm's products sanitary and safety quality: Design quality protocols Conduct inspections and tests Create quality documentation and traceability systems Report feedback from customers and analyse safety issues May impact trade: by increasing the efficiency of supply chains by helping the products to comply with regulatory requirement by enhancing the firm's reputation (by reducing hazards, Traceability and quality management system on firms competitiveness on domestic markets (Alfaro and Rabade 2009, Epelbaum and Martinez 2014, Aiello et al. 2015) Valuation of food traceability system by consumers (Graia et al. 2013, Liu et al. 2019) → No papers on quality management or traceability system and international trade DADS French administrative employee-firm-level database: number of employees, working hours, total salary, by firm and occupation From 2009 to 2019 Endogeneity of firm's decision to invest in quality management: could be linked to the firm's decision to export (or to export more / to some specific destination) or to its product specialization Instrumental variable approach, using the following IV : Share of firms in the same sector (APE) and department with quality management staff Share of exported products with NTM on the European market (1) (2) (3) (4) (5) All ∆Quality ft =0 All All All OLS OLS IV OLS IV Quality ft 0.187*** 0.195*** 1.962*** 0.025** 0.718*** (0.018) (0.040) (0.116) (0.012) (0.119) productivity ft 0.454*** 0.517*** 0.409*** 0.030*** 0.026** (0.013) (0.016) (0.016) (0.010) (0.012) Size 2ft 0.425*** 0.492*** -0.065 0.028 -0.095*** (0.024) (0.038) (0.047) (0.025) (0.035) Size 3ft 0.630*** 0.814*** -0.219*** 0.123*** 0.025 (0.030) (0.047) (0.066) (0.033) (0.040) Size 4ft 1.438*** 1.561*** 0.313*** 0.190*** 0.056 (0.030) (0.044) (0.081) (0.042) (0.052) N 594,383 393,903 490,878 593,758 490,773 r2 0.344 0.363 0.004 0.483 -0.004 Underidentification stat. 4769.369 1411.635 F stat for weak id 1773.104 1130.119 Weak id. p-value 0.000 0.000 Endogeneity test stat 229.228 35.994 p-value endogeneity test 0.000 0.000 destination-product-year yes yes yes yes yes firm no no no yes yes (1) (2) (3) (4) (5) All ∆Quality ft =0 All All ln vfjkt Xfjkt All OLS OLS IV OLS (1) (2) (3) (4) (5) (6) IV Quality ft 0.008*** 0.014*** 0.022*** 0.001*** All EUft =1 EUft =0 All EUft =1 EUft =0 0.018*** (0.000) (0.001) (0.002) (0.000) Quality ft × NTMjk 0.026** 0.022 0.042** 0.002*** 0.002*** 0.001*** (0.003) productivity ft 0.017*** 0.015*** 0.020*** 0.002*** (0.013) (0.015) (0.021) (0.000) (0.001) (0.000) 0.002*** (0.000) (0.000) (0.000) (0.000) Quality ft × noNTMjk -0.058 -0.141* 0.061 -0.007*** 0.007** -0.003*** (0.000) Size 2ft 0.021*** 0.019*** 0.015*** 0.006*** (0.056) (0.076) (0.076) (0.001) (0.003) (0.001) 0.003*** (0.001) (0.001) (0.001) (0.000) productivity ft 0.029*** 0.055*** 0.001 0.002*** 0.004*** 0.001*** (0.001) Size 3ft 0.034*** 0.028*** 0.023*** 0.012*** (0.010) (0.012) (0.017) (0.000) (0.000) (0.000) 0.008*** (0.001) (0.001) (0.001) (0.001) Size 2ft 0.040 0.077** 0.024 0.007*** 0.015*** 0.003*** (0.001) Size 4ft 0.057*** 0.054*** 0.042*** 0.015*** (0.027) (0.034) (0.042) (0.001) (0.001) (0.001) 0.010*** (0.001) (0.001) (0.002) (0.001) Size 3ft 0.124*** 0.194*** 0.016 0.015*** 0.028*** 0.007*** (0.001) N 11,127,999 7,209,619 (0.035) (0.041) (0.059) (0.001) (0.002) (0.001) 7,624,979 11,127,997 7,624,977 r2 0.124 0.132 0.007 0.171 Size 4ft 0.214*** 0.393*** -0.023 0.019*** 0.038*** 0.007*** -0.000 Underidentification stat. 94066.504 (0.044) (0.053) (0.073) (0.001) (0.002) (0.001) 41955.844 F stat for weak id 8157.149 N 541567 358155 183189 7830743 3199581 4631141 6562.125 Weak id. p-value 0.000 r2 0.49 0.53 0.47 0.18 0.21 0.16 0.000 Endogeneity test stat 60.305 destination-product-year yes yes yes yes yes yes 44.885 p-value endogeneity test 0.000 firm yes yes yes yes yes yes 0.000 destination-product-year yes yes yes yes Notes: All continuous variables are in logarithm. yes firm no no no yes yes Robust standard errors clustered by firm-year in parentheses.
		Emlinger Latouche recalls and complains, and potentially through certifications) EAAE congress, Rennes, August 2023 Emlinger Latouche EAAE congress, Rennes, August 2023 Emlinger Latouche EAAE congress, Rennes, August 2023 Emlinger Latouche EAAE congress, Rennes, August 2023 Emlinger Latouche EAAE congress, Rennes, August 2023 Emlinger Latouche EAAE congress, Rennes, August 2023 Notes: All continuous variables are in logarithm. Robust standard errors clustered by firm-year in parentheses. Emlinger Latouche EAAE congress, Rennes, August 2023 Notes: Emlinger Latouche EAAE congress, Rennes, August 2023 Emlinger Latouche EAAE congress, Rennes, August 2023

