Camilo Aguilar

Mathias Ortner

Josiane Zerubia

Adaptive birth for the GLMB filter for object tracking in satellite videos

Keywords: satellite-videos GLMB, RFS, adaptive birth, multitarget tracking, remote sensing

INTRODUCTION

Novel earth observation satellites and Unmanned Aerial Vehicles (UAV) capture content-rich ground information that opens opportunities for emerging applications. Many of these applications rely on detecting and tracking targets from highresolution videos. For example, the Jilin1-1 satellite constellations contribute to Chinese urban investigation by tracking vehicles and driver behavior across urban areas [START_REF] Du | Object tracking in satellite videos by fusing the kernel correlation filter and the three-frame-difference algorithm[END_REF]. Similarly, the French Zephyr Unmanned Aerial System (UAS) contributes to maritime surveillance by monitoring ships for piracy or smuggling of goods and narcotics [START_REF] Bauk | Review of unmanned aerial systems for the use as maritime surveillance assets[END_REF], or the American Maxar Worldview's satellite constellation contributes to military assessments in regions without local sensors [3].

MOT frameworks normally rely on data association such as Joint Probabilistic Data Association (JDPA) [START_REF] Fortmann | Multi-target tracking using joint probabilistic data association[END_REF], Multiple Hypotheses Tracking (MHT) [START_REF] Reid | An algorithm for tracking multiple targets[END_REF] or Random Finite Sets (RFS) [START_REF] Ronald | Statistical Multisource-Multitarget Information Fusion[END_REF]. Among these approaches, the RFS framework has gained popularity due to its elegant Bayesian formulation to jointly model object dynamics (births and transitions) and measurements as set-valued random variables. Common RFS-based filters include the Probability Hypothesis Density (PHD) filter [START_REF] Ronald | Multitarget Bayes filtering via first-order multitarget moments[END_REF] or the Cardinalized PHD (CPHD) filter [START_REF] Vo | The cardinalized probability hypothesis density filter for linear Gaussian multi-target models[END_REF]. These filters provide robust and computationally efficient solutions using first-order approximations for the multi-object distribution; however, they fail to assign object labels and recover object trajectories.

Recently, Vo and Vo [START_REF] Vo | Labeled random finite sets and multi-object conjugate priors[END_REF] proposed the labeled RFS framework to model both multi-object states and multi-object trajectories based on a rigorous mathematical foundation. The most popular approach is the Generalized Labeled Multi-Bernoulli (GLMB) filter and its computationally efficient derivation [START_REF] Vo | An efficient implementation of the generalized labeled (a) Ground truth trajectories (b) GLMB + measurement driven birth (c) GLMB + proposed adaptive birth Fig. 3. Area 34 tracking results[END_REF]. The GLMB filter has provided a solution for MOT requirements across several fields, such as in biological images [START_REF] Beard | A solution for large-scale multi-object tracking[END_REF] or radar applications [START_REF] Wu | Tracking multiple maneuvering targets hidden in the DBZ based on the MM-GLMB filter[END_REF].

However, despite the solid theoretical background, the GLMB filter highly depends on strong assumptions such as prior knowledge of the birth components' initial location and known clutter rate. These assumptions do not always hold on real-world scenarios as targets appear and disappear at often random locations. For example, in remote sensing images, ground vehicles can appear from incoming roads or parking lots; planes can appear from airports, and pedestrians can appear from buildings. Additionally, targets in satellite images are often tiny and have a white-blob-looking appearance. Targets are frequently lost in clutter, and object detectors often output several clutter measurements from static white-bloblooking objects.

To compensate for the object initialization drawback, numerous works have proposed the "measurement-driven birth" [START_REF] Lin | Measurement driven birth model for the generalized labeled multi-Bernoulli filter[END_REF], which consists in initializing components at unassigned, low-likelihood measurements. This approach presents two main problems: the initialization does not discriminate between clutter and birth measurements; hence, it can initialize tracks at faulty locations. Second, the velocity component is unknown, which causes the filter to lose fast-moving targets in future frames.

In this paper, we propose a birth initialization method based both on low likelihood components and on component history. We exploit the fact that ground targets in satellite images often follow similar directions to previously tracked objects (normally dictated by the direction of highways and roads). We utilize this information to adaptively learn the initial state of the birth component measurements and hence, improve the filter performance for fast-moving targets in low FPS datasets. We perform tests in a challenging, lowresolution, low-FPS dataset and show that our filter outperforms other state-of-the-art methods and variations of RFS filters.

We present further details of relevant literature review in Section 2, we discuss about the random finite set background in Section 3, we detail the proposed method in Section 4, we show results in Section 5, and finally we discuss our main findings and future work in Section 6.

RELATED WORK

The classical measurement-driven birth constitutes the conventional tool to approximate birth intensities in RFS-based filters. For example, [START_REF] Lin | Measurement driven birth model for the generalized labeled multi-Bernoulli filter[END_REF][START_REF] Ristic | Adaptive target birth intensity for PHD and CPHD filters[END_REF] use measurements with low association likelihood from the previous frame to initialize new components. This approach misses the first few detections of a new target but is robust to clutter measurements. Similarly, [START_REF] Pace | Stochastic models and methods for multiobject tracking[END_REF] uses measurements from the current frame to drive the birth intensity. This initialization captures targets' initial measurements but suffers from false positives initialized at clutter detections. These techniques usually initialize hypotheses with random velocity components and large uncertainties. The hypothesis velocity is updated during the filter update step if the filter associates the birth component with the object's subsequent measurement; otherwise, the filter initializes a new hypothesis with a new label and the original track is lost.

Additionally, the work in [START_REF] Liu | Adaptive generalized labeled multi-Bernoulli filter for multi-object detection and tracking[END_REF] uses a pre-processing step to approximate the birth distribution. This approach accounts for three measurements before estimating the birth RFS, and hence, it has a rough initial approximation of the object's initial conditions. This methodology helps to reduce clutter detections and to estimate the initial velocity at the cost of missing the first three detections for each object. Furthermore, the "birth" object proposal step highly depends on the association algorithm used as a pre-processing step.

Several papers present adaptive clutter rate estimation by combining the CPHD with the GLMB [START_REF] Vo | The cardinalized probability hypothesis density filter for linear Gaussian multi-target models[END_REF][START_REF] Reuter | Cardinality balanced multitarget multi-Bernoulli filtering using adaptive birth distributions[END_REF]. These approaches consist of using the CPHD filter's cardinality estimation to infer the detection and clutter rates of the GLMB. While these methods have shown improved performance with respect to the original GLMB filter, they still rely on pre-hardcoded parameters and do not exploit past track information.

Fu et al. [START_REF] Fu | Particle PHD filter based multiple human tracking using online groupstructured dictionary learning[END_REF] proposed an online dictionary learning method to learn object appearance and discriminate target measurements from clutter measurements based on the cor-related dictionary features. This approach shows promise; however, satellite image targets often lack distinctive features to discriminate them from clutter measurements.

Finally, it is worth mentioning deep-learning approaches such as MT3 [START_REF] Pinto | Next generation multitarget trackers: Random finite set methods vs transformer-based deep learning[END_REF]. This work uses transformers to track objects in highly cluttered and non-linear scenarios with a trackby-detection paradigm. MT3 obtained comparable results to model-based filters at the cost of using 18 million parameters and several days to train the network. However, target dynamics in satellite images can be modeled well with linear motion and matrix operations using significantly fewer parameters.

BACKGROUND

We model a single target kinematic state as x = [p, v] T where p ∈ R 2 denotes the target 2D location coordinates and v ∈ R 2 denotes the target 2D velocity components. Similarly, we model a single measurement as z = [p], where p ∈ R 2 represents the 2D coordinates for each measurement.

Labeled RFS

The RFS framework models multi-object states and measurements as finite-set value random variables. In this work, we use the labeled version of the traditional RFS framework, which assigns a unique label to each element in the multiobject RFS. The addition of labels allows the filter to recover both object states and object trajectories.

Let X be the state space and L be a discrete label space. We model a single labeled target as x = (x, ℓ), where x ∈ X is the target kinematic state and ℓ ∈ L is the label associated to the target. Subsequently, we characterize the collection of labeled multi-target states at frame k as

X k = {x (k) 1 , x (k) 2 , . . . , x (k) n k } ∈ F(X)
, where F(•) is a collection of finite subsets and n k ∈ N is a random variable associated with the number of elements in X k . Similarly, we define the measurement space as Z and define the measurement RFS as

Z k = {z (k) 1 , z (k) 2 , . . . , z (k) m k } ∈ F(Z)
, where m k is a random variable denoting the number of measurements and z (k) j is the j th measurement at frame k. Following a Bayesian setup, the multitarget density π k (X k ) is conditioned on measurements and is propagated through time following a prediction, π k+1 (X k+1 ) and update step π(X k+1 |Z k+1 ).

The GLMB Filter

The GLMB filter provides an analytical solution to the Bayes multi-target tracking by propagating a labeled multi-Bernoulli (LMB) density in time. For its implementation, the GLMB filter uses its analytical form known as δ-GLMB [START_REF] Vo | An efficient implementation of the generalized labeled (a) Ground truth trajectories (b) GLMB + measurement driven birth (c) GLMB + proposed adaptive birth Fig. 3. Area 34 tracking results[END_REF] given by the equation:

π(X) = ∆(X) (I,ξ)∈F (L)×Ξ ω (I,ξ) δ I (L(X))[p ξ ] X (1)
Where I ∈ F(L) denotes a set of object labels, ξ ∈ Ξ denotes the history of measurement-target association maps, and ω (I,ξ) is a non-negative weight for each (I, ξ) hypothesis. The term [p ξ ] X refers to the exponential notation of the product x∈X p ξ (x) with [p ξ ] ∅ = 1 and the term p ξ (•) denotes a probability density describing a multi-Bernoulli component's kinematic state. L denotes the labeling projecting function L : X × L → L and ∆(X) denotes the distinct label operator that is non-zero only when the labels in X are unique. Throughout this paper, we use the bold notation x, X for labeled states and the regular notation x, X for nonlabeled states, i.e. x = (x, ℓ)

The GLMB filter is propagated in time with the prediction step and update step. For this work, we use the jointprediction and update proposed by Vo and Vo in [START_REF] Vo | An efficient implementation of the generalized labeled (a) Ground truth trajectories (b) GLMB + measurement driven birth (c) GLMB + proposed adaptive birth Fig. 3. Area 34 tracking results[END_REF]. This efficient implementation uses Gibbs sampling to estimate likely realizations of the filter at each time step without exhaustively computing every possible combination of predicted and updated hypotheses. Similarly, we perform inference and cardinality estimation following the procedure listed by Vo and Vo [START_REF] Vo | An efficient implementation of the generalized labeled (a) Ground truth trajectories (b) GLMB + measurement driven birth (c) GLMB + proposed adaptive birth Fig. 3. Area 34 tracking results[END_REF].

