domain: spi phys

text:
Alessio Turchi
email: alessio.turchi@inaf.it

Guido Agapito

Elena Masciadri

Olivier Beltramo-Martin

Enrico Pinna

Jean-Francois Sauvage

Thierry Fusco

Benoit Neichel

Julien Milli

A. a , Agapito, G. a , Masciadri, E. a , Beltramo-Martin Turchi

Operational forecast of the PSF figures of merit

Keywords: turbulence, turbulence forecast, numerical modelling, adaptive optics, machine learning

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

INTRODUCTION

So far the abilities of models (atmospheric models, statistical models, etc.) in predicting the optical turbulence (OT) have been investigated. We know today that we can predict the optical turbulence (OT) with a very good accuracy, specifically the most relevant astroclimatic parameters, and we are able to do that in an operational configuration [ 1 ]. The next step is therefore to ask to ourselves if we can directly predict the point spread function (PSF) figures of merits. Specifically we are interested in forecasting the full width at half maximum (FWHM), the Strehl ratio (SR), the encircled energy (EE) and the contrast.

In ground-based observations supported by the adaptive optics (AO) the estimation of the PSF figures of merit is not a trivial problem. The complexity of such a topic is due to the fact that the PSF depends on the atmospheric conditions, on the physical characteristics of the observed objects and also on the instrument specifications. If we want to forecast (and not simply measure) these figures of merit the goal is even more challenging. Besides, the estimate of the PSF on-axis and off-axis implies a different level of complexity. If the PSF on-axis allows a simpler analysis as it can be treated as a scalar problem, because the figures of merits mainly depends on the integral of the optical turbulence along the line of sight (seeing or Fried parameter r 0 ), it is known that the PSF off-axis is a more complex problem as it depends on the vertical stratification of the turbulence in the atmosphere. This is due to the fact the direction with respect to which perturbations affecting the wavefront are measured is different from that along which the scientific object is observed. The turbulence that the wavefront passes through at the different heights of the atmosphere along the different lines of sight can therefore be different and the result is a non-optimal wavefront correction, that causes a distortion and an elongation of the PSF at large angular distances from the reference stars, the so called 'anisoplanatism effect' [ 2 ]. More sophisticated AO systems are used in order to overcome this problem, such as the laser-tomographic AO (LTAO), the multi-conjugated AO (MCAO) or the multi-object AO (MOAO) [ 3 ], whose main goal is to correct the wavefront perturbations on a field of view of a few arcminutes (typically 1-2 arcminutes for the LTAO, 2-3 arcminutes for the MCAO and 5-10 arcminutes for the MOAO). Such systems allows a more uniform and homogenous PSF on a large FOV but they require the knowledge of the vertical stratification of the optical turbulence (C 2 N ) and the wind speed. Both of them can be forecasted with the models/methods cited above [ 1, 4, 5 ].

The idea behind this contribution is to present a roadmap of a long-term study whose final goal is that to forecast the PSF figures of merits in operational configuration to be applied in different contexts, i.e. observations supported by narrow field of view (FOV) AO systems (SCAO systems) and observations supported by wide field of view adaptive optics (WFAO) where the problem of the off-axis PSF becomes relevant.

To simplify our approach and reduce the number of free parameters, we start analysing the PSF on-axis. For the forecast of the atmosphere we choose a hybrid system given by the simultaneous use of the Astro-Meso-Nh model and the autoregressive method (AR) that are able to forecast the optical turbulence with a very good accuracy [ 1 ]. The forecasts are used as an imput for the AO modeling software that is able to reconstruct the operation of an AO system from the passage of a wavefront through the atmosphere up the formation of the image of the detector. There are two typologies of such a models: the numerical end-to-end models and the analytical models. Both of them have pros and cons. We choose in this first step, an end-to-end model (PASSATA) [ 7 ] that is able to simulate a PSF and retrieve in post-processing various PSF figures of merit. We limit our attention, in this contribution, to the SR and FWHM but other might be implemented (e.g. EE, contrast, etc). PASSATA has to be configured for the two AO systems: SOUL (at LBT) and SAXO (at the VLT). We will analyse in this contribution the case of SOUL [ 13 ]. The configuration of PASSATA using technical specification for SAXO is in progress.

The final goal of this study is to set-up a system that is able to provide a forecast of the PSF figures of merit using an approach similar to the one used for the optical turbulence by ALTA Center. As described in Section 2, ALTA provides a long time scale forecast (the afternoon before the coming night) and a short time scale forecast that starts to produce data during the course of observations. The second approach provides, at each full hour of the night, a more accurate forecast extended in the successive four hours. Our intention is to perform a similar procedure for the SR and the FWHM. When the night starts, the idea is to provide, at each full hour, a forecast on the same time scale for three different magnitudes covering the whole range of magnitudes typically used by the SOUL and SAXO. In general we are interested in supporting the flexible scheduling of AO-assisted observations and in improving the efficiency of AO instruments.

In Section 2 we introduce the ALTA atmospheric model setup used for this study. In Section 3 we describe the AO modeling software configuration and the relevant key points related to this part of the implementation. In Section 4 we report the preliminary configuration used in this study in order to produce the PSF forecasts of FWHM and SR with the joined atmospheric and AO modeling systems. In Section 5 we present the results obtained with the FWHM and SR forecasts by comparing with the measurements coming from the SOUL AO system. Finally in the conclusion we sum up the results of this work,

THE ATMOSPHERIC MODEL

Meso-NH [ 9, 10 ] is a mesoscale atmosphere model that allows simulating the temporal evolution of atmospheric parameters in a volume defined over a finite geographical grid. Together with Astro-Meso-NH code [ 11 ], it is also able to model the OT parameters including the full C 2 N stratification. We refer to Turchi et al. [ 8 ] for more details of the numerical configuration used for the ALTA Center project. ALTA uses initial conditions (used for model initialization and periodical forcing of external conditions) provided by the General Circulation Model (GCM) run by the European Center for Medium Weather Forecasts (ECMWF), with an horizontal resolution of 9 km. ALTA Center simulates the whole observing night (approximately between 00:00 UT and 15:00 UT) at Mount Graham, where the LBT site is located (coordinates [32.70131, -109.88906], at an height of 3221 m above sea level). The standard forecast produced by the model is provided during the afternoon before the start of the night, however in recent years this system has been upgraded with a short-term forecast based on the usage of autoregression (AR) techniques [ 1 ]. This method uses the real-time measurements produced by the telescope telemetry (atmospheric sensors, DIMM monitor, etc...) in order to learn from the forecast discrepancies over the previous nights and improve the accuracy of the predictions over the next few hours in the future (currently up to 4 hours). This allows to maximize the accuracy and still gives precious information for observation planning.. This short-term forecast is produced each hour during the night and allows extreme forecast accuracy [ 1 ], up to a RMSE of 0.1 arcsec with respect to the seeing parameter at an hour in the future [ 1 ]. A system similar to ALTA is currently under development for ESO at VLT * and it has already been possible to prove its abilities in providing PWV forecast at very high accuracy [ 6 ] at short time scales.

In this contribution we are interested in trying to assess the best possible performance obtainable for the PSF forecast in order to drive the specifications of the next phases in which the real operational system will be constructed. For this reason, in this study we will use the ALTA short-term forecast as an input to PASSATA AO instrument simulations in order to obtain the best possible PSF forecast.

THE AO MODELING SOFTWARE

The outputs of the ALTA system, describing the status of the OT and the atmosphere, are injected into an endto-end AO numerical modeling software (PASSATA [ 7 ]) that is able to reconstruct the operation of an AO system from the passage of a wavefront through the atmosphere up to the formation of the image of the detector. Among the PASSATA outputs we mention therefore also the PSF and its figures of merit calculated in a post-processing phase. PASSATA can be adapted to any specific AO system by including their technical specifications. In this contribution we limit our attention to the Strehl ratio (SR) and the full width at half maximum (FWHM) but other might be implemented (e.g. Encircle Energy, contrast, etc). In this first contribution we limit our analysis to the SOUL AO system used at the Large Binocular Telescope (LBT). The setting-up of PASSATA with the SAXO specifications (AO system of SPHERE at the VLT) is currently in rapid progress.

