E A Viktorov

V A Srećković

N N Bezuglov

K Miculis

A Pastor

P Yu Serdobintsev

Collapse of Xe polarized atomic states in magnetic fields

Ionization of two-photon excited states 5p 5 ( 2 P 3/2 )6p[ 3 / 2 , 5 / 2 ] 2 , M=2 (jl-coupling) of xenon atoms by circularly polarized probe light was studied experimentally in a supersonic beam. The observed photoionization signals revealed oscillation structure due to the Larmor precession of atomic states in an external magnetic field. We derived analytical formulas for the photoelectron current and explained the diversity in the structure of the detected oscillations in terms of the principal lines among multiplet components of optical transitions. The obtained numerical data demonstrate collapse and revival (beating) behavior of the photocurrent due to nonlinearity of Zeeman shifts in the presence of the Paschen-Back effect. Our results indicate the possibility of implementing Doppler-free spectroscopy involving bound-free transitions.

Introduction

The analysis of temporal dynamics of fluorescence signals after excitation of atomic states by polarized light is an important area of modern spectroscopy [START_REF] Auzinsh | Optically Polarized Atoms. Understanding light-atom interactions[END_REF]. Observation of magnetic resonances in polarized gas media is the basis of constructions and implementations of sensitive magnetometers [START_REF] Alexandrov | [END_REF]3]. Applied controlled external magnetic fields result in diverse types of oscillating structures in detected fluorescence signals that allow making precision measurements of atomic state parameters beyond limitations due to Doppler broadening (Doppler-free spectroscopy) [START_REF] Auzinsh | Optically Polarized Atoms. Understanding light-atom interactions[END_REF][START_REF] Alexandrov | Interference of Atomic States[END_REF][START_REF] Budker | Atomic physics: an exploration through problems and solutions[END_REF][START_REF]Handbook of high-resolution spectroscopy[END_REF]. Traditional methods of spectroscopy are associated mainly with boundbound transitions with explicitly specified quantum numbers of the initial and final states involved into optical transitions. In the present report, we demonstrate, both experimentally and theoretically, a possibility to examine photocurrent oscillations at Larmor frequencies upon photoionization of polarized xenon atoms in a supersonic beam with polarised probe photons.

Our experimental scheme has a number of important advantages compared with the detection of 1 e-mail:mdimitrijevic@aob.rs photons due to the almost 100% efficiency of extracting photoelectrons from the interaction zone. Probing excited gas media by photoionization methods allows, as well, to examine important details of nonlinear optical pump processes resulting in polarization of atomic states [START_REF] Porfido | [END_REF]8]. We investigated cases of weak (linear Zeeman effect) and intermediate magnetic field values and revealed collapse and revival behaviour of oscillations in photocurrent signals as a result of the Paschen-Back effect [START_REF] Sobelman | Atomic Spectra and Radiative Transitions[END_REF][START_REF] Foot | Atomic Physics[END_REF].

Experimental setup

Xenon atoms were produced in a supersonic jet. A pulsed piezoelectric valve opens the bottle filled with mixture of xenon (8%) and helium gases under the pressure of 1 Bar into the vacuum chamber pumped out to 10 -8 Torr. The velocity of Xe atoms in the supersonic flow was about 10 5 cm/sec. The supersonic jet passed the skimmer (see Fig. 1). After the skimmer the atoms in the ground unpolarized state crossed the focused laser beams. The Ti-Sapphire femtosecond laser PULSAR 10 (Amplitude Technologies, France) [11] has the following characteristics: main wavelength -795 nm., pulse energy -5 mJ, pulse duration -50 fs, repetition rate -10 Hz. The outcoming pulse was divided into two parts: (i) 70% of the pulse power pumped parametric amplifier TOPAS and was converted to UV radiation for 2-photon excitation of atomic states. (ii) The rest 30% of the power was used as probe radiation in the form of the second harmonic for ionization of pump-excited atoms. The correlation function of the pump (exciting) and probe (ionizing) pulses was measured by the signal of nonresonant multiphoton ionization and amounted to 140 fs (FWHM). Circular polarization of both pump and probe pulses was performed using a Babinet-Soleil compensator.