387d: quality control manager and engineer 475b: quality control technician for the processing industries French Customs trade data: value and quantity exported by firm, product (HS6), destination and year FARE Data characteristics of firms (value added, turnover) Agri-food products only : 878 products Focus on agri-food producing firms (exclusion of wholesalers and retailers): 5,033 exporting firms Emlinger Latouche EAAE congress, Rennes, August 2023 Data Empirical specification Results Conclusion Data: Trade and quality management Emlinger Latouche EAAE congress, Rennes, August 2023 Data: Trade and quality management Emlinger Latouche EAAE congress, Rennes, August 2023 Data: Trade and presence of quality management Emlinger Latouche EAAE congress, Rennes, August 2023 fjkt Quality ft is a dummy indicating whether firm f has quality management the year t Π ft time variant firm characteristics (size, productivity) jkt fixed effects controls for characteristics of the market of country j and good k the year t f firm fixed effect controls for time invariant firms characteristics Exp fjkt = lv fjkt log of export values of f to j for the k at t X fjkt dummy=0 if f exports k to j at t * p < 0.10, ** p < 0.05, *** p < 0.01 *

Data


Clément Prouin
email: clement.prouin@gmail.com

Giovanni Fusco
email: giovanni.fusco@univ-cotedazur.fr

Matteo Caglioni
email: matteo.caglioni@univ-cotedazur.fr

Denis Overal
email: denis.overal@kcitylabs.fr

Supervised classification of the French Riviera morphogenesis using a machine learning approach

Keywords: Urban Fabric, Urban Morphometrics, Machine Learning, Urban Growth, Morphogenesis

published or not. The documents may come

This contribution focuses on the analysis of the evolution of urban forms on the French Riviera within the 20th and early 21st centuries. More specifically, it defines evolutionary paths and contextual factors behind them. To this end, a context-specific model is created, allowing for the analysis of contextual variables and determining to what extent they influenced the evolution of urban morphology. The analysis is carried out by breaking down space into urban blocks, within the compact city, and block sections, in more dispersed suburban areas. The contextual variables represent the external morphogenetic factors of site, situation/accessibility, morphological context and historic period. Old cadastral maps and airborne images are the raw input data of our analyses. Five different study areas within the French Riviera are used to identify the evolutionary paths of urban form, to quantify them, as well as their bifurcations and the possible impacts of the external factors. Together, they are representative of the variety of observable forms on the French Riviera and of their past development paths.

In a first phase, components of the urban fabric are pre-processed. In particular, the street network undergoes in-depth processing. The linear street segment data was transformed into network coverage data and planar graphs. The study also used street continuity according to the Morpheo approach [START_REF] Lagesse | Lire les lignes de la ville. Méthodologie de caractérisation des graphes spatiaux[END_REF]. The street network provides the following elements: accessibility to plots, the key element in the division of block sections and a structural element of the city's development [START_REF] Hillier | A theory of the city as object[END_REF]. Plots and buildings are also pre-processed to identify recurrent patterns in a simplified way.