ADAPTIVE MEASUREMENT DRIVEN BIRTH

Learning the Initial Velocities

During each frame, we perform inference to obtain the estimated label object state set Xk = {x i leaves a trace of its state at every inferred frame. Therefore, we create a velocity history map h k v : R 2 → R 2 , which updates iteratively at every frame k and h 0 v (i, j) = [0, 0] T ∀ i, j ∈ N. For the state x(k) i of each inferred object

x(k) i ∈ Xk , we learn the velocity history map h k v as follows:

h k v (p i ) = h k-1 v ( pi)+vi 2 if ||h k-1 v (p i )|| ̸ = 0 vi if ||h k-1 v (p i )|| = 0 (2)
Where pi denotes the i th object estimated location, and vi denotes the estimated velocity at frame k. The equation updates the velocity history map by averaging with new inferred velocity values. Additionally, we perform a linear interpolation between each labelled object in Xk with its past state in Xk-1 (in the case a target with the same label exists both in frames). Fig. 1 shows a sample velocity history map created from several time instances. The velocity 2D vector is encoded in the color channels.

Adaptive Measurement Driven Birth Intensity

During each iteration, we split new measurements into surviving and birth measurements Z k = Z S k ∪ Z B k depending on their distance to the predicted GLMB components. We call a measurement "surviving measurement" if is located less than a T birth distance from the location coordinates of the nearest Bernoulli component. Sequentially, we define the density of new-born targets π B (•) as:

π B (X + ) = δ(X + )ω B (L(X + ))[p B ] X+ (3)
Where X + denotes the predicted labeled object states, ω B is the probability of a birth component, and p B denotes the probability distribution of the kinematic states of the new-born targets. We define p B as:

p B (x, ℓ; z) = 1 |Z B k | zj ∈Z B k N (x; m B (z j ), P B ) (4)
Where P B is the initial covariance hyperparameter, ℓ ∈ N is an assigned new label, and the function m B (•) maps the birth measurements z j ∈ Z B k to the kinematic target states. The function m B (•) has a major impact in the filter's performance and is defined as:

m B (z j ) = [p j , h k v (p j )] T (5)
where pj denotes the location of measurement z j , and h k v (p j ) is the learned velocity function evaluated at location pj . This method differs from the classical "measurement driven birth" [START_REF] Lin | Measurement driven birth model for the generalized labeled multi-Bernoulli filter[END_REF] where the velocity component of m B (•) is unknown, random, or initialized to zeros.

EXPERIMENTS

Metrics

We evaluate the experiments using the ClearMOT [START_REF] Bernardin | Evaluating Multiple Object Tracking Performance: The CLEAR MOT Metrics[END_REF] metric. This metric reports the Multiple Objects Tracking Precision (M OT P ) and the Multiple Object Tracking Accuracy (M OT A). The M OT P depends on the average distance error between the track hypothesis and ground truth trajectories and ranges in [0, ∞), where 0 denotes a perfect score. The M OT A depends on False Positives (F P s), False Negatives (F N s), Identity Switches (IDSs) and the Number of Ground Truth objects (N GT s), and its score ranges from (-∞, 1], where 1 denotes a perfect score. Throughout this work, we call a hypothesis True Positive (T P ) if it has a uniquely matched ground truth object less than d = 5 pixels away.

Additionally, we name a trajectory Mostly Tracked (MT) if more than 80% of its ground truth trajectory is tracked. Similarly, we say a trajectory is Partially Tracked (PT) if it is not MT, but more than 20% of its trajectory is tracked; otherwise, we classify the trajectory as Mostly Lost (ML).

We test our method and compare it with the results obtained using the classical "measurement-driven" birth estimation (as used in [START_REF] Ristic | Adaptive target birth intensity for PHD and CPHD filters[END_REF][START_REF] Pace | Stochastic models and methods for multiobject tracking[END_REF][START_REF] Reuter | Cardinality balanced multitarget multi-Bernoulli filtering using adaptive birth distributions[END_REF]). We also compare with the modified track-GMPHD to recover trajectories proposed in [START_REF] Aguilar | Small moving target MOT tracking with GM-PHD filter and attention-based CNN[END_REF] and with the SORT [START_REF] Bewley | Simple online and realtime tracking[END_REF] algorithm as it has become a baseline for MOT-based works.

Results

We test our method with the WPAFB 2009 dataset available online [START_REF]Wright-Patterson air force base (WPAFB) dataset[END_REF]. This dataset contains videos recorded by a single sensor of the Wright Peterson Airforce Base in Ohio, USA. The images span an area of 19 km 2 at a resolution of 0.25m/pixel and a frame rate of 1.25 HZ over 512 frames. We use a downsampled version of this dataset at a resolution of 1.0m/pixel to mimic satellite videos and we register the images using the ORB stabilization algorithm similar to [START_REF] Aguilar | Small moving target MOT tracking with GM-PHD filter and attention-based CNN[END_REF]. We evaluate tracking results in specific areas of interest comprised of high-speed highways and a crossing. Particularly, we choose the areas of interest (AoIs) 02, 34, and 42 as shown in [START_REF] Lalonde | Clusternet: Detecting small objects in large scenes by exploiting spatio-temporal information[END_REF] to be consistent with the literature. We choose these regions as they present fundamental challenges for object trackers: objects move at high speeds, objects are often in crowded environments, and trajectories intersect regularly.

Table 1 shows that adding our adaptive birth improves the GLMB filter scores of the trajectory quality metrics across all three AoIs. For example, our filter attains a mean of 76.35% of MT trajectories while the traditional GLMB attains 53.59%, and the T-GMPHD attains only 20.75% of the MT trajectories. The reason behind this significant improvement is the adaptive birth estimation. Our approach initializes hypotheses with accurate velocity components. Therefore, the filter performs a correct data association between the predicted birth hypothesis and the actual frame measurements. The filters implemented with the traditional "measurementdriven birth" lose targets as the predicted birth hypotheses fail to track the target's future measurements. If the filters fail to follow targets, the hypotheses are considered clutter, or a new birth component is initialized at future untracked mea-surements. This issue is also manifested in the large number of identity switches shown in the seventh column of Table 1 where our approach obtains the lowest number of IDSs with respect to the number of detected objects.

The GLMB with default birth estimations obtains the lowest mostly lost (ML) scores. For all three cases, it has an ML score of 0.58%; this means the filter partially tracks objects but cannot fully recover whole trajectories. Similarly, the SORT tracker obtains the least number of IDSs across all three AoIs as it fails to track a large majority of objects. It is worth noting that in this work, we also consider static objects; hence, the results are artificially inflated even for weaker trackers such as SORT and the track-GMPHD.

CONCLUSION AND FUTURE WORK

This paper presented an adaptive birth estimation for the GLMB filter tailored for tracking objects in satellite images. The adaptive birth enhances the classical measurement-driven birth approach with the addition of velocity component initialization. Our approach significantly improves fast-moving object tracking on high-speed roads; hence, it reduces label switches, the number of false positives and false negatives.

While this addition shows significant advantages for tracking objects on high-speed roads, Table 1 shows that our tracker still has room for improvement. For example, visual appearance information could improve the targetmeasurement association and reduce clutter measurements. Similarly, the inclusion of visual information in different frames could contribute to estimating targets' initial velocities.

ACKNOWLEDGMENT

  label li and an estimated kinematic state x(k) i = [p i , vi ] T , where pi represents the estimated target location and vi denotes the estimated target's velocity at frame k, and i = {1, 2, • • • , n k } denotes the object index. Every tracked element x(k)

Fig. 1 .

 1 Fig. 1. Sample learned directions from past vehicles.

The authors are grateful to the OPAL infrastructure from Université Côte d'Azur for providing computing resources and support. Additionally, the authors would like to thank BPI France for the financial support under the LiChiE contract.

[3] Dexter Jagula, "A boom with a view: The satelliteimaging industry is exploding. Here's how to take advantage of it," IEEE Spectrum, vol. 59, no. 3, pp. 38-43, 2022.