It is known that the end-to-end models are in principle more complete and accurate than analytical ones but they require longer computational time. We therefore implemented a GPU dedicated server to be able to perform the simulation within a few minutes. This condition is necessary as our aim is to perform an operational short-term forecast of the PSF figures of merit in order to use the outputs of such a forecasts for the scheduling of the scientific programs, during the observing night. PASSATA is an IDL and CUDA based object oriented library/software capable of doing Monte-Carlo end-toend Adaptive Optics (AO) simulations. GPU acceleration is optional and limited to the most computationally demanding routines. CUDA functions are wrapped in a DLM extension that can be loaded by IDL at runtime. The end-to-end simulations constitute the modelling of all the steps involving the AO system main functionality and the input disturbance generation and propagation from the guide source to the wavefront sensor through the atmosphere and the deformable mirror. Inputs are the telescope, AO system and turbulence parameters and outputs are AO telemetry (slopes, mirror commands, ...) and residual phase. In a second step, PSF is computed from the residual phase at the desired wavelength, and then, SR and FWHM are evaluated on this PSF. This process can be repeated to get performance for different wavelengths.

To perform simulations that are fast enough for an operational configuration we calculated the time necessary to be simulated for different magnitudes to converge on a stable solutions. This has been done averaging results from a set of simulations done with different atmospheric and noise realizations. Given the current specifications, we initially plan to deliver a forecast of FWHM and SR with a timestep of 20 minutes, in order to have at least 3 points each hour, and for only few sample magnitudes. The selected configuration determines the number of GPUs required. The definitive setup is still to be defined but the idea behind it is that we want to guarantee a useful information but with limited costs. For this initial test we chose three magnitudes of 8, 12 and 16, which cover the typical range of observing targets. We chose different simulation times ranging from 2 to 4 seconds. As expected when the magnitude is brighter, thus the correction is better, a small number of simulations are required to get close to the median value as can be seen in Fig. 2. In the end we chose to run 1 simulation of 2s for magnitude 8 case, 3 simulations of 2s for magnitude 12 and 5 simulations of 3s for the faintest magnitude (16). With the previous setup we were able to obtain simulated outputs for the forecast in less than ten minutes for the different configurations, showing the feasibility of an almost-real-time operational forecast. With the above setup, we need at least one GPU for each simulation on the specified magnitudes and for each timestep. In order to cover few hours of forecast with at least three magnitudes in the near future, we are planning to either improve the performances by powering up our GPU hardware (additional GPUs or GPU servers) or either using a different faster (analytical) model, thus providing ample space for performance improvements.

PRELIMINARY CONFIGURATION

Several challenges lie ahead before being able to finalize the specifications for a PSF forecast tool. A key element is the quantification of the accuracy of the PSF measurements obtained by the AO instruments themselves, that is the reference with respect to which one has to quantify the goodness of a forecast. This means to define all the elements that contribute to the measured PSF variability. The other main challenge is to compare the accuracy of measurements with the performance of the forecasts, in the context of science operations, that is well different from the AO characterization during commissioning. A common source of uncertainty are, for example, telescope structure vibrations and non-common-path aberrations (NCPA).

As a preliminary step, in order to simplify our approach and reduce the number of free parameters, we start analysing the PSF on-axis for the SOUL case. PASSATA has been used extensively in SOUL design [ 12 ], however we had to modify the configuration in order to create a setup which is compatible with forecast requirements, as discussed in section 3. SOUL has a database of PSF measurements available, thus giving us the possibility to produce a preliminary evaluation of the feasibility of the PSF forecast, in terms of full width at half maximum (FWHM) and Strehl ratio (SR). Uncertainties on the final PSF forecast are coming both from the atmospheric model and from the AO modeling software.

For the forecast of the atmosphere we choose a hybrid system given by the simultaneous use of the Astro-Meso-Nh model and the AR method that is able to forecast the optical turbulence with a very good accuracy

[ 1 ].
The short term atmospheric and OT forecasts that are used as an input for PASSATA are provided by the operational forecast system named ALTA Center (http://alta.arcetri.inaf.it) running at LBT. In this study we selected, among the available set which had a corresponding PSF measurement provided by SOUL, the best matching seeing forecasts produced by the ALTA system with the short-term (AR) method. Specifically we selected the time windows in which the agreement between the AR forecast and the DIMM measurements was optimal. This will allow us to disentangle the analysis of contribution to the total uncertainty coming from the atmospheric model (Astro-Meso-Nh+AR) from those coming from the differences between the measured PSF (with SOUL) and the simulated PSF with the AO modeling software (PASSATA).

We limit ourselves to the PSF on-axis therefore we consider a fixed stratification of the optical turbulence and the wind speed. Specifically we consider both wind speed and C 2 N distributed in four layers of infinitesimal width located at 119m, 837m, 3045m, and 12790m (distances are given with respect to the conjugated pupil plane). On each layer the wind speed is 2 m/s, 4 m/s, 6 m/s and 25 m/s respectively, while the C 2 N is proportionally distributed on each layer with the following total percentages: 70%, 6%, 14% and 10%. This is the configuration that is currently used for the calculation of the SOUL SR during the commissioning and it refers to typical conditions. We decided to use those values as a first reference as it allow us to reduce the free parameters in this preliminary evaluation and it allows us to investigate the sources of uncertainties related to the AO modeling tool. Indeed since on-axis PSF mainly depends on the integrated quantities, the stratification of the C 2 N has a second-order impact on the final results. In future developments, especially when moving towards off-axis forecasts, the variability of the C 2 N will be taken into account. In the present preliminary configuration we inject in PASSATA only the seeing coming from Astro-Meso-Nh + AR corrected by the airmass correspondent to the line of sight of the specific astronomical observations. Beside the instrument and atmospheric OT specifications, PASSATA has to be configured with the observed target characteristics, specifically the magnitude of the reference star. Once this final ingredient is inserted, PASSATA produces as an output the correspondent PSF and its figures of merit (FWHM and SR).

We resume here the steps taken so far in developing this preliminary version of the PSF forecast tool, which is one of the goals of this preliminary work:

• We installed a GPU dedicated server allowing us to perform simulations with the end-to-end PASSATA software in a reasonable short time scale (few minutes). 5 obtained with our forecast configuration. In the colorbar we represent the different seeing values used for the simulations, ranging from 0.6 to 1.5 arcsec. Each data point represents a median of the respective quantity over a 10-minutes time interval.

• We identified temporal windows in which the agreement of the observed and forecasted seeing was good for a few test cases as this allows us to study the uncertainties of the atmospheric module and the AO models.

• We perform the simulations with PASSATA using as inputs seeing (from ALTA+AR forecast corrected by airmass) and magnitude of the reference star.

• From PASSATA simulations, we computed the FWHM and the SR for the wavelengths corresponding to SOUL PSF measurements (H, 1.64 µm, and Ks, 2.16 µm, bands) and we compared the results between the two.

• At present, AO vibrations and NCPA are not removed from the dataset.

Table 1. Table reporting the full measurement dataset used for this work, together with the forecasts produced by our models. Dates are reported in UT. All measurement values are medians over 10-minutes intervals. Columns with the same color represent the values that must be compared. DIMM and ALTA columns represent the seeing measured and forecasted by the ALTA AR model respectively (on the zenith), which, projected on the line of sight, is used as an input for the ALTA+PASSATA PSF forecast. The SOUL column contains the corresponding FWHM and SR measurements.

RESULTS

In this section we present the results obtained with the approach described before. In fig. 3 we report the PASSATA curves obtained with the standard SOUL configuration used for the commissioning evaluation, for different magnitudes and seeing values, for both FWHM and SR in H and Ks bands, together with the ALTA + PASSATA simulations that we performed with our modified PASSATA for the forecast configuration. The agreement shows the correctness of our PASSATA implementation with respect to the reference SOUL design.