In a second phase, the analysis requires supervised classification of the evolution of the form of the urban fabric. A specific label of evolutionary pathway is assigned to each spatial unit, as in previous research by the authors [START_REF] Prouin | Morphogenesis of urban peripheries in the 20th century: examples from the French Riviera[END_REF]. The expert classification is based on the classical approach of urban morphology [START_REF] Conzen | Alnwick, Northumberland: a study in town-plan analysis[END_REF]Caniggia and Maffei, 1979), and knowledge of the urban history of the study area [START_REF] Graff | Une ville d'exception[END_REF]. The main components of urban form are buildings, streets and plots [START_REF] Marshall | Streets and Patterns[END_REF][START_REF] Lévy | Formes urbaines et significations : revisiter la morphologie urbaine[END_REF], as well as the site (the orographic and hydrographic structure of the area). To explain their evolutions, we considered both path dependency (previous morphological states and how they were achieved) and the situation of these different analysis units, namely their value in relation to their urban environment.

In a final phase, the pathways of the morphological structure becomes the target of supervised classification. The machine learning model "Support Vector Classification" is used [START_REF] Maysam | Support vector machine for multi-classification of mineral prospectivity areas[END_REF] to predict labeled categories based on non-textual data optimized for a small number of referenced individuals. The model searches for the pathway of the morphological evolution based both on the current morphological status of the spatial units and on a few explanatory variables of site and situation. Therefore, the obtained results have a dual interpretation. Firstly, the identification of the current morphological state, regardless of their morphogenesis, based on the description of the elements of urban form. Secondly, a set of metrics capable retaining the traces of the morphological pathway and capable of identifying it. The goal is to reveal residual morphological structures of a particular morphogenesis.

The analysis shows to which extent a morphological process can be inferred by observable forms and a limited number of contextual variables. By contributing to the analysis of urban forms as contingent manifestations of transitional morphologies [START_REF] Trisciuoglio | Transitional Morphologies and Urban Forms: Generation and Regeneration Processes-An Agenda[END_REF], our model opens the way to assessing the evolutionary potential of present-day observable forms. The latter can thus be understood within different possible evolutionary paths, more or less plausible according to the contextual variables, and offer insight into future urban developments.

Proceedings of ECTQG2023, Braga, Portugal, 14 to 17 September 2023


Alicia Blanchi
email: alicia.blanchi@kcitylabs.fr

Giovanni Fusco
email: giovanni.fusco@univ-cotedazur.fr

Karine Emsellem
email: karine.emsellem@univ-cotedazur.fr

Toponymic representation of spaces within the city through real estate ads

Keywords: Spatial analysis, real estate ads, toponym, spatial representation, fuzzy geographical location

come

Toponyms mark, segment and organise the urban space since their creation. They evolve with time and space, reflecting the historical, social, and cultural evolution of cities, including in terms of urban planning [START_REF] Le Squère | Analyse des perceptions, usages et fonctions des toponymes actuels des territoires ruraux et urbains de Bretagne[END_REF][START_REF] Jordan | Role of Place Names in Relating People and Space[END_REF][START_REF] Giraut | Place Naming as Dispositif: Toward a Theoretical Framework[END_REF]. They are perceived and identified by populations, thus contributing to the social representation of the different subspaces that compose the city. Toponyms respond to both spatial and social dimensions, making them difficult to identify. Their location and characterization present blurred and uncertain boundaries [START_REF] Bunel | Un état de l'art sur l'imprécision spatiale et sa modélisation[END_REF]. Several studies have dealt with the delimitation of fuzzy socio-spatial phenomena [START_REF] Hu | A natural language processing and geospatial clustering framework for harvesting local place names from geotagged housing advertisements[END_REF][START_REF] Vasardani | Locating place names from place descriptions[END_REF].

In this direction, we propose to reconstruct and characterise the toponymic landscape of the city from geolocated real estate ads, using an appropriate spatial analysis of the pieces of information on the urban space present in their text.

A geographic database was used, containing tens of thousands of pieces of geographic information extracted from real estate ads texts of the French Riviera through a combination of natural language processing (NLP) and artificial intelligence [START_REF] Cadorel | Geospatial Knowledge in Housing advertisements: Capturing and Extracting Spatial Information from Text[END_REF]. The geographical information extracted, cleaned, and structured, is based on the places and their socio-spatial context, made of spatial relationships and associated attributes, recognizable in expressions like "in the residential neighbourhood of Cimiez".

The naming and delimitation of places based on a multitude of extracted information are complex processes, leading to blurred toponyms with unclear boundaries, even if spatial barriers can sometimes segment their use. To model the significance of toponyms in space, we have developed a protocol based on spatial analysis of geographical information extracted and geolocated with decametric precision on the street network. The street network is a fundamental feature for the perception and cognition of urban space [START_REF] Lynch | The image of the city[END_REF]), and we can assume that it can be a pertinent basis for its segmentation through toponymy.