Joao Carlos

Azevedo Goncalves

Issa Alaji

Daniel Gloria

Vincent Gidel

Frederic Gianesello

Sylvie Lepilliet

Guillaume Ducournau

Francois Danneville

Christophe Gaquière

François Danneville

On wafer millimetre wave power detection using a PN junction diode in BiCMOS 55 nm for in-situ large signal characterization

Keywords: power detector, millimeter wave, Large signal characterization, BiCMOS 55 nm

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

Thanks to progress of Silicon Technology cut-off frequencies, complex integrated circuits are increasingly designed in millimetre-wave frequency range, and beyond 110 GHz. Increasing the system frequency allows higher bandwidth and therefore leads to new applications in the scope of high data rates or THz scanning [START_REF] Chevalier | A 55 nm triple gate oxide 9 metal layers SiGe BiCMOS technology featuring 320 GHz fT / 370 GHz fMAX HBT and high-Q millimeter-wave passives[END_REF]. The design of such complex systems is based on accurate and reliable models of active devices like MOS or bipolar transistors. These models are extracted and validated by high frequency (HF) measurements, including small signal, large signal and noise characterization. However, these models are based on measurements below 110 GHz and are extrapolated beyond due to the lack of industrial measurement tools at those frequencies. For this purpose, high frequency measurements above 110 GHz are of utmost importance for the validation of such models and circuit design in the mmW frequency range. Large signal characterization aims to extract compression point, power added efficiency and power gain under single tone excitation. In mmW frequency range, calorimeter detectors are typically used because no solutions based on diodes are available up to now. However, due to the long-time of acquisition this is not compatible for industrial use, especially for low power detection. Furthermore, these detectors can be used only in steady state. High frequency power detectors have been reported in the literature, using zero bias Schottky diode (SBD) [START_REF] Hesler | NEP and responsivity of THz zero-bias Schottky diode detectors[END_REF], [START_REF] Han | A 280-GHz Schottky Diode Detector in 130-nm Digital CMOS[END_REF], heterostructure low barrier diode (HLBD) [START_REF] Nadar | High Performance Heterostructure Low Barrier Diodes for Sub-THz Detection[END_REF] and P-N diode [START_REF] Ahmad | THz Detection Using p #x002B;/n-Well Diodes Fabricated in 45-nm CMOS[END_REF]. However, part of these solutions has power limitations or are not compatible with silicon technology for Built-in self-test (BIST) application to perform integrated test. Recently, investigations have been done to perform on wafer large signal characterisation, based on load pull methodology setup using in-situ impedance tuner [START_REF] Bouvot | A D-band tuner for in-situ noise and power characterization in BiCMOS 55 nm[END_REF] and high frequency power source [START_REF] Bossuet | A 10 dBm Output Power D-Band Power Source With 5 dB Conversion Gain in BiCMOS 55nm[END_REF] up to D band frequency range. In addition, to perform on wafer characterisation, integrated power detector is required with high dynamic range and high voltage responsivity to increase measurement accuracy. For this purpose, this paper proposes and describes mmW in-situ power detection solution in BiCMOS 55 nm STMicroelectronics technology.

II. TEST STRUCTURE AND SMALL SIGNAL MODEL

EXTRACTION The device used for on wafer mmW power detection is a P-N junction diode available in BiCMOS 55 nm technology from STMicroelectronics. The test structure is composed of a diode mounted in transmission 2-ports configuration connected to dedicated RF pads through access lines on metal level 8 and vias performing connection between Silicon level and the access lines. Figure 1 shows a photography of test structure. and can be extracted from the I-V characteristic of the diode, where is deducted from the slope of the I-V curve at a given operating point, and is calculated at relatively high biasing point in the ohmic zone.

A measurement of the S parameters was performed from 0.1 to 110 GHz, in order to extract the values of the model parameters. Extrinsic parasitic elements ( , and ) were extracted using open and short dummies. Complete short and complete open are defined on the diode reference planes. is extracted using the complete short structure (RF pads effects de-embedded). Considering the complete open, and can be extracted. In this study, Cdiode_sub, Rsub and Csub are supposed to be negligible in this frequency range, and the capacitance is supposed to be negligible compared to . All of those assumptions will be validated by comparing the extracted model to the measurements results. Based on the assumptions above, we can consider that the model of the deembedded diode is the same as the intrinsic model in figure 2. The impedance of the intrinsic model is provided by the equation ( 1) and can be concluded as the solution of the equation (2).

j j j j j j j s C R w C wR J C R w R R Z + - + + = (1) 0 ) ( ). . ( ). . ). ( ( 2 2 2 2 = + + Z imag C R w C R w Z imag j j j j (2)
Where w is the angular frequency and imag(Z) is the imaginary part of the measured impedance of the de-embedded diode structure. is the junction resistance which is already extracted from the I-V characteristic. Respecting two conditions: (i) that the extraction of is done at high frequency and (ii) having a high value of (which is the case of this study) can be also deducted using equation 3 which gives approximately the same result of equation 2.

) ( . 1 Z imag w C j - ≈ (3)
Extracted values of model elements are reported in Table 1 for 1 µA and 5 µA biasing point. To validate the model, the element values have been extracted and used to simulate the complex input impedance. These results have been compared to the measurements. Figure 3 shows a comparison between the model and the measured diode impedance. A good agreement is noted over the whole frequency range the fact that confirms our assumptions and validates the proposed model.

III. LARGE SIGNAL MEASUREMENT AND VOLTAGE

RESPONSIVITY EXTRACTION METHOD Figure 4 shows the block diagram of the setup used in order to perform on-wafer detection by probing the diode on dedicated RF pads compatible with a pitch of 50 µm. The diode was biased in its forward regime through the integrated bias tee of RF Infinity probes i325. Using a DC source meter KEITHLEY-2440, the bias current was applied and the corresponding DC voltage was measured presenting high impedance (>10 GΩ). The used 300 GHz power source is composed of a frequency multiplier by six and three, which leads to an overall frequency multiplication factor of eighteen, this multiplier is driven by 50-GHz Agilent E8257D PSG, and operating in its compression regime to ensure a constant output impedance. The output power is controlled through mmW manual attenuator. To perform wide frequency range extraction of the on-wafer diode detector sensitivity, the 300 GHz source was substituted by a VNA extender on 220 to 320 GHz frequency range; the latter was used as a power source, providing -30 dBm in the operating frequency range. In case of biased detection operation, the diode is controlled with its DC current. The corresponding voltage value (VOFF) when the power source is OFF, is not equal to zero as shown on figure 6. Hence, when the power source is switched in its ON state, the corresponding voltage value is shifted to (VON). Thus, the ratio between the delta voltage and the injected high frequency input power corresponds to the sensitivity of the detector (γ), described by equation (4).

=

( 4 ) Part of measurement uncertainty is related to the DC source meter. The voltage measurement accuracy is defined according to the used voltage range. In our case the 2V range gives a voltage measurement uncertainty of +/-300 μV. Second part of extraction accuracy, is related to the assumed input injected power, which is due to source power calibration accuracy. In our case we assume an uncertainty of 5 % of input power related to power calibration and provided by power meter datasheet = PIN*5%. Equation ( 5) describes the uncertainty of the corresponding voltage responsivity, by taking into account both and . Figure 7 shows the as a function of the injected power . The uncertainty of the voltage responsivity is dominated by the voltage measurement accuracy of the DC source meter, that take more importance for lower injected powers. IV. VOLTAGE RESPONSIVITY EXTRACTION The voltage responsivity of integrated diode was extracted over 220 to 320 GHz frequency range using VNA extender and mmW power source between 280 GHz and 320 GHz for dynamic extraction. The γ bias dependency measured at 320 GHz plotted in Figure 8 shows a peak of voltage responsivity of 3836 V/W at -33 dBm for a bias current of 1 nA. However, this point is already on saturated regime. Monitoring the bias current condition, the diode features a voltage responsivity varying between 426 to 3836 V/W and allows dynamic range optimisation to increase PIN_sat, corresponding to the power at which the diode saturates. However, the increase of PIN_sat induces a reduction of voltage responsivity. The previously extracted model was simulated on same configuration by taking into account access line, RF pads and the impedance presented by the probe. The simulated responsivity is close to measured values and has the same bias dependency function of injected power.

| | = | | ± ( 5 )
Figure 9 shows the extracted and the simulated γ in 220 to 320 GHz frequency range preformed using VNA extender for a bias current of 500 nA. The uncertainty defined previously was accounted for γ extraction. The VNA extender provide around -30 dBm on pad plane, leading to a of +/-300 V/W. We observed discrepancy between extraction performed with 300 GHz source and VNA extender. This is attributed to the presented impedance of the source through the probe on pad plane. To highlight the impedance dependency of this detector configuration, the responsivity was simulated for three configurations; (i) on plane [BB'] taking into account impedance of source through the probe, (ii) on plane [BB'] for a presented impedance of 50 Ohms, (ii) on plane [AA'] for a presented impedance of 50 Ohms. These simulations highlight the dependency of the responsivity on the presented impedance, that inducing ripples on wide frequency range. Table [START_REF] Hesler | NEP and responsivity of THz zero-bias Schottky diode detectors[END_REF] provide performance summary and comparison with prior state of the art. However, the unmatched configuration leads to high dependence of voltage responsivity on the source impedance. The monitoring of bias current allows wide range γ value and adjustable power detection dynamic range. Study performed on extraction accuracy demonstrates minor impact of measured voltage and power source uncertainties. This study allows potential integration of detector to be used in a wide range of in situ measurement applications such as low noise amplifier, receiver chain, couplers or load pull characterization test structure. The extracted model of the diode was simulated and exhibits a voltage responsivity close to measured values. The model being validated by the aforementioned comparison, it will enable to determine the optimal topologies for the design of more complex detectors.

Fig. 1 .

 1 Fig. 1. Test structure photography Figure 2 shows the test structure model including the intrinsic and extrinsic elements. This model includes: the capacitance of the pads (CPAD), inductance of transmission access lines and vias (LS), parasitic capacitance between anode and cathode (CP), resistance and capacitance of the substrate (Rsub and Csub), series resistance of the ohmic contacts (RS) and the resistance and capacitance of the junction (Rj and Cj).

Fig. 2 .

 2 Fig. 2. Test structure model including the intrinsic and extrinsic elements

Fig. 3 .

 3 Fig. 3. Real and imaginary part comparison of measured and simulated model of the PN diode junction intrinsic impedance for a biasing voltage of 0.75 V

Fig. 4 .

 4 Fig. 4. Test bench block diagram to perform on wafer power detection Output power calibration was performed after the attenuator, using VDI PM4 power meter; in figure 5 a dynamic power

Fig. 5 .

 5 Fig. 5. Available output power of used 300 GHz source

Fig. 6 .

 6 Fig. 6. I-V curves for input constant power at 2 states (RFOFF on blue curve and RFON on red curve).

Fig. 7 .

 7 Fig. 7. Measurement uncertainties impact on voltage responsivity extraction function of input power.

Fig. 8 .

 8 Fig. 8. Extracted and simulated voltage responsivity function of input power for variable bias current at 320 GHz

Fig. 9 .

 9 Fig. 9. Simulated and measured voltage responsivity and corresponding uncertainty on 220 to 320 GHz frequency range for a bias current of 500 nA and -30 dBm of input powerTable 2. Detector performances comparison

Table 1 .