Photoelectrons were trapped in an inhomogeneous magnetic field and their energy spectra were analysed by a magnetic-bottle time-of-flight electron spectrometer. In our experiments, the the azimuthal quantum numbers M along with the indices q of the polarization moments correspond to the "excitation coordinate system" with the quantization z-axis, while numbers

x M re-fer to the system associated with the magnetic field, that is, with the x-axis as the quantization axis.

It is convenient to consider the effects of coherent interaction of polarized quantum particles with light in the framework of the technique of irreducible tensor operators for density matrices, which deals with the polarization moments of atoms q   and photons

q   [1, 2, 4, 9].

Partial photoionization signals

An explicit expression for the photoionization cross-section  was provided by authors of manual [START_REF] Auzinsh | Optically Polarized Atoms. Understanding light-atom interactions[END_REF] (Section 20.2). In what follows, we will use their result in a slightly different form, which involves the photo-signal , ( )

I t    0 0 1 1 2 2 , 0 0 0 0 1 1 0 0 2 2 0 0 ( ) / ~( ) ( ) ( ) ion I t J D M t D M t D M t           , (1)
and is more suitable for our purposes. Here ( 1)

| ( || || ) | JJ Dd JJJ              (2)
and the reduced dipole matrix elements ( || || )

d  
 for bound-free optical transitions [START_REF] Auzinsh | Optically Polarized Atoms. Understanding light-atom interactions[END_REF][START_REF] Sobelman | Atomic Spectra and Radiative Transitions[END_REF]. Although the coefficients M  are trivial ( 1

M  
) in the case of partial transitions, they play an important role in calculating the total photocurrent (see Eq. 5).

Zeeman shifts and density matrices temporal dependence

Effects of an interaction between atoms and magnetic fields are described in terms of Zeeman shifts [START_REF] Auzinsh | Optically Polarized Atoms. Understanding light-atom interactions[END_REF][START_REF] Sobelman | Atomic Spectra and Radiative Transitions[END_REF]. Due to the spin-orbit interaction, the state   in a coordinate system associated with the applied magnetic field (quantization x-axis) can be found in subsection 8.2 of book [START_REF] Sobelman | Atomic Spectra and Radiative Transitions[END_REF]. In our experimental conditions with comparatively weak magnetic fields, it is sufficient to restrict ourselves to considering of the linear and quadratic terms in ( )

x M   over the Larmor frequency L  [9]: 2 2 2
( ) / ( )

x x L L x M M J M          h ; 2 2 K 2 11 /4 K J g gJ         h . (3)
Here K g and J g denote Landé g-factors for the state The temporal dynamics of density matrices ( ) M M t  % and the relevant polarization moments ( ) q t   in the presence of a magnetic field can be directly calculated using the Wigner rotation matrices [START_REF] Auzinsh | Optically Polarized Atoms. Understanding light-atom interactions[END_REF][START_REF] Landau | Quantum Mechanics: Non-Relativistic Theory[END_REF]. The latter provide a transformation between representations of an atomic density matrix associated with different quantization axes, which are directed along the magnetic field (x-axis) or laser beams (z-axis). In more general situations with several components (in our case, there are two of them) in a multiplet atomic state (as for the hyperfine components), it is preferable to numerically solve the Bloch equations for the density matrix based on, for example, the split propagation technique [START_REF] Sydoryk | [END_REF][START_REF] Efimov | Numerical simulation of dynamical chaos regime for Rydberg atoms based on the Split Propagation Technique[END_REF].