Geolocated ads can be seen as a spatial sampling of toponym use. We thus interpolated toponym use with a kernel density-based approach on the street network with adaptive parameters for each toponym [START_REF] Gelb | spNetwork, a package for network kernel density estimation[END_REF][START_REF] Lachance-Bernard | Network based Kernel Density Estimation for Cycling Facilities Optimal Location Applied to Ljubljana[END_REF]. The toponyms are those present in the database of extracted geographical information associated with a relationship of spatial situation [START_REF] Blanchi | Studying urban space from textual data: Toward a methodological protocol to extract geographic knowledge from real estate ads[END_REF].

From there, we extracted the relevant phenomenon (use of a given toponym) by imposing a minimal threshold and some spatial coherence in toponym use. Artefacts linked to erroneous geolocations or low presence of ads (a known bias introduced by the real estate market) could thus be reduced. Nevertheless, the presence of toponym use in space is not sufficiently indicative of its representation within the urban toponymic landscape. We therefore also assessed its absence within the same space, using the same interpolation method of all geolocated real estate ads that do not mention the toponym through a notion of situation.

Finally, we assessed the strength of a toponym in space using the concepts of core-space and support-space, derived from fuzzy set theory. First, the ratio between the kernel densities of presence and absence of toponym use on each street segment is used to model graduated presence of the phenomenon. Then, using the equivalent of an alpha-cut approach, the core was defined as the space where toponym use was predominant, and the support as the space of extended but more contested use. More precisely, morphological closures and connection checks were also carried out to impose spatial coherence on core-and support-spaces. Their mapping reveals how place-name usage produces meaningful patterns in intra-urban space, independently of administrative constraints.

However, some subspaces can be shared by different place names. Within the context of real-estate valorisation, some toponyms can be used more widely beyond their core. Supports overlap cores in an asymmetric way, showing the different power exerted by toponyms in the social representation of space. A local hierarchy among neighbouring toponyms can thus be calculated and mapped, producing new insight in the social meaning of the identified spatial patterns.

It was also possible to further characterise toponyms through their associated geographic entities. Entities like "neighbourhood", "sector", "street", "hill" have different meanings in social perception and cognition. Finally, a correspondence analysis was carried out using toponyms, associated attributes, and localisation factors (features of space put forward by real estate ads, including proximity to interest points, urban services and environmental amenities and view factors). The interpretation of the factorial axes allowed for the identification of main oppositions within the toponymic landscapes of the cities of the French Riviera. In Nice, for example, a first major opposition is between what are perceived as toponyms of residential places on the hills surrounding the city, and two different subspaces within the latter: the historic and tourist-oriented city and the more utilitarian city signified by the presence of urban facilities and services.

In conclusion, the spatial analysis of toponyms and their relationships in space allowed us to represent the patterns of toponymic landscape as they are perceived, appreciated, and identified by people. However, it is important to note that our data comes from real estate ads, which are punctual data influenced by the dynamics of the real estate market and real estate valorisation.

Proceedings of ECTQG2023, Braga, Portugal, 14 to 17 September 2023


Alessandro Araldi
email: alessandro.araldi@univ-cotedazur.fr

Giovanni Fusco
email: giovanni.fusco@univ-cotedazur.fr

Morphological Regionalisation of French Cities -A methodology for street-based analysis of urban form

Keywords: Urban Morphometrics, Streetscape, Urban Fabric, Multiple Fabric Assessment, France

come

Morphological Regionalisation of French Cities -A methodology for street-based analysis of urban form

Since the second after-war, urban morphology and its different schools, has produced considerable knowledge of traditional morphotypes and their constitutive elements. The Italian school [START_REF] Caniggia | Lettura dell'edilizia di base[END_REF] highlighted the contribution of building types and their historical evolution to the formation of the urban fabric. The French school [START_REF] Castex | Lecture d'une ville[END_REF], studied the role of plot patterns. The British school [START_REF] Conzen | Alnwick, Northumberland: a study in town-plan analysis[END_REF]) set out the most ambitious goal of regionalising urban space in terms of observable forms of the urban fabric [START_REF] Larkham | Drawing lines on maps: morphological regions and planning practices[END_REF]. However, the identification and characterization of the urban fabric, as well as the regionalization of cities, remained challenging tasks. They relied on expert-driven and labour-intensive qualitative and manual measurements, which had limitations in terms of reproducibility and scalability. Consequently, comparative studies across different urban regions were hindered. Additionally, morphological research primarily concentrated on historical central areas, overlooking the forms of peripheral and suburban growth prevalent in contemporary urbanization.