 1 Extracted model elements values

	Current	CPAD	CP
	1 µA 5µA	3 fF	0.6 fF	30 pH	60 Ω	4 fF 6.5 fF 5 kΩ 23 kΩ

ACKNOWLEDGMENT

This work has been supported by ECSEL TARANTO project toward advanced BiCMOS nanotechnology platforms for RF and THz application and EURAMET ADVENT project "16ENG06 advanced: Metrology for advanced energy-saving technology in next generation electronics applications"


This paper describes millimeter wave (mmW) onwafer continues wave (CW) power detection using dedicated high frequency diode junction, integrated on SiGe BiCMOS 55 nm technology from STMicroelectronics. This extraction was performed for two test structures configurations in order to evaluate the potential of this diode junction for power detection as well as for sub-Terahertz Transmission Link on 220 to 320 GHz Frequency Range. The power detection is performed by biasing the diode on its forward regime. That allows to obtain a voltage responsivity (γ) for variable bias current increasing from 1 nA to 5 µA and exhibiting a corresponding γ decreasing from 3000 V/W to 500 V/W at 320 GHz.

I. INTRODUCTION

HE wireless communication application growth with video and music streaming leads to data traffic increasing exponentially and tends to saturate the allocated frequency bandwidths. That requires higher data rate with up to 100 Gb/s by increasing operating frequency. Sub-THz communication represents a great opportunity in order to reach data rates higher than 10 Gb/s. However, Atmospheric attenuation of THz waves is utmost important and leads to transmission distance limitation. THz communication for medium distance have a window between 200 GHz and 320 GHz frequency range. Several links have already been demonstrated in this frequency range using photonics and electronics technologies [START_REF] Koenig | Wireless sub-THz communication system with high data rate enabled by RF photonics and active MMIC technology[END_REF], [START_REF] Nagatsuma | Terahertz communications technologies based on photonic and electronic approaches[END_REF]. THz link has been reported at 300 GHz using photonics device on transmitter chain and III-V Schottky barrier diode (SBD) on receiver chain, by performing intensity modulation and direct detection [START_REF] Nagatsuma | Millimeter-Wave and Terahertz-Wave Applications Enabled by Photonics[END_REF]. Silicon devices development becomes competitive to III-V semiconductors featuring higher integration level for electronics [START_REF] Grzyb | A 240 GHz high-speed transmission link with highly-integrated transmitter and receiver modules in SiGe HBT technology[END_REF] or photonics [START_REF] Lacombe | 10 Gbps indoor THz communications using Industrial Si Photonics Technology[END_REF].

II. TEST STRUCTURES

Figure 1 shows the two diodes test structures configurations which have been characterized. The first structure is dedicated to continuous wave power detection composed of diode with one anode finger of 1 µm, on two-port configuration. The second structure is dedicated to modulated signal detection. Composed of a diode with one anode of 5 µm, on "T" configuration. Both configurations were characterized for CW on wafer power detection, for a first evaluation of their voltage responsivity on modulated signal configuration. Figure 2 shows the measured I-V characteristic of both diodes.

III. SIGE PN JUNCTION DETECTION SENSITIVITY EXTRACTION

Figure 3 shows the block diagram of the setup used in order to perform on-wafer CW detection on test structure configuration a. The diode was biased on its forward regime through the integrated bias tee of RF probes. The current bias was applied and the corresponding DC voltage was measured. VNA extender was used as high frequency signal source on 220 GHz to 320 GHz frequency range providing available power around -30 dBm at contact pads plane. The 50 Ω mmW load connected after output RF probe helps to minimize any reflection at waveguide interface and stationary waves in the right probe. Joao Carlos Azevedo Goncalves1,2 , Issa Alaji 1 , Daniel Gloria 2 , Sylvie Lepilliet 1 , François Danneville 1 , Christophe Gaquière 1 and Guillaume Ducournau 1

In the case of biased detection operation, the diode is controlled with its DC current. The corresponding voltage value (VOFF) when the source is OFF, is not equal to zero. Hence, when the source is switched in its ON state, the corresponding voltage value is shifted to (VON). Thus, the ratio between the delta voltage (VON-VOFF) and the injected power of millimeterwave signal corresponds to the sensitivity of the detector (γ). Figure 4 shows the extracted voltage responsivity of test structure a. The sensitivity of detector was extracted on 220 GHz to 320 GHz frequency range for variable bias current increasing from 1 nA to 5 µA and exhibiting a corresponding voltage responsivity decreasing from 3000 V/W to 500 V/W at 320 GHz. This unmatched detector is highly sensitive to source impedance. In addition, on the used setup for the on-wafer power detection, the sensitivity extraction depends on the presented impedance of the RF probes to the device and induce ripples on extracted values function of frequency. The main limitation on used measurement methodology comes from the measurement accuracy of voltage response. For bias power detection, a few mV of delta voltage is measured using 2 V voltage range measurement of the DC Source/meter, inducing an uncertainty of +/-200 µV on the measurement values for (VON) and (VOFF). The uncertainty was accounted for γ extraction. This limitation becomes more important for very low power detection. The test structure a. induces the measurement of the voltage response between the two-bias tee (Input and Output). In case of modulated signal detection, the limitation is directly related to bias tee cut off frequency (DC path). Thus, the configuration b allows the device polarization through the bias tee and the measurement of demodulated signal at a lower frequency through the output RF probe (in coaxial configuration). Figure 5 shows the block diagram of the setup used in order to perform on-wafer CW power detection on configuration b, based on the constraints of modulated signal detection. The RF signal on 220 to 320 GHz frequency range is provided to the device as for the configuration a. However, in this case, the diode was biased on its forward regime through the integrated bias tee of input RF probe, and 50 GHz RF probe was used on the right side. In order to reproduce the influence of impedance presented on the right side, like on configuration of a modulated signal detection.

Figure 6 shows the extracted voltage responsivity of configuration b. The extracted response keeps the same variation function of bias polarization as the configuration a. As for configuration a, the detector sensitivity was extracted on 220 GHz to 320 GHz frequency range for variable bias current increasing from 1 nA to 5 µA and exhibit a corresponding voltage responsivity decreasing from 2000 V/W to 700 V/W at 300 GHz. The test structures availability induces the use of two different diodes size, leading to un-comparable response.

IV. CONCLUSION

The described detector based on diode junction in a BiCMOS 55 nm technology from STMicroelectronics exhibits interesting features for Sub-Terahertz detection power detection as well as towards future receivers for data links in the 300 GHz band. The monitoring of bias current allows competitive and wide range γ value. Next step will be to use synchronous detection (lock-in amplifier) to increase accuracy for lower power signal detection and evaluate the potential of these structures for modulated signal detection.

Fig. 1 .

 1 Fig. 1. Test structures configurations, a. L1N1 dedicated to CW power detection, b. L5N1 dedicated to modulated signal detection.

Fig. 2 .

 2 Fig. 2. Measured I-V characteristic of used diodes: one anode finger for 1 and 5 µm finger length.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Test bench block diagram to perform on wafer power detection on test structure configuration a.

Fig. 5 .

 5 Fig. 5. Test bench block diagram to perform on wafer power detection on test structure configuration b.

Fig. 6 .

 6 Fig. 6. Configuration b. Extracted voltage responsivity on 220 to 320 GHz frequency range for a variable bias current from 1 nA to 5 µA and -30 dBm of input power

IEMN, UMR CNRS 8520, Avenue Poincaré -CS 60069, 59652 Villeneuve-d'Ascq, France

STMicroelectronics, 850 rue Jean Monnet,

Crolles, FranceInvestigating the potential of SiGe Diode in BiCMOS 55nm for power detection and datacom applications at 300 GHz

ACKNOWLEDGMENT

This work has been supported by ECSEL TARANTO project toward advanced BiCMOS nanotechnology platforms for RF and THz application and EURAMET ADVENT project "16ENG06 advanced: Metrology for advanced energy-saving technology in next generation electronics applications"


S J Petit Safran

J Bect

SAE J Demange

S Da Veiga

Safran Tech

E Vazquez

Relaxed Gaussian process interpolation: a goal-oriented approach to Bayesian optimization

Gaussian process (GP) interpolation and regression [see, e.g., 1, 2] is a very classical method for predicting an unknown function from data. It has found applications in Bayesian optimization, a popular derivativefree global optimization technique for "expensive-to-evaluate" functions.

A GP model is defined by a mean and a covariance functions, which are generally selected from data within parametric families. The most popular models assume stationarity and rely on standard covariance functions such as the Matérn covariance. The assumption of stationarity yields models with relatively low-dimensional parameters. However, such a hypothesis can sometimes result in poor modeling when functions to be predicted have different scales of variation or different local regularities across the domain. This is the case, for instance, in the motivating example given by [START_REF] Gramacy | Bayesian treed Gaussian process models with an application to computer modeling[END_REF] or in the even simpler toy example shown in Figure 1. This function, which we shall call the Steep function, has a clear global minimum around the point x = 8, which is overshadowed by the variations on the left. A stationary GP fit is shown in Figure 2 (a): observe that the confidence bands are too large and that the conditional mean varies too much in the neighborhood of the global minimum. One expects Bayesian optimization techniques to be somehow inefficient on this problem.

Going beyond the stationary hypothesis has been a very active direction of research. One can distinguish two categories of approaches that all use stationary Gaussian processes as a core building block: local models [see, e.g., [START_REF] Gramacy | Bayesian treed Gaussian process models with an application to computer modeling[END_REF][START_REF] Rasmussen | Infinite mixtures of Gaussian process experts[END_REF] and composition of models [see, e.g., [START_REF] Rychlik | Modelling and statistical analysis of ocean-wave data using transformed Gaussian processes[END_REF][START_REF] Damianou | Deep Gaussian processes[END_REF]. The gain in expressiveness has usually the counterpart of an increasing number of parameters to be estimated from data, relying on advanced inference techniques, or leaving to the user the choice of key parameters.

In this work, we suppose that there are regions of interest in the output range. We propose to explore goal-oriented GP modeling, where we want predictive models in regions of interest, even if it means being less predictive elsewhere. The proposed method is based on the relaxation of the interpolation constraint outside the region of interest. This yields goal-oriented interpolation models designed to be accurate for a subset of the range of the function, which are very beneficial for Bayesian optimization, as in Figure 2 (b). This work presents three main contributions. First, we propose new models called Relaxed Gaussian processes (GP-R) for goal-oriented modeling with noiseless observations. Secondly, we give theoretical and empirical results justifying the method and its use for Bayesian optimization. Finally, we propose a new scoring rule called truncated continuous ranked probability score (tCRPS) designed for the problem of goal-oriented modeling.