In Table 5 we report the full list of the data obtained in this study, as medians over 10-minutes intervals. As previously stated, by construction, the ALTA column values are extremely accurate with respect to the DIMM. This allows us to study in a clean way all the source of uncertainties between the AO model and the SOUL measurements (see columns ALTA+PASSATA and SOUL), which is the focus of our study at this stage. This eventually allows us to highlight all the critical points in the evaluation of the measurement accuracy. Between the sources that are not perfectly modeled in PASSATA are the telescope structure vibrations that impact on the final PSF figures of merit. Another source which is currently included in the data and is not modeled by PASSATA are the NCPA. These are supposed to be corrected during science operations [ 14 ], however must be taken into account for the validation of the PSF forecast. We are currently trying to evaluate the impact of NCPA and if it is possible to address the latter source during post-processing inside our model. but this exercise allowed us to define the conditions of analysis. The next step is to enrich the statistical sample and to quantify the sources of uncertainty as those already mentioned (i.e. AO vibrations and NCPA). Part of the large BIAS experimented in this study, especially for the SR, may be explained by the NCPA which are not corrected in this SOUL dataset. This should eventually not affect the science data because in that case NCPA are typically corrected [ 14 ], however in order to quantify the performance in post-processing we must be able to disentangle this contribution from the measurements. Looking at the perfomance on-sky of NCPA correction [ 14 ], this may impact the SR by a factor greater that 15%, thus our results in 5 are indeed promising. To this we should add the uncertainty from the atmospheric model, which however is already well characterized and small (around 0.1 arcsec) [ 1 ].

We report in

CONCLUSIONS

We present in this contribution a preliminary evaluation of the feasibility of a forecast system for the PSF figures of merit. Specifically we investigate if an atmospheric model of the OT coupled with an end-to-end AO modeling software (PASSATA), can be effective in forecasting the FWHM and SR for PSF measurements obtained with AO instruments. This study was initially applied to SOUL at LBT. We chose an initial simplified setup deciding to limit our study to the on-axis case, which gives no dependency of the PSF on the turbulence stratification, and thus our forecasts uses only the seeing value from the atmospheric forecasts as an input. Preliminary results of this study tells us that the uncertainty on the AO modeling/AO measurement is of the order of 12.5% for the SR and 11 mas for the FWHM. By considering the typical impact of NCPA observed on-sky, our results can be considered promising. During the study we pointed out the critical problem of the assessment of the measurement accuracy, and the capability of PASSATA to model correctly the measurement variability. For the prosecution of our work, we intend to achieve the following steps:

• to disentangle the contribution to the measurements, variability coming from noise sources such as AO vibrations and NCPA

• to enrich the sample of PSF measurements from SOUL in order to increase the statistics for the forecast validation,

• to implement SAXO/SPHERE inside PASSATA, allowing us to use the SAXO larger measurement sample,

• to include the uncertainty produced by the atmospheric model (which however is already known to be around 0.1 arcsec on 1-hour timescale),

• to consider also the off-axis PSF cases by including the full C 2 N and wind stratification into the model.

Future key milestones of this project will be addressing the previous issues. In future studies we aim to investigate also the possibility to use intrinsically faster analytical models, such as the one described in Neichel et al. [ 15 ], and possibly confront the accuracy obtainable with both approaches. The final goal of this work is the development of an operational forecast system for the PSF figures of merit, including FWHM, SR, but also Encircled Energy and contrast, could greatly benefit AO-assisted observation planning in flexible scheduling and also contribute to the runtime tuning of AO instrumentation.

Figure 1 .

 1 Figure 1. Example of a forecast of the seeing obtained with the AR filter at a time scale of 1h.

Figure 2 .

 2 Figure 2. PASSATA convergence times with respect to the number of realizations. Plots were obtained with magnitudes 8, 12 and 16. The different lines correspond to different lengths of the simulated time. The dashed line represents the median value which is the target of the convergence.

Figure 3 .

 3 Figure 3. Simulated curves for FWHM (upper row) and SR (lower row) in H (left) and Ks (right) bands respectively, with different magnitudes from 8.5 to 17.5, obtained with PASSATA as configured for SOUL. The dots represent the ALTA + PASSATA simulations from Table5obtained with our forecast configuration. In the colorbar we represent the different seeing values used for the simulations, ranging from 0.6 to 1.5 arcsec. Each data point represents a median of the respective quantity over a 10-minutes time interval.

Table 2 .

 2 Table 5 the average statistical indicators obtained from the comparison of the ALTA + PAS-SATA FWHM and SR forecast and the SOUL corresponding measurements, with an RMSE on FWHM and SR of 11 mas and 12.5% respectively. The statistical sample is still too small to be quantitatively representative Standard statistical indicators obtained by comparing the ALTA+PASSATA PSF forecasts and the SOUL measurements from Table 5, for FHWM and SR respectively.

		FWHM (mas) SR (%)
	RMSE	10.9	12.5
	BIAS	-4.5	9.8
	σ	9.9	7.8

ACKNOWLEDGMENTS

The study has been co-funded by the FCRF foundation through the 'Ricerca Scientifica e Tecnologica' action -N.45103. by the project ALTA Center (ENV001, ENV002) and by the European Union's Horizon 2020 research and innovation programme under grant agreement No 824135 (SOLARNET).


Pedro Henrique

Suruagy Perrusi

Anna Cazzaniga

Paul Baksic

Eleonora Tagliabue

Elena De Momi

Hadrien Courtecuisse

P H Suruagy Perrusi
email: phsuruagyperrusi@unistra.fr

Robotic needle steering in deformable tissues with extreme learning machines

teaching and research institutions in France or abroad, or from public or private research centers.

I. Introduction

Robotic assistance for needle-based therapies has been the subjects of many study [START_REF] Adagolodjo | Robotic Insertion of Flexible Needle in Deformable Structures Using Inverse Finite-Element Simulation[END_REF], [START_REF] Baksic | Robotic needle insertion in moving soft tissues using constraint-based inverse Finite Element simulation[END_REF]. Given the high nonlinearity of the needle and tissue interaction, the precise control of these robots remains an open challenge. A promising control framework which accounts for deformations of both the needle and the tissue is the inverse finite element (FE) simulation [START_REF] Adagolodjo | Robotic Insertion of Flexible Needle in Deformable Structures Using Inverse Finite-Element Simulation[END_REF], [START_REF] Baksic | Robotic needle insertion in moving soft tissues using constraint-based inverse Finite Element simulation[END_REF]. It is an automatic needle insertion strategy to steer needles at a constant velocity along a predefined trajectory inside soft tissues. The needle-tissue interaction is compensated via optimization in a realistic FE simulation. In its latest formulation [START_REF] Baksic | Robotic needle insertion in moving soft tissues using constraint-based inverse Finite Element simulation[END_REF], reduced computational time increased the dynamic of the robotic allowing for more stability when subject to perturbations.

On another hand, recent Machine Learning models can learn to predict non-linear soft tissue deformations with very low computation time [START_REF] Mendizabal | Data-Driven Simulation for Augmented Surgery[END_REF]. Since patient-specific organ deformation data is uncommon, they rely on FE simulations to generate their training set. The synthetic data demonstrated high representativity of the physical scenario as they were able to estimate accurate elastic deformations 500 times faster than using FE simulations.

In particular, the Extreme Learning Machine (ELM) [START_REF] Huang | Extreme learning machine: A new learning scheme of feedforward neural networks[END_REF] is a neural network architecture which presents promising results in solving the inverse kinematics of robots with high non-linearities between the control signal and their position [START_REF] Porto | Position control of medical cable-driven flexible instruments by combining machine learning and kinematic analysis[END_REF]. We propose here to solve an analogous problem, that is: solving the inverse kinematics linking the needle tip motion to the robot end-effector motion using ELM, while considering the needle-tissue interaction.