If we are dealing with linear Zeeman shifts, there are simple explicit formulas for 0 ( )

q t    (see
L t t t     ; 2 2 2 00 ( ) (3cos ( ) 1) / 2 ( 0) L t t t        (4)

Total photoionization signal

Expression (1) gives information on the partial cross section of photoionization when the quantum numbers , , l K J    in the final channel are fixed (i.e., measured). Since we did not separate the photoelectrons by , , l K J    numbers in the experiments, all the partial signals contribute

to the final cumulative photocurrent signal , ( ) ( )

I t I t      
. Importantly, the sum rule for the product of three 6j-symbols (see Eq. (4.85) in [START_REF] Sobelman | Atomic Spectra and Radiative Transitions[END_REF]) makes it possible to perform explicit summation over the quantum numbers K and J  , provided that quantum defects of final states in the energy continuum are independent on , ( 1)

1/ 2 J l j KK JK KK ll M J J j                 (5)

Results and discussion

Our main result boils down to the statement that the observed photocurrent signal ( )

I t ' 1 ( ) ( ) ll ll I t I t      ; 2 ( || || ) l nl d l     (6)
is obtained as the sum of two partial signals ( )

l I t  2 0 0 0 0 ( ) ( ) l I t I D M t           , (7)
statistical weights l   of which are determined with the reduced dipole matrix elements (6) of bound-free optical transitions of the valence electron. The multiplier 0 I depends on intensities of applied lasers and experimental set-up parameters.

It is important to note that immediately after the excitation process at time 0 t  , the angular momentum vector ( 0) J t  r of the two-photon excited atomic state i  is directed along the wave vector (quantization z-axis) of the probe photons. The angular momentum ph S r of the photons (photon spin) has a unity value and is also directed along the z-axis. Upon the ionization at time t, the atom acquires the photon spin, i.e. are ionized by the right-circularly polarised probe photons. The corresponding photonic and atomic polarization moments are expressed via Wigner 3j symbols [START_REF] Auzinsh | Optically Polarized Atoms. Understanding light-atom interactions[END_REF] 0 ( 0)

2 1 0 JJ t MM           ; 0 1 1 21 1 1 0           . ( 9
)
with the numerical values shown in Table 1 (J=2, M=2).

)

ph ph L m ph ph J J J J J J S S S S t          (10)
The solutions arccos( 1/(2 3))

1.863 Lm t      of Eq. (10) for 2, 1 ph JS 
 are in excellent agreement with the data of graph 2 in Fig. 4.

Aggregated signal ( )

I t

The calculated values of the aggregated photoionization current I (6) are shown in Fig. 2 (solid curve). A good agreement between the theoretical predictions and the experimentally obtained photoelectron signals can be seen provided that the ratio We also performed numerical simulations to describe the experimental signal depicted in Two well-known processes, that can contribute to the attenuation of the detected photocurrent, do not explain, however, the small value of the fitting parameter  . (i) The natural life- time of Xe 5p 5 ( 2 P 3/2 )6p[ 3 / 2 ] 2 state is ~ 27 ns while (ii) the decay time, corresponding to the transit time depletion [START_REF] Bruvelis | [END_REF] due to the escape of moving Xe atoms from the volume of the probe laser beam, turns out to be an order of magnitude larger. On the other hand, the magnitude of the applied magnetic field is not sufficient to obtain the fitting value L    = 1/100, necessary for the appearance of beats. This means that both the damping and the observed beats in the experimental signal in Fig. 3 have additional physical sources due, for example, to the rich isotopic composition of the Xe samples we use. Landé g-factors values for different isotopes can vary within 3%. From the point of view of a formal mathematical description, the role of these variations in phase decoherence processes is similar to nonlinear Zeeman shifts and will be analyzed in our future publication.

Conclusion

This paper presents experimental and theoretical studies of photoionization processes with the participation of two-photon excited states of Xe atoms in the presence of a magnetic field. The experimental setup did not distinguish between extracting photoelectrons in terms of quantum numbers and scattering angles. The observed temporal dynamics of the photocurrent revealed, nevertheless, an oscillatory structure due to the preparation of ionizing atoms in strongly polarized states, which are affected by the Larmor precession. We derived analytical formulas for the photocurrent explaining the variety of forms of recorded oscillations. The numerical data carried out demonstrate characteristic beats in oscillations (collapse followed by revival) due to the quadratic nonlinearity in the Zeeman shifts. We would like to emphasize the possibility of observing the effects of coherent quantum states interference (in our case, photocurrent oscillations) in the energy continuum. This allows, in particular, the realization of Doppler-free spectroscopy involving bound-free transitions. Additionally, such studies may be of interest and for magnetic star atmospheres investigations, where xenon is present and its spectral lines were observed. We note as well that such investigations may be of interest and for tokamak plasma where xenon may be added as impurity.