Joint work with J. Bect and E. Vazquez.

[1] M. L. Stein. Interpolation of Spatial Data: Some Theory for kriging. Springer New York, 1999.

Figure 1 :

 1 Figure 1: We show (a): the Steep function, and b): also the Steep function, but with a restriction on the y-axis for illustration purposes.

Figure 2 :

 2 Figure 2: We show (a): a vanilla stationary Gaussian process fit on the Steep function based on some observations (black squares), and (b): a GP-R fit; the quantity t is a relaxation threshold that is chosen automatically. The red lines are the conditional means and the gray bands represent the uncertainty estimates.


Emmanuella Martinod
email: emmanuella.martinod@lisn.upsaclay.fr

Claire Danet
email: claire.danet@lisn.upsaclay.fr

Michael Filhol
email: michael.filhol@lisn.upsaclay.fr

Two New AZee Production Rules Refining Multiplicity in French Sign Language

Keywords: AZee, Sign language, Formal representation, Multiplicity, Plural !

This paper is a contribution to sign language (SL) modeling. We focus on the hitherto imprecise notion of "Multiplicity", assumed to express plurality in French Sign Language (LSF), using AZee approach. AZee is a linguistic and formal approach to modeling LSF. It takes into account the linguistic properties and specificities of LSF while respecting constraints linked to a modeling process. We present the methodology to extract AZee production rules. Based on the analysis of strong form-meaning associations in SL data (elicited image descriptions and short news), we identified two production rules structuring the expression of multiplicity in LSF. We explain how these newly extracted production rules are different from existing ones. Our goal is to refine the AZee approach to allow the coverage of a growing part of LSF. This work could lead to an improvement in SL synthesis and SL automatic translation.

Introduction

The framework of this study is sign language (SL) formal description with the AZee model [START_REF] Filhol | Non-Manual Features: The Right to Indifference[END_REF]. One of the outcomes of SL formal description is the potential use for SL generation with an avatar. Current approaches are often elaborated based on spoken languages, which are linear systems (see [START_REF] Hadjadj | Modeling French Sign Language: a proposal for a semantically compositional system[END_REF] for a review of existing systems). This may pose some fundamental problems since SLs are multi-linear visual-gestural languages. In contrast, AZee aims at integrating all the forms and phenomena observable in SL. It is a corpus-based approach that defines systematic links between observed forms and interpreted meanings. This article deals with a specific problem related to one of these form-meaning associations: the case previously marked as "Multiplicity", which covered a vague notions of plurality. We propose a systematic study of this phenomenon in French Sign Language (LSF). After briefly presenting the basics of the AZee approach, its production rules system, and a methodology to identify them (section 2), we will introduce the notion of multiplicity and explain why it needs refinement (section 3). Then, we will present the LSF data we analyzed (section 4) and detail the application of the methodology (section 5). We expose the obtained results, i.e. two new production rules (section 6). We will discuss this contribution (section 7) and finish with some propositions for future studies (section 8).

The AZee Approach

AZee is a formal approach for representing SL utterances and discourse. This is done by constructing recursive expressions that combine production rules applied to arguments. Production rules are systematic links between observable forms (a set of articulators and the way they are synchronized or arranged in time) and semantic functions (an interpretation of such observable forms, i.e. their meaning). The forms can be parameterised with arguments, which can be mandatory or optional [START_REF] Hadjadj | Modeling French Sign Language: a proposal for a semantically compositional system[END_REF]. For example, rule vêtement associates the meaning "clothing" with the form given in Figure 1, and has no arguments. Rule all-of, with list argument items, creates the meaning of a set containing all the items, focusing on the set as a whole [START_REF] Mcdonald | Natural synthesis of productive forms from structured descriptions of sign language[END_REF]. The associated form is the concatenation of each item in items, 1 recursively produced in an accelerated manner. The set of all identified production rules is called the production set. It is then possible to combine them and build tree-structured expressions that represent complex utterances in SL, called discourse expressions. The AZeefication process consists in elaborating an AZee expression to represent a given SL utterance. This has recently been done on the corpus of real-life short news items 40 brèves v2 [START_REF] Challant | A First Corpus of AZee Discourse Expressions[END_REF], totalling 120 AZee discourse expressions covering 1 hour of signed discourse. AZee provides a corpus-based methodology to identify production rules through the analysis of SL data. It consists in alternating search criteria of form and meaning until regular form-meaning associations are determined. In general, form observations are done on videos with the naked eye, which is the case in the work reported here, although additional software measurements would be possible for more accurate data, in particular for better analysis of dynamics. Meaning interpretation, though, is assumed to be performed by a human in the process. We explain the steps of the process below [START_REF] Hadjadj | Modeling French Sign Language: a proposal for a semantically compositional system[END_REF], as we will be applying it later in section 5:

1. start with a form or meaning criterion X to explore; 2. locate and list all occurrences of X in a selected SL corpus, and let Nocc be the number of occurrences; 3. for each occurrence of X listed, add description elements:

• elements of interpretation if X is a form criterion;

• elements of form if X is a semantic criterion; 4. identify groups of at least two occurrences with similar description elements, and let:

• Ngp be the number of identified groups;

• Nout be the number of occurrences not included in any group;

5. if all of the following conditions are satisfied:

• X is a meaning criterion; • Ngp = 1;

• Nout is less than a threshold, e.g. 15% of Nocc; then the form elements defining the unique group X.1 can be considered invariant, and we define a new production rule associating X with the invariant form, and this iteration stops; 6. if this iteration has not stopped, for each group X.k, k ∈ 1..Ngp:

• if X is a meaning that can already be expressed using known production rules justifying the form X.k or, conversely, X.k is a meaning that can already be expressed using known production rules justifying the form X, then no new rule is to be found, nor any new search to be fired;

For information, the language of the name of the production rules (French and English here) is arbitrary, as any gloss 1 can potentially be.

! 2

• otherwise, recursively apply this methodology with a new iteration starting with the criterion defining group X.k.

The Multiplicity Issue

The AZeefication of the 40 brèves v2 corpus (LIMSI and LISN, 2022a) mentioned above resulted in some phenomena that AZee could not represent. In the AZee expressions, the authors have filled the parts covering those instances with an "ellipsis", using a dummy rule application and marking it with %E. Many of these ellipses were tentatively marked as multiplicity when concerning the expression of plurality. For instance, Figure 2 shows two examples of motion repetition labeled multiplicity. Arrows show the trajectory of movement repetitions, and crosses stand for each of these repetitions. On the left side, the signer represents a series of three aligned poles. His left hand stands for a roof while his right hand shows the set of successive aligned poles. On the right side, the virtual signer repeats three times the sign for "town" in LSF, with the meaning "towns everywhere". Previous work in SL linguistics also mentions movement repetition as a strategy for expressing plurality in some SLs [START_REF] Pfau | Pluralization in sign and in speech: A cross-modal typological study[END_REF][START_REF] Kuhn | Cross-categorial singular and plural reference in sign language[END_REF]. Although differences between SLs have been observed [START_REF] Perniss | Visible Variation: Comparative Studies on Sign Language Structure[END_REF][START_REF] Steinbach | Plurality[END_REF][START_REF] Van Boven | Phonological restrictions on nominal pluralization in sign language of the Netherlands: evidence from corpus and elicited data[END_REF]), it appears to be a possible strategy in LSF as well [START_REF] Sallandre | La Langue des Signes Française (LSF)[END_REF]. However, these studies often use as examples a few isolated signs but there is no systematic analysis based on a corpus of SL data. The problem with the multiplicity instances is that while the meanings might be captured with a common notion of quantity (count, duration, repetition...), no stable invariant form can be associated with it. Looking at Figure 2, we can observe that in the left case, the trajectory is straight whereas in the right case, the trajectory is in contrast a circular one. In terms of meaning, finer distinctions seem also to be possible: the example on the left means for the geometric alignment to be interpreted, as opposed to that on the right. It would be wrong to interpret the towns as aligned on a circle. Our objective was to clarify what rules should account for these repetitions and better define the "multiplicity" phenomenon with true form-meaning pairs extracted from SL data. To do this, we chose to apply the methodology for the extraction of production rules, starting from the most salient element that seems common to all cases in question, i.e. the repeated movement criterion (R), which we define as follows: R Succession of deliberate motion strokes similar in path, by a same or symmetric body part, with no other significant motion in between. By similar, we mean to allow for geometric translation, symmetry and scaling.

! 3

We will apply the methodology to two different LSF video sets, which we present below.

Mocap1

Mocap1 is a corpus of LSF recorded with a motion capture system and an HD camera. It was designed with the goal of carrying out multidisciplinary studies in Movement Sciences, Linguistics, and Computer Science. This corpus is composed of 5 different tasks. The task on which we focused is a description task of 25 images, performed by eight deaf signers facing the camera, as shown in Figure 3, 94 videos out of 187 video files corresponding to this task were analyzed. The nature of these data is challenging for the formal representation of LSF since they are descriptions of spatialized elements, where the signers use less lexical signs but instead rely on the iconic representation potentialities of their language.

Rosetta-LSF

Rosetta-LSF is an LSF corpus captured by a motion capture system (Vicon) with retroreflective markers recording at 100 Hz and a head-mounted oculometer (MocapLab MLab 50-W) recording at 50 Hz and rendered as a 3D avatar animation (Figure 4). This 3D rendering in good quality allows us to see the necessary details (movement, facial expression, gaze, etc.) to do the analysis. It was designed in the framework of a French public/private project that studied accessibility solutions for audiovisual content [START_REF] Bertin-Lemée | Rosetta-LSF: an Aligned Corpus of French Sign Language and French for Text-to-Sign Translation[END_REF]. In contrast with Mocap1, the news titles translation task was chosen among the four of the ROSETTA project. This constitutes a list of nearly 194 news titles from a French public information channel. News content exhibits clean language, deals with any topic, which makes it a more conventional nature of the data.