II. Material and methods

In this study we propose to predict robotic position commands which account for needle and tissue deformations by using ELM. The proposed network is trained with synthetic data generated from inverse finite element (FE) simulations of robotic needle insertions within the SOFA Framework [START_REF] Faure | SOFA: A Multi-Model Framework for Interactive Physical Simulation[END_REF]. Finally, the model's inference is used to drive a robotic needle insertion in a FE simulation with increased command dynamics.

II.I. Inverse Simulation

In [START_REF] Baksic | Robotic needle insertion in moving soft tissues using constraint-based inverse Finite Element simulation[END_REF], the authors formulate the needle insertion as a minimization problem. A realistic FE simulation is used to linearize the relationship between the end-effector pose and a set of objective functions. This linearization is then used to derive a robot pose command. A first objective 𝒆 = 𝑷 𝒕𝒂𝒓𝒈𝒆𝒕 -𝑷 minimizes the error between the needle tip position 𝑷 and a target position that moves along a predefined trajectory 𝑷 𝐭𝐚𝐫𝐠𝐞𝐭 . The other two objectives reduce tissue damage at the level of the entry-point and enforce a remote center of motion (RCM) constraint to the optimization problem.

II.II. Dataset generation

The training dataset is generated using realistic FE simulations of robotic needle steering in a rectangularshaped foam, as in [START_REF] Adagolodjo | Robotic Insertion of Flexible Needle in Deformable Structures Using Inverse Finite-Element Simulation[END_REF]. FE models use linear co-rotational formulation of elasticity. The needle is modeled as serially linked beam-elements following Timoshenko's formulation. The needle tissue FE interaction follows [START_REF] Duriez | Interactive simulation of flexible needle insertions based on constraint models[END_REF].

In order to explore multiple needle-tissue interaction scenarios, a set of 105 straight trajectories were created. Each trajectory passes through the insertion point at the center of the 𝑋𝑌 plane of the foam. Their endpoints are distributed in a regular grid at insertion depth of 110𝑚𝑚.

For each trajectory, the inverse simulation control of needle insertion is performed. In order to facilitate the generalization to new unseen trajectories, isotropic uniform AUTOMED 2021 noise of ±0.25𝑚𝑚 is added to 𝑷 𝑡𝑎𝑟𝑔𝑒𝑡 during the data generation. Finally, for each sample 𝑖, the current effector 3D position 𝑬 𝒇𝒇 (𝒊) , the current needle tip to target error 𝒆 (𝒊) and respective robotic displacement output 𝑪 (𝑖) are saved. The complete dataset generated from the inverse simulations on the straight trajectories is composed of 100000 samples, in which 90% is used as training set and 10% are left for as test set. It is assumed the 𝒙 (𝒊) can be measured at each time step. In this study, the ELM will be tested in a realistic FE simulation in the same scenario used to generate the dataset. The robotic end effector translates at a constant speed towards the inferred position 𝑪, while its orientation is imposed to respect an RCM between the needle base and the entry-point.

III. Results and discussion

In a first phase, the ELM is trained and validated with synthetic data acquired from inverse simulations (see sec. II.II). Results on the synthetic data show a test phase final root mean squared error (RMSE) of 0.164 𝑚𝑚. The trained weights of the ELM are then conserved for the remaining experiments.

In a second phase, its ability to steer a needle in a FE simulation is tested. A computation time analysis shows the ELM inference takes 0.91 ± 0.67𝑚𝑠 to perform predictions while the inverse simulation needs 2.69 ± 0.34𝑚𝑠. When comparing the tip-to-target precision in all trajectories, the ELM follows the straight trajectories with a final RMSE of 91 ± 23𝜇𝑚. while the inverse simulation presents 70 ± 1𝜇𝑚. It remains to be tested which precision the method achieves in a realistic scenario such as [START_REF] Adagolodjo | Robotic Insertion of Flexible Needle in Deformable Structures Using Inverse Finite-Element Simulation[END_REF], [START_REF] Baksic | Robotic needle insertion in moving soft tissues using constraint-based inverse Finite Element simulation[END_REF].

In order to test the ELM generalization capability on previously unseen trajectories, an additional set of 200 curved trajectories were generated. They present a 10𝑚𝑚 sinus overlay to the straight trajectories in X and Y directions. As a result, the ELM remained stable and performed the needle insertion with final RMSE of 213 ± 517𝜇𝑚. The inverse simulation followed these same trajectories with a final RMSE of 818 ± 108𝜇𝑚. Higher errors on both methods were expected as more significant deformations are imposed to follow a curved trajectory [START_REF] Adagolodjo | Robotic Insertion of Flexible Needle in Deformable Structures Using Inverse Finite-Element Simulation[END_REF].

As a first feasibility study, results show that the ELM was able to learn how to perform stable needle insertions, achieving a reduction in the average computational time by 66% when compared to the inverse simulation. This performance boost might improve the dynamics of the control system in a real application. The precision observed in the experiments is sub-millimetric and remains acceptable for percutaneous needle insertion procedures. In terms of limitations, this study assumes constant biomechanical parameters and simplistic geometry for the models both in the synthetic data generation and in the experiments.

IV. Conclusions

This study presents a first feasibility study to train a neural network to control robotic needle insertions in soft tissues and achieve appropriate precision in a realistic simulation environment. The ELM presented a promising ability to account for tissue deformation and trajectory generalization ability for the straight and curved trajectories tested. Future works will build upon these findings to improve insertion precision and transfer to different scenarios. A sensitivity study of network performances when varying such parameters will be carried out in future works. An experimental validation in a controlled environment will also be an important milestone to advance the studies towards a clinical environment.

Figure 1 :

 1 Figure 1: FE simulation with a curved trajectory used to validate the ELM needle steering. The robotic endeffector position 𝐸 𝑓𝑓 and the needle tip-to-target error 𝒆 = 𝑷 𝒕𝒂𝒓𝒈𝒆𝒕 -𝑷 are the model inputs. II.III. Neural Network Architecture ELM is a feed forward neural network with a single hidden layer. In this study it was implemented with 25 neurons with sigmoid activation functions. This model maps the inputs 𝒙 𝒊 = [ 𝑬 𝒇𝒇 (𝑖) 𝒆 (𝒊)] 𝑇 into displacements of the robotic end-effector: 𝒚 𝑖 = [𝑪 (𝒊) ].

AUTHOR'S STATEMENT

Research funding: This work was supported by French National Research Agency (ANR) within the project SPERRY ANR-18-CE33-0007 and the Investissements d'Avenir program (ANR-11-LABX-0004, Labex CAMI).


Jinze Du

Bin Wu

Yi Yang

Chao Yuan

Raj Parth

Singh

Amit Karel

Lian Li

Bistatic MIMO System with Uniform Circular Arc Arrays for Single near Field Target Localization

Keywords: near field target localization, uniform circular arc array, MIMO system

Near field sources cannot be located by using far field assumptions without compromising the precision. To solve this issue, many passive near field sources localization techniques have been proposed in the last few decades. There exists a lot of research work in which circular receiving array is used to locate a single near field source in 3D. In this paper, this domain is extended to active localization by proposing a low complexity closed-form method based on least squares estimation to locate a near field target using a bistatic MIMO system with uniform circular arc transmitting and receiving arrays. The simulation results indicate that the proposed method is capable to estimate the spherical coordinates of the target and also shows acceptable performance like the most of the existing near field source localization methods.

I. INTRODUCTION

A source in the space surrounding an antenna or an array falls under near or far field region based on its distance with respect to the largest dimension of the antenna or the array [START_REF] Swindlehurst | Passive direction-of-arrival and range estimation for near-field sources[END_REF]- [START_REF] Zhi | Near-field source localization via symmetric subarrays[END_REF]. We can find enormous research work dealing with far field sources localization because it plays important role in the applications like radar, sonar, and wireless communication. However, near field sources localization is equally important. It has applications in medicine, robotics, smart devices, etc. Near field sources can not be located by using far field assumptions without compromising the precision. Therefore, many passive near field sources localization techniques have been proposed in the last few decades. Among which, there is a unique interest in single near field source localization techniques using uniform circular array (UCA) because of its attractive geometry and capability to localize source in 3D as compared to a unifrom linear array (ULA) [START_REF] Jung | Closed-form algorithm for 3-D single-source localization with uniform circular array[END_REF]- [START_REF] Wu | Simple and accurate two-dimensional angle estimation for a single source with uniform circular array[END_REF].