Figure 1 .

 1 Figure 1. Experimental setup. OPAoptical parametric amplifier; DLdelay line; DM -dichroic mirrors; DCdoubling crystal; Ppolarizer; BS -Babinet-Soleil compensators; CMconcave mirror.

  Teslameter PIE.MG R-2 magnetometer has measured the magnetic field value | (± 0.006) Tesla at the entrance to the magnetic bottle. The field orientation / x e B B  r r along x-axis was perpendicular to the quantization z-axis, which coincided with the direction z e r of the propagation of both laser beams.

Figure 2 .

 2 Figure 2. Delay dependence of photoionization signal I for the polarized Xe state 5p 5 ( 2 P 3/2 )6p[ 5 / 2 ] 2 (78120cm -1 ), M=2. The points indicate the experimental data, while the solid curve corresponds to analytical results (Eqs. (4), (6), (7)) with the ratio of l-channels weights as 1: 3.4.

Figure 3 . 3

 33 Figure 3. Delay dependence of photoionization signal I for the polarized Xe state 5p 5 ( 2 P 3/2 )6p[ 3 / 2 ] 2 (79212,5cm -1 ), M=2.

ionJ 2 jP

 2 photoelectrons energy. It is assumed that the quantum state 2

  nl K respectively.

  Appendix A). The first three atomic polarization moments 0

Figure 4 .Figure 4 1 J

 441 Figure 4. Temporal dependence of the partial photoionization signals ( ) l I t  (7) in two outgoing channels l'=2 (curve 1) and l'=0 (curve 2). The case of linear Zeeman shifts. The initial polarized atomic state is P 3/2 6p[ 3 / 2 ] 2 , M=2

Figure 5 

 5 Figure 5 demonstrates dramatic changes in the dynamics of partial signals ( ) l I t 

Figure 5 .

 5 Figure 5. Same as in Fig. 4 in two outgoing channels l'=2 (upper frame) and l'=0 (lower frame) when the applied magnetic field results in the Paschen-Back effect. The value of the dimensionless parameter



  of the statistical weights is chosen equal to 3.3. The latter value corresponds to the Bethe rule[START_REF] Sobelman | Atomic Spectra and Radiative Transitions[END_REF][START_REF]Qualitative Methods in Quantum Theory[END_REF][START_REF] Bethe | Quantum mechanics of one-and two-electron atoms[END_REF], which ascribes a dominant role to photo-processes with the highest possible value of the orbital moment l  of the escaping photoelectrons.

Figure 6 .

 6 Figure 6. Same as in Fig. 3 for the aggregate photosignal ( ) I t (6). Our numerical results are obtained for the fol- lowing parameters: the product

Fig. 3 .

 3 Fig. 3. The calculated photocurrent ( ) I t temporal evolution is shown in Fig. 6. Signal fading was taken into account by introducing the decay fitting function: ( ) exp( / ) ( ) I t t I t   with the decay constant  =6 ns. Satisfactory agreement between experimental and theoretical results can be observed. The formation of a beat structure in the signal ( ) I t is clearly seen as a result of a nonlinear quadratic response in the Zeeman energy shifts.

F,

  Eq. (4)).In the case of the alignment moments (2  ), let's construct two matrix operators ˆ( )  is formed by the product of the spherical components of the unit vector where  is the Kronecker delta function. In the next step, we consider the trace of the matrix product: hand, the trace can be viewed as the scalar product of the involved matrices[START_REF] Sobelman | Atomic Spectra and Radiative Transitions[END_REF], i.e.the trace may be written in terms of their irreducible tensor operators[1,

Table 1 .