! 4

Applying the Methodology

This section follows the methodology presented in section 2, starting with the form criterion R.

Iteration R

The first step is to identify and list all occurrences of criterion R (form criterion defined above, of a repeated movement) in the selected corpus. We found 756 occurrences (640 in Mocap1 and 116 in Rosetta-LSF). For each occurrence of R, we then indicate elements of interpretation since R was a form criterion. For instance: a set of countable and counted elements. After the description of the occurrences, 25 groups of at least two entries could be constituted on the basis of similar features, covering a significant portion of the list but leaving out 52 entries. We summarize this below:

• Nocc = 756 • Ngp =25 • Nout = 52
Of the 25 groups formed, we give the first ten in size below, with the common semantic feature defining them and examples. R.1 Set of countable but uncounted elements (448 entries) Examples: "many flowers on the ground", "rows of trees", "companies" R.2 Set of countable and counted elements (157 entries)

Examples: "four chairs set around a table", "three people" R.3 Set of uncounted countable and numerous elements (57 entries)

Examples: "laying of tiles", "carpet mesh" R.4 Permanence of a capacity/function for an object (25 entries)

Examples: "curtain opening", "mechanical arm motion" R.5 Wood (9 entries) ! 5 R.6 Clothing (8 entries) R.7 Salt (6 entries) R.8 Construction (5 entries) R.9 Wine (5 entries) R.10 House (3 entries) ... Following the methodology requires that we now take each of these groups separately and either recognize a meaning-form association already accounted for by other rules of the known production set, or explore further by going through the steps again, starting with the criteria defining the group. All groups numbered R.5 and up happen to be trivial cases of known signs (dictionary entries) for which we already have a production rule justifying the observed form. For example R.6, whose form is that of Figure 1, is easily explained with an application of rule vêtement. These groups need therefore not be explored any further. In contrast, the other groups R.1 to R.4 must be explored recursively because no trivial way can be found to justify form R with a combination of known rules that would match the meaning defining the group. We do this below for R.1 and R.2, the last two R.3 and R.4 being marked as future research and not covered in this paper. For every cascading iteration, we report on the values for Nocc, Ngp and Nout, followed by a definition of each formed group in the iteration.

Iteration R.1

This iteration starts with a search for all occurrences meaning "set of countable, but uncounted, elements." The result of this search follows:

• Nocc = 427 • Ngp = 2 • Nout = 21
Most of the occurrences include either or both of the following conditions on a repeated motion:

(a) attenuation of precision or amplitude over the repetitions (r) relocation of the successive repetitions

The two groups formed in this iteration are given below. R.1.1 Repetition of a movement with (a) and (r) Example: "shelves", the repeated movement being that for each flat shelf under the previous (see Figure 5) R.1.2 Repetition of a movement without (a) or without (r)

Example: "traffic jam", repetition of the shape of a car with forward relocation This is not a stopping case, and none of those groups can be entirely accounted for with known rules. Two new iterations, one for each group, are necessary. They are presented below.

Iteration R.1.1

Search for form: repeated movement with attenuation and relocation.

! 6 • Nocc = 406 • Ngp = 2 • Nout = 96
We found two groups defined by meaning in this iteration. R.1.1.1 Set of countable but uncounted elements without any order Examples: "towns" (Fig. 2) (right), "roofs" R.1.1.2 Set of countable but organized uncounted elements Examples: "poles", "shelves" This is still not a stopping case. Two new iterations are necessary, one for each of those groups. The meaning defining R.1.2.1 can be constructed using the known all-of rule applied to the item list, which creates an expression meaning the set of items, focusing on the set as a whole. Such expression generates a form compatible with R.1.2.1, which means that R.1.2.1 needs no further exploration. This being the only group in the iteration, no further exploration is needed for R.1.2. This indeed terminates R.1 all together.

Iteration R.2

Search for meaning: set of countable and counted elements.

• Nocc = 156

• Ngp = 3 • Nout =1
Three groups formed: R.2.1 repeated and relocated movement without attenuation Example: "four plates" R.2.2 repetition of a movement where each hand realizes an item Example: "both sides of a river" R.2.3 repetition of a movement with a hold and a blink between each repetition Example: "two lamps"

We notice that all groups are defined by forms that we can already generate with combinations of existing rules such as all-of, simultaneous, each-of or place-object [START_REF] Mcdonald | Natural synthesis of productive forms from structured descriptions of sign language[END_REF], which match the meaning of the current criterion R.2.

No groups are left to explore under iteration R.2. And as we said above, R.3 and R.4 are left for future research, which makes this the end of exploration R.

! 8

Figure 5: Example of R.1.1: movement repeated with attenuation and relocation, from Mocap1: i08l2, 00:34:17

Results

Figure 6 provides a summary of the study. It allowed the identification of two new regular formmeaning associations. This constitutes two new production rules, as detailed below (section 6.1). We will test these new production rules by applying them to other data (section 6.2). • arguments: signed item, path • meaning: multiple instances of item aligned along path, with the exact count unknown • form: item repeated along path, with attenuation of the movement

Two New Production

Evaluation of the New Production Rules

To evaluate our newly extracted production rules, we applied them to another LSF corpus, the 40 brèves v2. Indeed, [START_REF] Challant | A First Corpus of AZee Discourse Expressions[END_REF] initially found 207 occurrences of cases labeled multiplicity in this data. We have reviewed them to identify the occurrences now covered by our two production rules. In total, 63.5% of these cases are now covered by our new production rules. More precisely, 36.5% are mult-around occurrences, and 27% are mult-in-a-row occurrences: their form and meaning correspond to these rules.

Figure 7 shows examples of each of the two production rules in this data (mult-around, and mult-in-a-row). As in Figure 2, arrows stand for the trajectory of movement repetitions. On the left, the signer repeats the item for "dead," and, on the center, the signer repeats the item for "inhabitant,". Another outcome of this study is that it allows increasing the portion of LSF phenomena AZee can cover. In total, including the two new production rules, 96.1% of the LSF discourse from the 40 brèves v2 can be formally represented with AZee.

! 9

Figure 6: Overview of AZee production rules extraction process from R

Discussion

In addition to enriching the existing production set, this study to us also exhibits the precision of the existing rules, which we explain in this section.

In our work, 70.27% of R.1.2 occurrences are occurrences of an existing rule we already mentioned, all-of. This observation means that all-of is both formally and semantically close to the two rules that were finally highlighted. As a reminder, Rule all-of, its arguments, and its meaning are given hereinafter [START_REF] Mcdonald | Natural synthesis of productive forms from structured descriptions of sign language[END_REF]):

• All-of (items): Set of items, with focus on the set as a whole

In other words, this rule presents the association between the form of a list of items produced in an accelerated manner, and a meaning corresponding to "Set of items, with focus on the set as a whole".

From the meaning point of view, the two new production rules (i.e., mult-around and multin-a-row), on one side, and all-of on the other, are disjoint subsets of the previously labeled multiplicity. Our application of methodology highlighted that this assumption was not supported by the data. all-of creates the meaning of a set containing items, focusing on the set as a whole. But in the case of mult-around and mult-in-a-row, it is the same item that is repeated, and this item is necessarily countable and not counted, and either without any order or aligned.

From the form point of view, some cues are decisive in differentiating all-of from our two new production rules: the attenuation of the amplitude (or precision) of the repeated movement and the presence of a relocation of movement repetitions. This observation overall underlines the semantic finesse of the different production rules, in line with semantic nuances observed in LSF. 2

Conclusion and Prospects

The present study provided a better understanding of regular form-meaning associations regarding movement repetition in LSF. This contributes to enriching and refining the AZee LSF production set by adding two new production rules. This contributes to increase the ever growing proportion of the language that AZee can describe. Other studies could be conducted on the basis of this one. Firstly, groups left unexplored (R.3 and R.4) might lead to other new production rules. Secondly, among the initial 207 occurrences in 40 brèves v2, we noticed that 36.7% are similar to what we observed in Nout from R.1.1 in our data. These occurrences displayed a specific type of relocation resulting from an alternation of movement of both hands. Moreover, this form seems to often refer to the same element. Indeed, in our data, 53.6% of these cases of specific relocation concerned the item "people" in LSF. In 40 brèves v2, it represents 36.25%. Thus, these occurrences seem to share a similar form criterion. This subset could also be submitted to another iteration to reveal a possible specific form-meaning association. Thirdly, we intend to test our two new production rules using a small-scale experimental study. Image stimuli containing only various multiplicities of entities (disordered or aligned) will be presented to a deaf signer equipped with a motion capture system. Their task will be to describe this plurality of entities. This will allow us to verify that the form cues included in the two rules (attenuation of movement and specific trajectories) are systematically verified in production.

Finally, AZeefication of more data in LSF could also be a good evaluation of these two new rules and the AZee system in general.

Acknowledgement

This work has been funded by the Bpifrance investment "Structuring Projects for Competitiveness" (PSPC), as part of the Serveur Gestuel project (IVès and 4Dviews Companies, LISN -University Paris-Saclay, and Gipsa-Lab -Grenoble Alpes University).

In this regard, we notice that mult-in-a-row captures the possibility in LSF to project time into the signing space.

2 Indeed, items repeated along path can represent items aligned in space, or repeated in time.

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Figure 1 :

 1 Figure 1: Form of production rule vêtement (IVT, 1997)

Figure 2 :

 2 Figure 2: Two examples of motion repetition with different forms and meaning. Left side: from Mocap1: i06l1, 00:09:32 ; Right side: from Rosetta-LSF: RST X0047.demonstrateur1.mp4 00:03:60

Figure 3 :

 3 Figure 3: Screenshot of a video from Mocap1 corpus

  Repetition of a movement along a circular path, with attenuation Example: "towns" in Fig.2(right) Because a unique group formed in an iteration started with a meaning criterion, and only one out of 49 occurrences falls out of the group (below 15% threshold), this is a stopping case. As explained in step 5 of the methodology, a new production rule, named mult-around, can now be defined. It associates meaning R.1.1.1 with form R.1.1.1.1, depending on a signed item and an optional location loc (default is neutral space in front of signer). A stand-alone specification is given in the result section recap. Repetition of a movement along a straight path, with attenuation Example: "shelves" (Fig.5)Again this is a stopping case of the methodology. A new production rule is defined: mult-in-arow, depending on a signed item and a path along which the items are placed. See the result section for a full specification. This terminates iteration R.1.1. Set of items, with exact count known Example: "four chairs positioned at [...]"