In this paper, we extend this scenario to active localization by using a bistatic MIMO system with uniform circular arc transmitting and receiving arrays. All the antennas of both arrays are considered to lie on a big circle, forming two separate arcs on the circle for each array. This configuration simply replaces the circular array, therefore, this can be used in the applications of circular array. Classically, a 3D MUSIC based approach can be used to obtain a good estimation of the range, elevation angle, and azimuthal angle of a near field target, however, it will be computationally very costly due to three non-separable variables. Therefore, we propose a least squares (LS) based closed-form approach.

In the following, we formulate the signal model of the received signal reflected by a target in the near field region of a bistaic MIMO system with uniform circular arc array in section 2. In section 3, we explain the proposed method. Followed by, simulation results and conclusion in section 4 and section 5 respectively.

II. NOTATIONS

The scalars are represented by normal lower or upper case alphabets. A bold lowercase alphabet represents a vector whereas a bold uppercase alphabet denotes a matrix.

, , and are the sets of all integers, real, and complex numbers respectively. and respectively denote the transpose and conjugate of a matrix. , , and represent the absolute value, argument, and principal value of a complex number. E{ } gives the expected value. . III. SIGNAL MODEL Consider a bistatic MIMO system with uniform circular arc transmitting and receiving arrays containing and omnidirectional antennas respectively. The inter element spacing in both arrays is as shown in Fig. 1. The center elements of the arrays are taken as their phase reference points which are located on the y-axis at distance from the origin. As shown in Fig. 1, all the antennas are located on a circle of radius in xy-plane making two arcs corresponding to each array. Here, we have considered single target situation whose radial distance, radelevation angle, and azimuthal angle with respect to the origin are denoted by , , and respectively. In case of a bistatic MIMO system, the matched filtered received signal for a single target can be written as [START_REF] Yan | Multitarget identification and localization using bistatic MIMO radar systems[END_REF] (1) where is the zero mean noise vector with variance complex Gaussian entries, is the complex reflection coefficient of the near field target varying with time according to Swerling case II [START_REF] Swerling | Probability of detection for fluctuating targets[END_REF] . and are respectively the directional vectors of departure and arrival which can be expressed a

(2) and [START_REF] Zhi | Near-field source localization via symmetric subarrays[END_REF] where is the wavelength of the carrier.

is the distance traveled by the signal transmitted by the th transmitting antenna to reach the target.

is the distance traveled by the reflected signal from the target to the th receiving antenna. and are the relative indexes of the antennas with respect to their corresponding reference antennas. In terms of , and can be expressed as ( 4), (5) ( 4) and ( 5) where [START_REF] Eun-Hyon | Closed-form 3-D localization for single source in uniform circular array with a center sensor[END_REF] In case of a single receiving array, near field region is defined by Fresnel region which is bounded by the following upper ( ) and lower ( ) bounds (3), [START_REF] Wu | Simple and accurate two-dimensional angle estimation for a single source with uniform circular array[END_REF] and [START_REF] Yan | Multitarget identification and localization using bistatic MIMO radar systems[END_REF] with , the largest dimension of the array. On extending this concept to a bistatic MIMO system, we can have three such regions. Two corresponding to the individual arrays and one for the whole system. For the whole system, . And, for the transmitting and receiving arrays, and respectively.

IV. PROPOSED METHOD

The following subvectors can be written from ,

and [START_REF] Tribolet | A new phase unwrapping algorithm[END_REF] where and are the respective noise subvectors. Further, we can say [START_REF] Golub | Total least squares[END_REF] and ( 12) where denotes the component of corresponding to the th transmitting antenna. The components of the remaining vectors are denoted in the similar manner.

The argument of a complex number can only be calculated in its principal form. The arguments and principal values of and are related as, and

, where denotes the number of rotations around the origin. From ( 11) and ( 12), we can say, and . However, for the proposed method, we need and . For a single complex number, deducing its argument from its principal value is impossible. However, for a vector of complex numbers with unambiguous phase differences between the consecutive components, we can use unwrapping algorithm proposed in [START_REF] Tribolet | A new phase unwrapping algorithm[END_REF] to deduce the arguments. The unwrapping of the principal values of vector components often adds a phase shift to all the unwrapped phases. This phase shift can easily be removed by subtracting the unwrapped phase corresponding to the reference antenna from every unwrapped phase of that directional vector. Let and . Further, using (4) and ( 5) with some mathematical manipulations, we can transform these equations as In ( 18), and appear on the either sides of the equations, therefore, total least squares (TLS) is a better approach here than the conventional least squares (LS) [START_REF] Golub | Total least squares[END_REF]. Let be the right-singular-vector corresponding to the smallest singular value of . Then, the estimated radial range . Through out the simulation, is taken as the unit of length and the angles are expressed in degrees. Based on the considered radar parameters, the Fresnel bounds of the system and transmitting and receiving arrays are given in Table I. To analyze the performance of the proposed method, we have compared the root mean square errors (RMSE) in the estimations of , , and with their Cramér-Rao lower bounds (CRLB) for different signal-to-niose-ratios (SNR) in Fig. 2.

samples and Monte Carlo trails are used to compute RMSE. From Fig. 2, we can say that the proposed method is capable to estimate the spherical coordinates of the target. However, the RMSE of target parameters are far from their respective CRLB. The primary reason of this poor performance is the partial exploitation of the available information.

VI. CONCLUSION

A low complexity single target localization method using a passive radar system is proposed here. The arrays of the bistatic MIMO system are assumed to lie on a big imaginary circle to simplify the model which allows us to estimate the spherical coordinates of the target using closed from expressions. The proposed method can also show acceptable performance for , like the most of the existing near field source localization methods.

Figure 1 .

 1 Figure 1. Uniform circular arc array

  system of linear equations can be written as(18)

  Consider the system shown in Fig.1 with () transmitting and ( ) receiving antennas. The inter element spacing,

Figure 2

 2 Figure 2. RMSE versus SNR; , , , ,, , , and .

TABLE I

 I

	. FRESNEL BOUNDS
	Transmitting
	array
	Receiving
	array
	System

ACKNOWLEDGEMENT

The authors would like to express their gratitude to all the subjects that participated in the experiments. This study is supported by Science and Technology Innovation Project of Foshan City, China (Grant No. 2015IT100095), the Fundamental Research Funds for the Central Universities (Grant No. lzujbky-2016-br03), CERNET Innovation Project (Grant No. NGII20150603) and Science and Technology Planning Project of Guangdong Province, China (Grant No. 2016B010108002).


Richard -Service Dickinson

Inist Traduction

Xavier Granier

ADERA Pascal Mora

ADERA François Daniel

Archeovision Production

Jean-Baptiste Barreau

Jean-François Bernard

Hervé Bohbot

Philippe Fleury

Olivier Marlet

PREAMBLE

This document is the result of an ongoing effort to enable SSH and 3D actors to interact around a common vocabulary. This lexicon is intended to accompany the different deliverables of the 3D consortium. It is also intended to help enrich TaDiRAH 1 , "Taxonomy of Digital Research Activities in the Humanities", which is part of the European consortium DARIAH. This continuous nature of this process is illustrated by the fact that this is the second version of this document [START_REF] Granier | Les recommandations du Consortium 3D SHS[END_REF]. This effort to define common concepts is based on two tools. The first is the 3D data sequence graph (Figure 2). It presents the steps of the production process in a simplified way. The system of the graph has been defined to follow a logical path with notably the use of loops to express the recursive aspect of the work on data, especially during the hypothesis and restitution stages. The archiving, which is the subject of the white paper dedicated "Perennial archiving of 3D digital data for humanities and social sciences", is present at all levels.