Lately, increasing availability of geospatial fine-grained data, greater computational power, and developments in spatial analysis, paved the way to a data-driven stream of urban morphology, referred to as urban morphometrics [START_REF] Araldi | From the built environment along the street to the metropolitan region. Human scale approach in urban fabric analysis[END_REF][START_REF] Bobkova | Structure of plot systems and economic activity in cities: Linking plot types to retail and food services in London, Amsterdam and Stockholm[END_REF][START_REF] Dibble | On the origin of spaces: Morphometric foundations of urban form evolution[END_REF]Fleishmann et al. 2022;[START_REF] Gil | On the discovery of urban typologies: data mining the many dimensions of urban form[END_REF][START_REF] Oliveira | Morpho: Combining morphological measures[END_REF]. Urban morphometrics, stimulated by the dialogue with traditional urban morphology, proposes innovative data-driven computer-aided protocols for the spatial analysis of urban form in general, and the urban fabric in particular, producing new insight on the internal morphological structure of cities. This presentation will focus on Multiple Fabric Assessment (MFA, [START_REF] Araldi | From the built environment along the street to the metropolitan region. Human scale approach in urban fabric analysis[END_REF]. MFA is a computer-aided urban morphometric protocol for morphological regionalization: it mainly differs from other protocols by using a street-based perspective, thus allowing a multiscale description of the built environment as observed from the public space of the street. The perceptive-based framework underlying MFA allows for the convergence of urban typo-morphology with streetscape analysis [START_REF] Harvey | Urban streetscape design and crash severity[END_REF] within a coherent analysis protocol. The pedestrian-based modelling approach proves essential in light of the renewed interest in the issues of perception, use, and design of public spaces. What is most specific to MFA and of particular interest to theoretical and quantitative geographers is its integration of geostatistically significant spatial patterns, along with machine learning methodologies, for the identification and characterization of morphotypes.

MFA has been applied to various urban areas in different sociocultural contexts and geographical scales [START_REF] Fusco | The Nine Forms of the French Riviera: Classifying Urban Fabrics from the Pedestrian Perspective[END_REF][START_REF] Perez | Identifying building Typologies and their spatial patterns in the metropolitan areas of Marseille and Osaka[END_REF], Guyot et al. 2020, Fusco et al. 2021). Based on these experiences, MFA has undergone further development and upscaling to analyse and compare larger study areas. The presentation focuses on recent methodological advancements in MFA, which were needed to implement it on the largest French metropolitan areas. Advancements include: improved streetscape morphometrics; development of a building typology for the entire country prior to morphotype detection through MFA [START_REF] Araldi | Ordinary building types of France and their geographic distribution. Automatic quantitative analysis using official national-scale spatial data[END_REF]); use of Gaussian mixture models to identify different values for each morphometric feature; creation of a new Bayesian clustering algorithm called INBIAC (Iterative Naive Bayesian Inference Agglomerative Clustering) to generate numerous clustering models; selection of the best clustering models based on log-likelihood; use of a hierarchical clustering algorithm to combine the best models and create a nested taxonomy of morphotypes for each study area; final hierarchical clustering of place-specific morphotypes using the original streetscape morphometrics to obtain a general nested taxonomy of morphotypes across all study areas.

The improved protocol opens the way to a multiscale comparative analysis of contemporary urban forms in France. It has been implemented over the eight largest metropolitan areas of France (Paris, Lyon, Marseille-Aix-en-Provence, Lille-Roubaix-Tourcoing, the French Riviera, Bordeaux, Toulouse, and Nantes) obtaining both place-specific morphotypes and a general taxonomy of the urban fabric in French metropolitan areas. The eight study areas could thus be regionalised using both their specific morphotypes and knowledge of their position within a common taxonomy. Common spatial structures emerge from regionalisation, as well as a few specificities linked both to site constraints and to the different spatial extent of morphotypes. These results are a first contribution to a national atlas of morphologically regionalized metropolitan areas.

Proceedings of ECTQG2023, Braga, Portugal, 14 to 17 September 2023


Marion Schulz

Valérie Delmas

Mélodie Cadillon

Ivan Dubois

Madeleine Bouzon

Volker Döring

Paving the way for the construction of an autotrophic Escherichia coli strain

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

  Métabolique CEA, Institut de Biologie François Jacob, Genoscope, Université d'Evry Van d'Essonne, Université Paris-Saclay, France


Valérie Marion Schulz

Valérie Delmas

Mélodie Cadillon

Ivan Dubois

Madeleine Bouzon

Volker Döring

Paving the way for the construction of an autotrophic Escherichia coli strain

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

  Métabolique CEA, Institut de Biologie François Jacob, Genoscope, Université d'Evry Van d'Essonne, Université Paris-Saclay, France