  Rules mult-around discovered in iteration R.1.1.1 • arguments: signed item, point location loc (default is in front of signer) • meaning: multiple instances of item scattered or spread out on a surface around loc, with the exact count unknown • form: item repeated along an arc trajectory sweeping around loc, with attenuation of the movement mult-in-a-row discovered in iteration R.1.1.2

Figure 7 :

 7 Figure 7: Examples of new production rules in 40 brèves v2


Lorène Siegwart

Isabelle I Bertrand

Maxime Olivier Roupsard

Maxime Duthoit

Christophe Jourdan

Root litter decomposition in a Sub-Sahelian agroforestry parkland dominated by Faidherbia albida

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

Root litter decomposition in a Sub-Sahelian agroforestry parkland dominated by Faidherbia albida

Root litter decomposition in a Sub-Sahelian agroforestry parkland dominated by Faidherbia albida

Methods

Experimental set-up:

2 locations (under the tree and far (+30m) from the trunk)

x 4 soil layers (0-20, 20-40, 40-90, 90-180 cm) x 3 plant species (Faidherbia albida, pearl millet and cowpea)

x 3 replicates

x 5 sampling dates

Results

For all species and soil depths, root litter decomposition occurred mainly during the first 1.5 months (k1), when the soil is still wet from the previous wet season (Fig. 4).

The objective of this study was to measure the decomposition rate of root litters from annual and perennial species according to soil depth (down to 180 cm deep) and location (under and far from the trees) in a Sub-Sahelian agroforestry parkland dominated by Faidherbia albida in Senegal.

Siegwart Lorène1 , Bertrand Isabelle 1 , Roupsard Olivier 1,2,3 , Duthoit Maxime 1,2 , Jourdan Christophe 1,2

Fig. 2 One of the pits with the buried litterbags

Fig. 1

 1 Fig. 1 Experimental Site -Faidherbia-Flux (Senegal)

Fig. 3

 3 Fig. 3 Rainfall (a), soil water content (b) and soil temperature (c) along time and litterbag sampling

UMR Eco&Sols, Univ Montpellier, CIRAD, INRAE, IRD, Montpellier SupAgro, Montpellier, France

CIRAD, UMR Eco&Sols, F-34398 Montpellier, France

LMI IESOL, 18524, Dakar, Senegal lorene.siegwart@supagro.fr

Acknowledgments

The authors thank Ibou Diouf (Sob, Senegal) for extensive help in the field and Patricia Moulin (LAMA/IESOL, Senegal) for conducting all soil analyses.

5th World Congress on Agroforestry 2022. 17-20th of July, 2022. Québec City, Canada.


Lorène Siegwart

Isabelle Bertrand

Christophe Jourdan

Root distributions and traits in a semi-arid agroforestry parkland dominated

2 locations (under the tree and far (+30m) from the trunk)

x 5 soil layers (0-10, 10-30, 30-50, 50-100, 100-150 cm) x 2 plant species (tree and annual crop)

x 2 rotations (2020: pearl millet and 2021: groundnut)

x 3 replicated trees

Results

Deep tree roots with low biomass density vs. shallow crop roots with high biomass density p-value = 6.31 × 10 -3

 complementarity theory for associated plants (Van Noordwijk et al. 1996) At 30cm deep, tree roots were found at +30m from the trunk, in higher quantity than under the tree p-value = 3.88 × 10 -3

 compromise of the tree between water acquisition in deeper soil layers during the dry season (Fig. 3) and nutrient acquisition in topsoil during the wet season  plasticity of the perennial root system (Zanetti et al., 2015) The objectives of this study were:

-to assess the tree and crop root distribution and traits down to 150 cm

  Root distributions and traits in a semi-arid agroforestry parkland dominated by Faidherbia albida: potential impacts on soil C and nutrient stocks? Root distributions and traits in a semi-arid agroforestry parkland dominated by Faidherbia albida: potential impacts on soil C and nutrient stocks? Methods Experimental set-up of the pits (1m * 1m * 2m deep):

•

  Fig. 1 Faidherbia reversed phenology across the seasons

UMR Eco&Sols, Univ Montpellier, CIRAD, INRAE, IRD, Montpellier SupAgro, Montpellier, France

CIRAD, UMR Eco&Sols, F-34398 Montpellier, France lorene.siegwart@supagro.fr

Acknowledgments

The authors thank Ibou Diouf (Sob, Senegal) for technical support in root observations and Patricia Moulin (LAMA/IESOL, Senegal) for conducting all soil analyses, and Aline Personne, Nancy Rakotondrazafy and Didier Arnal from Eco&Sols for helping with the root processing and analyses.


Farida Nchare
email: farida.nchare@facsciences-uy1.cm

Hippolyte Tapamo

Semantic segmentation of high-resolution aerial imagery using a fully convolutional network

Keywords: Road Extraction, FCN, Semantic Segmentation, Aerial Imagery

Semantic segmentation applied to aerial imagery allows the extraction of terrestrial objects such as roads, buildings and even vegetation. Having large, detailed datasets of navigable roads, is of paramount importance in several application fields; namely urban planning, automatic navigation, disaster management. To reach this goal, extracting all roads in a given territory area is the first step. This paper presents a modern method to semantically segment aerial images for a road network extraction. We employ an encoder-decoder architecture to approach the problem of disconnected road regions faced by some existing methods. Using an FCN approach, the localization information was combined to the semantic one, to enable the reconstruction of the road by the proposed model, while being consistent with following the spatial alignment. The method was implemented and evaluated on the public dataset Massassuchets Roads. Results appear to be in full agreement with the theorical predictions and a significant improvement in road connectivity over some previous works; the proposed network achieved a precision of 87.86% and a recall of 87.89%.

I INTRODUCTION

Roads play an essential role in the economy of a society, allowing the transportation of goods, people and merchandise. Consequently, the possession of large datasets of navigable roads in a given territory area is of crucial importance in many fields such as urban planning, traffic management, creation of land use maps which is carried out at the National Institute of Cartography in Cameroon. These road datasets are usually created manually. The process is thus very slow and more expensive with the increasing volume of aerial images data [START_REF] Pantelis | Road Detection from Remote Sensing Imagery[END_REF]. There is therefore, a need to automate the process to ensure functional continuity of the underlying systems [START_REF] Pantelis | Road Detection from Remote Sensing Imagery[END_REF]. The task to accomplish throughout this work is to propose an automatic system, that, given an aerial image, will produce an output image presenting the existing road network on the input image. The associated scientific problem is called semantic segmentation. Many researches have been conducted in this field, which led to the development of several techniques, including the work of Tapamo et al. [START_REF] Hippolyte | Linear vs non-linear learning methods A comparative study for forest above ground biomass, estimation from texture analysis of satellite images[END_REF], which proposes a texture descriptors extraction for a forest biomass prediction, using several supervised classification methods such as k-NN (k-nearest neighbors), SVM (support vector machines) and Random Forests. This work is inspired by different previous works using a deep learning approach, in particular, convolutional neural networks that succeeded in obtaining good feature extractors automatically [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF][START_REF] Saito | Building and road detection from large aerial imagery[END_REF][START_REF] Shunta | Multiple Object Extraction from Aerial Imagery with Convolutional Neural Networks[END_REF]; to solve the road extraction problem.

II STATE-OF-THE-ART

Related works

Recently, deep learning techniques have excelled in numerous areas, including semantic segmentation. In this section, related works proposing CNN-based approaches that serve as a foundation to understand the topic are presented. It should be noted that CNNs principally learn the contextual information. Mnih et al. [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF] proposed a single-class prediction system using a patch-based CNN. Thus, to learn and evaluate roads and buildings, they train two CNNs separately. They predict those objects existence probability distribution from aerial imagery and formulate the problem of extracting relative pixels as obtaining a mapping from an aerial image patch to a label image patch. In their method, firstly an input aerial image is divided into 64×64 patches, to better integrate the local context, and normalized using a Gaussian as a preprocessing step. Then, the normalized patches are input into a 3 convolutional layers followed by 2 fully connected layers, which ouput a 256-vector, reshaped as a 16x16 label patch. They have tested their approach with two datasets that consist of large aerial imagery and binary road and buildings labels images. In order to extract road and buildings from Mnih [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF] datasets, Saito et al. [START_REF] Saito | Building and road detection from large aerial imagery[END_REF] extend the previous problem [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF] into a multi-class dense classification problem. They proposed a single CNN approach to predict roads, buildings and the background simultaneously. They used the same CNN architecture as Mnih [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF], but instead of a 256-vector, the ouput was reconfigured to produce a 768-vector, reshaped into a 16x16x3 RGB label patch. The model outperforms the baseline [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF] both for the road and the building classes. This stems from the fact that the single CNN architecture has the advantage of being able to exploit the correlation when it exists, between a road and a building on the same image. Further on, the authors applied a channel-wise inhibited softmax (CIS) function to suppress the effect of the background.

Although the contextual features are neccessary in a semantic segmentation, object location is of a very importance in the field. The fundamental problem with CNNs for semantic segmentation is that, they can combine pixel location (in their fully connected layers) resulting in a loss of this information. Consequently, a set of new architectures, FCNs, have been proposed to preserve this location information. Long et al. [START_REF] Jonathan | Fully convolutional networks for semantic segmentation[END_REF] introduced the FCN network, which is the first endto-end architecture to apply CNNs to semantic segmentation in the literal sense. The idea of this method is, instead of creating a new network from scratch, they proposed an algorithm called the convolutionalization, to convert a base convolutional neural network (CNN) into a fully convolutional network (FCN). Their method transforms the fully connected layers of a CNN into corresponding convolutions. In addition, they introduced a technique of upsampling using deconvolutional layers, which allows them to output a segmentation map. Maggiori et al. [START_REF] Emmanuel | Fully Convolutional Neural Networks For Remote Sensing Image Classification[END_REF] addressed the buildings extraction task by suggesting a FCN approach. Their architecture is based on the encoder-decoder concept, in which the input image is compressed using Mnih [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF] convolutionalized CNN, into a smaller representation before being reconstructed to the label size using upsampling layers in the decoder. The authors succeed in filling the gaps observed in the buildings [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF], but some irregularities at the edges of the predicted objects are noticed. Rasha et al. [START_REF] Alshehhi | Simultaneous extraction of roads and buildings in remote sensing imagery with convolutional neural networks[END_REF] also used an FCN architecture to extract roads and buildings from two datasets with different spatial resolutions and image conditions. They used the normal downsampling process of the base CNN [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF] but at the end of the network, the fully connected layers are replaced by a GAP (Global Average Pooling) layer to address the problem of low computing efficiency. Their model outperforms the previous models [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF][START_REF] Saito | Building and road detection from large aerial imagery[END_REF] for roads and buildings by using a multi-class approach.