The lexicon that we are proposing has been built with the aim of clarifying and specifying, and not to entirely redefine the notions related to digital heritage. Existing definitions have thus been adapted to the practice of 3D in SSH, and more specifically to heritage. The aim was to focus on a few essential definitions, categorized by steps and substeps, in accordance with the sequential graph rather than to rebuild a complete dictionary. Questions arise when working on such a document. For example, it is necessary to recapitulate the objectives of SSH research by specifying the notions of recording and scientific study, as understood in the digitization of heritage. It is also necessary to try to remove semantic ambiguities such as, for example, the one that exists that between virtual reality and 3D with the necessary distinction between interactive mock-up and pre-calculated rendering. We also wanted to distinguish the stages of the model creation process by defining the terms consolidation and cleaning. The need emerged to clarify terms that are increasingly used in our domains like metadata or paradata, in order to avoid their use in a roundabout or misunderstood sense. Finally, we tried to clarify other terms and adapt definitions to the world of 3D in SSH, such as the notion of restitution.

FUNDAMENTAL 3D CONCEPTS

Geometry

In this section, we first discuss all the properties that define an object by the position and volume it occupies in a 3D environment. For original definitions in Computer Graphics and 3D, the reader may refer to the book "Computer Graphics: Principles and Practice" [START_REF] Foley | Computer Graphics: Principles and Practice[END_REF] 3D point:

A 3D point corresponds to a position in a 3 dimensional space (i.e. with three values or coordinates, often denoted by X, Y and Z). This 3D point can also be associated with other information valued at this position (see normal, color)

Point cloud:

A simple list of 3D points without creating any structure to link them (Figure 3).

Mesh:

A mesh is a list of 3D polygons that are a set of linked 3D points spanning on a common plane. The 3D points are thus named vertices (Figure 4). The most common polygon is a triangle with three vertices. The links between the points give a structured version of the 3D point cloud.

It is important to note that there are several possibilities for creating a mesh from a given set of points (Figure 5): the result of the meshing process of a point cloud depends on a number of implicit assumptions. Some choices can be left to the user a priori or a posteriori to opt for more relevant solutions than the automatic ones.

Normal of 3D point:

Orientation of the surface passing through a 3D point. For a manifold surface, it points outwards (Figure 6).

Volume:

In Computer Graphics, a volume is a 3D data that is not simply characterized by its surface, but by all the variations that can occur within this surface (see tomography). For the SSH, volume often refers to the occupation of an object in space.

Appearance & Color

Everything that helps to define what we see of an object beyond its position in space and, in its digitized version, all the data that allows us to produce a visualization of it once again, beyond simple geometry (for example, for the restitution of polychromy -Figure 7). Basically, this can be the color associated with each 3D point.

Color:

According to Lexico from Oxford, color includes many notions, ranging from the sensation on an eye of the reflected light on an object, to the pigments. In the 3D community, the notion of color mainly refers to the value that can be displayed on a screen or measured with a camera. It is often a red-green-blue (RGB) triplet.

Color by vertex:

A color can be associated with each 3D point. It represents either a directly displayable color or a reflection property (mainly an albedo).

Albedo:

Albedo, a fundamental concept in radiometry [START_REF]Radiometry: Albedo, Crookes Radiometer, Intensity, Lambert's Cosine Law, Pyrometer, Bolometer, Ellipsometry[END_REF], is the proportion of the received light power (or light flux) that is reflected. It is therefore a value between 0 and 1.

Reflectance:

Reflectance is often synonymous with albedo and generalises this notion by extending it to a ratio of power received in one direction and reflected in another.

Shader:

For the 3D field, the term Shader [START_REF] Cortes | The RenderMan Shading Language Guide[END_REF], [START_REF] Wolff | OpenGL 4.0 Shading Language Cookbook[END_REF] refers to a small program used to produce the final appearance of an object in the process of computing an image. This program can simply modify the final color, calculate the light reflection to obtain this color, or even modify the shape of an object.

(2D) Texture:

In Computer Graphics, a texture is a function that attributes a value (in general a color) to each position on a 3D object. In this document, a texture defines an image used to map part of, or an entire object (Figure 8).

Texel:

Pixel of a 2D texture.

Colorimetry:

Colorimetry can have many different definitions. According to the "CIE Fundamentals for Color Measurements", it is "the science and technology used to quantify and describe physically the human color perception." For 3D data in the SSH field, this definition is extended to include all the information about the conditions in which the color measurements were made in order to best calibrate the process [START_REF] Ohno | CIE Fundamentals for Color Measurements[END_REF] [START_REF] Ohno | CIE Fundamentals for Color Measurements[END_REF].

Point light (source):

Digital light source corresponding to a 3D point that emits energy or assimilated in all directions. The distribution is uniform in all directions for a Lambertian source [START_REF]Radiometry: Albedo, Crookes Radiometer, Intensity, Lambert's Cosine Law, Pyrometer, Bolometer, Ellipsometry[END_REF]. A goniometric diagram allows the definition of the distribution in other cases. Real point light sources are rare and this model remains an approximation used for small sources such as candle flames or light bulbs.

Directional light (source):

A digital, sizeless light source that is characterized by a single direction of reception of an energy or assimilated. The sun's illumination is often approximated by a directional light.

Area light (source):

Digital light source defined by a finite surface area. Ceiling lights can be approximated by area lights.

3D Model and Scene

3D Model:

A set of digital data that are linked to a single object of study and that are obtained after 3D acquisition or modelling. It is a synthetic digital document intended to evolve with the state of research knowledge. The model can thus have several versions after each step of the sequential graph of data life cycle (Figure 2) until a final version is delivered for a specific purpose. The terms 3D model -virtual model -digital model are considered to be synonyms.

3D scene:

In Computer Graphics, a 3D scene contains one or more 3D objects in the same 3D referential, associated with other data such as light sources.

DATA QUALITY

The concepts presented in this section correspond to those commonly used for writing specifications when digitization is requested. They are presented to help standardize their use.

Outliers:

Outliers [START_REF]What are outliers in the data[END_REF] are data whose values seem too far away or inconsistent with the whole or a sub-set of the data set (Figure 9). Out-of-frame points are an example of this.

Un-relevant data:

Data that does not belong to the object of study. An example is the support on which the object is placed, which may be in the measurements at the same time as the object itself (Figure 10).

Redundant data:

Over acquisition of very similar points according to the chosen resolution or accuracy.

Measurement noise:

Deviation

(Figure 11) of the measurements by a non-repeatable or random phenomenon that results in a difference between the measured value and the true quantity value. The most well known is the noise or chromatic grain obtained in a photographic shoot under low light conditions with long exposure time and high gain.

Measurement bias:

Systematic deviation of the measurements by a repeatable phenomenon which results in a difference between the measured data and the actual value (Figure 12). This can be for example an error in the size of the object or a constant deviation between measured and actual values. The measurement bias can often be corrected by calibrating the measuring system.

Accuracy:

Maximum deviation between measured value and true quantity value. It is either absolute (e.g. a deviation of ±1mm) or relative (e.g. a deviation of ±1%)

(Spatial) Resolution:

In general, the resolution is the spacing between two measurements. This corresponds to the minimum detail of the model.



For a subject this corresponds to the distance between two adjacent measuring points.



For a scanned image this is related to the pixel density of an image (e.g. number of pixels per centimeter) 2 .  For a screen this depends both on the number of pixels and the size of the screen. [START_REF] Ferdani | Terminology, Definitions and Types for Virtual Museums[END_REF].



For any other image, the resolution depends on the size of the projection of a pixel on the study object (e.g. a texture).



For a photograph, the resolution therefore depends on the number of pixels (reference to the notion of definition), the distance between the subject and the camera, the size of the subject and/or the field of view.



In the context of aerial photography, we speak of ground sampling distance or GSD [START_REF] Leachtenauer | Surveillance and Reconnaissance Imaging Systems: Modeling and Performance Prediction[END_REF])

(Image) Definition:

The definition of an image is the total number of pixels that a sensor can acquire to form an image. HDR or "High Dynamic Range": HDR [START_REF] Reinhard | High Dynamic Range Imaging: Acquisition, Display and Image-Based Lighting[END_REF] refers to both an image format and a set of techniques for creating and manipulating such images. In the case of HDR images, this corresponds to an increase in dynamics, i.e. the ratio between the maximum and minimum value per pixel. and per color, by comparison with conventional images such as BMP, JPEG, GIF, etc. These images allow values closer to the light power of a real scene to be captured thus limiting under-and over-exposures.

When we talk about HDR in terms of processing (as on most of today's cameras), it means that the software and/or the acquisition peripheral will multiply the shots with different exposures and recombine them in order to limit under-and over-exposures. However, it is important to remember that colorimetric treatments such as white balance do not have comparable behavior on an image resulting from such a process although the image format remains a classical one.

Figure 13 -Sequence (a-c) of photographs of the "memorial church" of Harvard University for different exposure times which, once merged, allows to reconstruct an HDR image (d) containing details in the previously under-or over-exposed areas. Images from the article by Debevec and Malik (ACM SIGGRAPH 1997).

GOALS

Recorded data:

Survey of characteristic information of the state of what remains of a heritage object (topographic survey, architectural survey, orthophotography, photogrammetry, lasergrammetry, etc.). The purpose is to provide later dematerialised access to the heritage object. It is also a backup, within the limits of what has been recorded.

Communication:

Dissemination of scientific knowledge and methodologies resulting from the study of the object to a scientific public and/or the general public.

Valorization:

According to the Collins dictionary, valorization is the action of "conferring a value upon something". For the data we are dealing with in this document, it is any action that makes use of them in a context other than a scientific study, such as the production of a popularisation document.

Figure 14 Example of valorization: interactive visit of ancient Rome by night (University of Caen Normandy, CIREVE, Map of Rome)

RAW DATA -ACQUISITION: A0

Scientific 3D reconstruction must be based on existing documents using different techniques for survey and representation. We shall discuss the vocabulary for these two aspects.

Instrumental acquisition

Acquisition:

In the context of this document, an acquisition is a measurement of 3D data using photogrammetry, lasergrammetry, tomography, a topographic survey, or any other technology or combination of technologies that allow this.

Photogrammetry:

The Collins dictionary defines photogrammetry [START_REF]Photogrammetric Applications for Cultural Heritage. Guidance for Good Practice[END_REF] as "the process of making measurements from photographs". It is thus a technology that calculates a set of 3D points from a set of photographs or digital images. This set of 3D points is defined in a single reference and at a scale or size to be determined. Color information can be associated with each point by an extraction from the original images.

Lasergrammetry:

Lasergrammetry [START_REF]Historic England 2018 3D Laser Scanning for Heritage: Advice and Guidance on the Use of Laser Scanning in Archaeology and Architecture[END_REF] brings together all the acquisition techniques that use a laser to calculate the distance between the object of study and a emission point of a laser in a given direction. The intensity of laser reflection can also be measured.

Laser scanning produces a set of 3D points. Some devices allow the acquisition of color information using an additional dedicated sensor.

Topography:

Study and description of the shape of a terrain on a map, with the details of the natural or artificial elements it contains, in order to determine the position and altitude of any point located in a given area. Often, a total station, tacheometer, satellite positioning (GPS) or laser telemeter is used to carry out a topographic survey. In the case of historical topography, according to the definition of the lexicon given by the French National Center for Textual and Lexical Resources (CNRTL), it is the set of methods using topography, toponymy, archaeology, etc., in a convergent way to identify ancient sites.

Figure 15 -3D acquisition by lasergrammetry of a Gallic helmet found on the Tintignac-Naves archaeological site. The laser scanner is a Faro scan arm (Archeovision production -2018)

Tomography:

These techniques are widely used in medical imaging [START_REF] Suetens | Fundamentals of medical imaging[END_REF] and allow the estimation of the internal characteristics of an object from images. Examples of these characteristics are density, absorption (X-ray imaging), refractive indices [START_REF] Ihrke | Tomographic Reconstruction and Efficient Rendering of Refractive Gas Flows[END_REF], etc. The resulting data are often in the form of a regular 3D grid of values. One of the most commonly used techniques in archaeology is CT scan (for X-ray computed tomography or Computed Tomodensitometry).

Sound recording:

In the context of 3D production, this is the recording of sounds produced by or which come from a heritage object (Figure 16). This recording is to be distinguished from the collection of oral or musical sources around a heritage object, which is a complementary collection of information by sources. We may cite for example, the sound recording of different materials (wood, concrete, stone, etc.) of an architectural ensemble, to determine its acoustics.

RTI or "Reflectance Transform Imaging":

This was originally designed to obtain textures that depend on light directions ("Polynomial Texture Map" -PTM [START_REF] Malzbender | Polynomial Texture Maps[END_REF]) and now refers to both (1) a setup to acquire images for a fixed view-point with different light directions or positions of light, and ( 2) the approximation of these data in the form of PTM with the corresponding visualization tools. These techniques were popularized in the field of SSH by the "Cultural Heritage Imaging" association. In terms of visualization, this allows offsite replays of changes due to lighting variations and, manipulations to improve the appearance of studied object [START_REF] Mytum | The Application of Reflectance Transformation Imaging (RTI) in Historical Archaeology[END_REF]. Approximation is generally carried out using standard functions (e.g., polynomials) chosen a-priori and without relation to the properties of the considered surfaces.

Documentation and sources of information

These are the different categories of iconographic sources (photographs, drawings, paintings, engravings) that bear witness to the state of a building or object at a particular moment of its history.

Iconography:

A collection of images related to the object to be portrayed in 3D (surveys, sketches, photographs, mosaics, numismatics, paintings, etc.).

Texts:

All forms of writing related to the studied object: primary literature (ancient texts, inscriptions), secondary literature (excavation reports, excavation journals, scientific publications, etc.). Examples of the form of these writings are manuscripts, prints, engravings, etc.

Oral sources:

Documentation which comes directly from individuals, groups concerned by the studied object. It is recorded in audio format or transcribed.

PREPROCESSED DATA / PREPROCESSING: V0

These are the data resulting from a series of technical operations involving cleaning, consolidation, completion and semantic enrichment of the raw acquisition. This processed data constitutes an initial version of the 3D model (V0). In the case of an acquisition, the V0 is the first complete model with the minimum of human intervention. As soon as the scientist acts, we name this "processing". Each level of pre-processing should go with metadata that details (1) the algorithms/ methodologies/etc. used, (2) the chosen value of the parameters and, (3) a quality level.

Cleaning:

A cleaning step consists of removing irrelevant, redundant or aberrant data. It can also consist of reducing measurement noise and correcting measurement bias. Cleaning can be automatic or manual. It is important to know the parameters of the measuring instrument and to take them into account to avoid removing useful information. It is equally important that those involved in the acquisition (1) either perform this task or, at least, work in close collaboration with the team performing the pre-processing and (2) validate the result together with the scientists that asked for digitization to be carried out.

Registration:

In the case of point cloud registration, a single acquisition (e.g., from a single point of view) is never sufficient to record a heritage ensemble regardless of the acquisition device that was used. Different acquisitions are thus required , especially when the goal is to record an entire building, or a site, at several levels of detail. It is therefore necessary to transform point clouds collected separately into a single coordinate system in order to prepare their fusion. Consolidation is therefore the controlled fusion of several acquisitions into a unique representation. An example is the alignment of different acquisitions from an object from different points of view thanks to the estimation of points sharing the same position on the object [START_REF] Mohr | Géométrie projective, analyse numérique et vision par ordinateur[END_REF]. The process can be carried out automatically, manually or semi-automatically (a first manual registration is carried out and then automatically optimized).