Limitation with patch-based CNN

((a)) Mnih [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF] ((b)) Saito and Aoki [START_REF] Saito | Building and road detection from large aerial imagery[END_REF] Figure 1: Examples of predicted road chunks that ignore patch continuity.

The limit that will be the focus of this work is the disconnected road segments observed in Mnih et al. [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF]. This limitation is visually perceptible in Figure 1.

A close observation of the figure shows that the predictions at the extremities of the patches are not continuous for some road areas. This is due to the fact that not having kept the location information of the pixels, the networks [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF][START_REF] Saito | Building and road detection from large aerial imagery[END_REF] succeed in predicting the road but the expected spatial alignment is not always respected.

Research question

Is it possible to develop a segmentation model that improves road connectivity using a deep learning approach?

III PROPOSED METHOD

Pixels location is a key element in semantic segmentation. The usual CNN architectures lose this information in the fully connected layers, usually added at the end of the network and designated as the classifier. Due to their fully connected nature, there is no way to determine on these classifiers which input contributed to the prediction result of an output. The network of Mnih et al. [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF] captures semantics but at its fully connected layers, there is a loss of spatial information. However, the FCN of Maggiori et al. [START_REF] Emmanuel | Fully Convolutional Neural Networks For Remote Sensing Image Classification[END_REF] manages to combine semantics and pixels location, which allows them to fill in the gaps on the buildings [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF] during predictions. In a similar way, this work proposes an FCN approach to solve the problem of disconnected road segments [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF].

Since the FCN of Maggiori et al. [START_REF] Emmanuel | Fully Convolutional Neural Networks For Remote Sensing Image Classification[END_REF] is a conversion of Mnih network [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF], the idea of the proposed method is to also convert the base CNN [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF] into an FCN. This is what Long et al. [START_REF] Jonathan | Fully convolutional networks for semantic segmentation[END_REF] called a convolutionalization. A CNN can hence be converted into an FCN as follows:

1. First, the fully connected layer that performs the classification is rewritten as a convolution. The resulting connections are comparable to a fully connected layer if the chosen convolution kernel has dimensions that match the previous layer. Continiously, the other fully connected layers are turned into convolutions.

2. At this step, the output image is of very low resolution. So to recover the size of the label, a deconvolution is added to the network. This layer will learn filters to increase the size of the output mask. In the case of this work, the deconvolution which is actually a transposed convolution, will receive in an input of size 7x7 and will multiply it by a 4x4 filter and a factor of 2 to produce a patch label of size 16x16. The architecture of the proposed model shown in figure 2 has two modules, an encoder or the convolutional network and a decoder or the deconvolutional network.

The main goal of the first module is to produce a reduced representation of the input image, by analyzing each sub-region of the image and performing mathematical convolution and maxpooling operations on the pixel values [START_REF] Bogdan | Detecting Roads from Aerial Images using Deep Learning[END_REF]. The output produced will represent the probability that a road appears on each of the analyzed sub-regions. Then, the deconvolutive module will transform the probability vector produced by the first module, into a final road topology output.

IV EXPERIMENTATIONS

Dataset and evaluation metrics

In this work, the public dataset Massachusetts Roads [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF] was used. It contains more than 1108 aerial images with a size of 1500x1500, each. This roads dataset consists of 1107 images for training, 49 for the validation and 14 for the testing part. But in order to be consistent with the previous baseline methods, in this work also, only 137 aerial images and the associated binary label images have been retained for training, 10 for testing and 4 for the validation part.

In order to prepare the data for the network, the images are split into 64x64 patches, which amounts to 8844 patches per image. A rotation of 90 • is then applied to each patch, which allows us to increase the dataset.

The evaluation of the model was done at two stages: a quantitative evaluation which consists in calculating the precision and the recall of the model and a qualitative evaluation which consists in a visual inspection of the prediction results. Nevertheless, just as Mnih et al. [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF], the quantitative metrics used are the relaxed precision and relaxed recall.

Implementation details

The model training was done after initializing several hyperparameters. Indeed, all neural networks were trained for 60 epochs instead of 400 [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF][START_REF] Saito | Building and road detection from large aerial imagery[END_REF][START_REF] Alshehhi | Simultaneous extraction of roads and buildings in remote sensing imagery with convolutional neural networks[END_REF] on the training data, by minimizing the binary cross-entropy loss and using a stochastic gradient descent, with a momentum of 0.9, a learning rate that varied between 0.001 or 0.0005, and was reduced by a factor of 0.1 when there were no further improvements in the performances after nearly 5 consecutive epochs. In addition, each network was regularized using the L2 regularization method with a weight decay of 0.0002. To justify the reduced number of epochs, as the necessary resources are not constantly available over 5 consecutive days, which is the minimum required for 400 epochs, we have limited this number to 60, to ensure that the models can be run without an interruption on the workstation used.

Results

Examples of the results obtained after testing the base CNN and the proposed FCN are shown in figure 3. To compare the proposed method in this work with those in the state of the art [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF][START_REF] Saito | Building and road detection from large aerial imagery[END_REF][START_REF] Alshehhi | Simultaneous extraction of roads and buildings in remote sensing imagery with convolutional neural networks[END_REF], an implementation of the architecture of each model was done under the same conditions and using the same environments. The results presented in brackets are the results published in their respective works while those outside are those obtained after the conducted experiments (Rasha model [START_REF] Alshehhi | Simultaneous extraction of roads and buildings in remote sensing imagery with convolutional neural networks[END_REF] was implemented without the post-processing).The models [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF][START_REF] Saito | Building and road detection from large aerial imagery[END_REF][START_REF] Alshehhi | Simultaneous extraction of roads and buildings in remote sensing imagery with convolutional neural networks[END_REF] were trained for 60 epochs instead of 400, due to some constraints. This work also compares the proposed model to other models tested on the same dataset and published more recently Cf. V CONCLUSION AND REFERENCES

Discussions

Even after a short training time, lasting only one day (rather than a minimum of 5), it can be easily noticed that the results are promising and that the network started to recognize the road network in an accurate way. From table 1, it can be seen that the proposed model achieves better performance than the baseline model [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF]. Firstly, the proposed method shows a 1.63% improvement on precision which is explained by an accuracy of the predicted road pixels at the borders of some road segments; secondly, a 1.11% improvement on recall is observed, which is justified by a more apparent road pattern. Let us now turn to a qualitative evaluation, that can verify the previous statements. Figure 4 shows for the model of Mnih [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF], a disparity of the road network at some edges of segments which is not the case for the proposed FCN. Moreover the road marking of the proposed FCN is more pronounced compared to the base CNN.

((k)) ((l)) ((m)) ((n)) ((o))
Another qualitative evaluation (Cf. Figure 4, line 2) shows that, the proposed model succeeds in predicting road tracks that are not referenced on the labels. This could lead to a satisfaction with the model's performance, but it should be noted that the proposed model will be penalized for correctly predicting a road.

The strength of the proposed method, although it has been trained on a small dataset, reside in overcoming some of the main challenges consisting firstly, in recognizing several road patterns despite having large visual differences and isolating thin objects. Besides, the predictions are visually not coarses, quite smooth, and for the most part of the road network, they are continuous and free of noise.

However, our model had trouble generalizing a wide variety of patterns, predicting unexpected objects like parking spaces and missing many roads segments, mostly the intersections and the two-lane roads (Cf. Figure 4, line 3). The qualitative evaluation of the results shows the limits of the proposed method, as the model does not annotate in prior to the road topology (road corners, complex shapes). Consequently, many prediction failures are due to this shortcoming.

Conclusion

A road extraction method to solve the problem of disconnected road segments, has been proposed in this work. The FCN architecture of the proposed model consists of two modules, namely the convolutional module and the deconvolutional module. The first module will use contextual information to produce a coarse representation of the road while the 2nd module will use spatial information to reconstruct the existing road topology. The obtained results can be qualified as competitive after a quantitative and qualitative evaluation.

The main advantage of this method is that it increases the connectivity of the road of the base network [START_REF] Mnih | Machine Learning for Aerial Image Labeling[END_REF]. Nevertheless, a limit is identified by observing the edges of the predicted roads, which are rough and can be refined.

As perspectives, the execution of the proposed model on another dataset for example images of roads in Cameroon is planned, also an adaptation of this model for the simultaneous prediction of several classes, and finally a future work could focus on the correction of the errors of the Massachusetts Roads dataset.

Figure 2 :

 2 Figure 2: Proposed architecture.

(Figure 3 :

 3 Figure 3: Prediction results of the different models

Figure 4 :

 4 Figure 4: Qualitative evaluation on different models. ((k)): Original image. ((l)): Label. ((m)): Mnih et al. [2] ((n)): Rasha et al. [8] ((o)): proposed FCN

Table 1 .

 1

	Dataset	Model	Precision	Recall
	Massachusetts Roads	Mnih [2] (2013)	86.23 (88.73) 86.78
		Saito [5] (2015)	88.66 (90.05)	-
		Rasha [8] (2017)	89.10 (91.7)	-
		Proposed model	87.86	87.89
		ASPP-UNet-SSIM [12] (2019)	87.10	80.50
		JointNet [13] (2019)	85.36	71.90

Table 1 :

 1 Comparison of road extraction models on Massachusetts Roads dataset.