Georeferencing:

Position and geographic orientation of 3D models without modifying the original source data. This operation consists of moving from a relative location of 3D data to an absolute location in a recognized geographic coordinate system [START_REF] Hackeloeer | Georeferencing: a review of methods and applications[END_REF]

HYPOTHESIS / RESTITUTION: FROM V0 TO V2

Processing:

Steps of scientific involvement on a 3D model, starting from the initial structured model (V0) to all the resulting processed models (V1n). Processing performed to move from one state to another must be recorded in the paradata.

Restitution 3 :

Restitution is a digital reconstruction based on scientific data used in the cultural heritage community. It consists of representing a given state in time of an archaeological site, building or object from archaeological or historical sources. It can be a set of drawings, digital 3D models, scale or full-size models, etc. Restitution helps researchers gain better understanding of remains and can also help them validate archaeological and/or architectural hypotheses. Restitution is thus continuously ongoing work since it takes into account research in the field and also the evolution of technologies.

Structuring the 3D model:

The creation of a digital object that contains all 3D data and metadata, prior to any educational, scientific use or conservation. From this stage, the model can take kinematics aspects (movements, mechanical actions) into account. 3 In French Selon le traité de la réalité virtuelle [START_REF] Fuchs | Le traité de la réalité virtuelle : Outils et modèles informatiques des environnements virutels[END_REF], "Les modèles fournis (…) comportent régulièrement trop de polygones pour «être utilisés dans une application de réalité virtuelle"

Semantic enrichment

Added information at the 3D data level [START_REF] De | 3D Modelling and Semantic Enrichment in Cultural Heritage[END_REF]. This enrichment is an interpretation of the acquired data and is often necessary to understand the object of study. This information can be added by coloring a point cloud or applying a texture, adding text, or filtering or classifying a point cloud or a sub-part of it.

Textual semantic enrichment may use thesauri and ontologies to structure the relationships between terms used in the text.

Figure 18: Aioli a reality-based annotation platform for collaborative semantic enrichment (UMR MAP 3495)

Kinematics:

Description of movements from different parts of a 3D model together with the mechanical movements they may maintain between them. By adding the temporal dimension to the kinematics, a dynamic model can be obtained which enables simulations to be made.

Simulation:

Computation based on the 3D model to recover or estimate one or several parameters of a model in order to validate hypotheses (kinematics of the model [START_REF]Virtual reconstruction and kinematic simulation of a marble sawmill through the integration of historical and archeological data[END_REF], [START_REF]Inverse Kinematics Techniques in Computer Graphics: A Survey[END_REF], restitution of texture, lighting [START_REF] Happa | Illuminating the past: state of the art[END_REF], movement of crowds in a given space [START_REF]AI and virtual crowds: Populating the Colosseum[END_REF], etc.)

Animation:

Virtual movements of objects in a 3D scene (static or dynamic). This can include (Figure 20) the movement of people such as mechanical parts, falling objects, etc.

It should be noted that this movement can be defined either ad-hoc by trajectories in space without physical constraints (contrary to kinematics) or by the result of a physical simulation (like in kinematics: falling trajectory of an object under the influence of gravity, collisions, etc.). It is therefore up to the expert to take the time to validate such behavior.

Metadata:

Data used to describe a dataset, a 3D model (date of acquisition, authors, rights of use). The surrounding data (context) are filled in as paradata.

Paradata:

Data specific to the context, but not directly constituting metadata, such as the methodological report or the acquisition process (scientific choices, hardware, software and techniques). Term specific to statistics used to inform the survey process.

Figure 19 -Example of a kinematic case study of the BERTRAND Company in BATZ-SUR-MER (44): dynamic 3D modeling of the factory and the salt washing machine (1914-1966) (F. Laroche -LS2N) Figure 20 -Restitution of a factory of the former Renault factory of Boulogne Billancourt (workshop C5) with animation of the work chain showing the production of the car chassis. (Factory project 3D-Archeovision Production)

DELIVERABLES

Virtual Reality:

The concept of virtual reality encompasses all the technologies that make it possible to digitally recreate and render the world around us. It involves the use of digital models, algorithms for image synthesis (or any other signal that can stimulate the human senses as well as sound), displays such as screens, headphones, etc. in the context of images (or sound restitution peripherals for sound) as well as all the techniques and tools for interactions between humans and this data [START_REF]Virtual Reality: Concepts and Technologies[END_REF].

Augmented reality:

As in [START_REF]Virtual Reality and Augmented Reality: Myths and Realities[END_REF], the goal of AR is to enrich the perception and knowledge of a real environment by adding digital information relating to this environment. It thus includes all the techniques that make it possible to associate a real world with a virtual world. In the context of image creation, it often consists of superimposing real images and synthetic images on screens or with the help of dedicated devices such as augmented reality headsets/glasses.

Mixed Reality:

Extending the notion of augmented reality, mixed reality includes all the technologies [START_REF] Milgram | Augmented Reality: A Class of Displays on the Reality-Virtuality Continuum[END_REF] such as augmented reality that combine a greater or lesser proportion of real data with virtual data (Figure 21).

Interactive model:

A 3D scene in which users can interactively move or manipulate some 3D objects.

Precomputed rendering:

A 3D model containing some elements from lighting, animation, kinematics that are computed prior to the visualisation rather than directly. It can be for a fixed or a predefined path. An application can propose several pre-calculated renderings (user's choice) [START_REF] Ramamoorthi | Precomputation-Based Rendering[END_REF].

Stereoscopy:

As far as display is concerned, stereoscopy includes all the techniques that allow a user to have the impression of a 3D image by displaying a dedicated image for each eye.

Orthoimage:

A geometrically rectified and measurable image, projected on a reference plane (orthogonal, zenithal, etc.). When an orthoimage is recomposed from several photos, it is called mosaic orthophotography [START_REF] Chiabrando | SfM for Orthophoto to Generation: A Winning Approach for Cultural Heritage Knowledge[END_REF]. As in [START_REF] Schroeder | Decimation of triangle meshes[END_REF], the aim of a decimation algorithm is to reduce the total number of triangles in a (..) mesh, preserving (..) a good approximation of the original geometry. Validation of the simplified model must be based on scientific advice to ensure the quality of the final model.

Figure 5 -

 5 Figure 5 -Two meshes of the same quality obtained from the same four 3D points.

Figure 4 - 3 Figure 3 -

 433 Figure 4-Mesh obtained from the point cloud from figure 3

Figure 6 -

 6 Figure 6 -The normal (red vector) indicates on the selected point the orientation of the surface (here a sphere).

Figure 7 -

 7 Figure 7 -Colored 3D model of a Madonna and Child (Musée des Augustins -Toulouse) for the restitution of various polychromies. (Digitization and restitution by Archeovision Production -2005)

Figure 8 -

 8 Figure 8 -2D texture (bottom) mapped on a sphere.

Figure 9 -

 9 Figure 9 -Example of outliers: the point in red is very different from the other points in blue and certainly corresponds to a measurement error.

Figure 10 -Figure 11 -

 1011 Figure 10 -Not relevant data. If the object of study is the sphere, the blue dots are relevant and the red dots on the ground are not relevant

2

  http://www.pixelvalley.com/appareilnumerique/definition-resolution.php

Figure 12 -

 12 Figure 12 -Example of measurement bias: the measuring device has introduced on certain areas (red dots) a constant offset with respect to the actual position on the sphere.

Figure 16 -

 16 Figure 16 -Sound recording ( Projet IMAPI porté par Julien Ferrando ) https://www.prism.cnrs.fr/projets/projetscollaboratifs/imapi/

Figure 21 -

 21 Figure 21-Ortho-image developed, from the chevet of the Chapel of the Trinity, Saint-Honorat Islands Cannes (S.Sorin -CEPAM)

Figure 22 -

 22 Figure 22-Milgram's continuum

http://tadirah.dariah.eu/vocab/index.php

Completion:

The process of adding absent or missing information into a point cloud or a mesh to complete the original data.