 1 Photon and atomic polarization moments.

						( ) J t r		( ) J J t S   r r r	ph	(8)
				 	0	 	1	 	2
				1/ 3	1/ 2	1/ 6
			0
		0 ( 0) t   	1/ 5		2 /( 5)	2 /( 7)
	4.1 Partial signals ( )
								in two outgoing channels
	1 ll       1 1 0, 2	when the polarized Xe states	i  	3 / 2 PM 2 6p[3/2,5/2] ,		2

l I t  We first consider the features of photoionization signals ( ) l I t

Acknowledgements

This work was supported by the Latvian Science Council Grant No lzp-2019/1-0280 and by the Russian Science Foundation under the grant No 18-12-00313 in the part regarding the theoretical analysis of photoionization signals observed in experiments with Xe atoms. The equipment of the Resource Center "Physical Methods of Surface Investigation" of the St. Petersburg State University was used in experiments. We thank Professor M. Auzinsh for useful discussions on issues related to our work.

Author contribution statement

All authors contributed equally to the paper.

Appendix A. Temporal dependence of polarization moments

If we restrict ourselves to the effects of linear Zeeman shifts, we can independently study the evolution of the polarization moments of atoms ( )  does not depend on t .

In the "excitation coordinate system" (quantization z-axis), three components 1 ( ) q t  correspond to spherical components 0 , J  of the vector ( ) J t r [START_REF] Auzinsh | Optically Polarized Atoms. Understanding light-atom interactions[END_REF][START_REF] Alexandrov | Interference of Atomic States[END_REF] which is initially oriented along the unit vector z e r (see discussion regarding Eq. ( 8)). In other words 1 ( 0) 0 t

 is some constant depending on the excited states parameters). The vector J r precession around the magnetic field (x-axis) results in


Anthony Pamart
email: anthony.pamart@map.cnrs.fr

François Morlet
email: francois.morlet@map.cnrs.fr

Livio De Luca
email: livio.deluca@map.cnrs.fr

Philippe Véron

Philippe Veron
email: philippe.veron@ensam.eu

A Robust and Versatile Pipeline for Automatic Photogrammetric-Based Registration of Multimodal Cultural Heritage Documentation

Keywords: close-range photogrammetry, Structure from Motion, MicMac, OpenMVG, data-fusion, remote-computing, multimodal imaging, Cultural Heritage

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

Introduction

Image-based modeling (IBM) states nowadays as one of the most used technique in the CH field thanks to its flexibility and cost efficiency compared to Range-based modeling. Nonetheless, it requires specific technical skill and expertise in data acquisition but also in the processing stage. Regarding this point, CH oriented applications are still split between the complexity of open-source packages and the opacity of commercial "black-boxes" to process the data. In this context the development of user friendly and open-source based solution seems a relevant choice for CH scientific purposes. However, combining and balancing the prerequisites between automation and accuracy are never an easy nor straightforward to goal. CH domain has also to deal with overgrowing massive and complex data while having to anticipate its over time management. Our contribution to this challenge is called TACO (Totally Automated Co-registration and Orientation of image sets). This toolbox formalizes a methodological approach dedicated for photogrammetric documentation of CH artifact including features like iterative registration or interoperable functions. It has been developed initially as the photogrammetric engine for AIOLI, a reality-based 2D/3D annotation platform for the collaborative documentation of heritage artefacts (see Appendix A). Conceived as a flexible and evolutive tool it aims to support a global data fusion methodology allowing to handle and merge multiple sources of data. In CH the field, multimodality means to manage multidimensional data provided by the use of different sensors, scales, spectral bands and/or simultaneously acquired or in a multi-temporal context, to document and study heritage assets. Based on previous photogrammetric fusion experiments [START_REF] Pamart | Toward a multimodal photogrammetric acquisition and processing methodology for monitoring conservation and restoration studies[END_REF][START_REF] Pamart | Multispectral Photogrammetric Data Acquisition and Processing for Wall Paintings Studies[END_REF][START_REF] Pamart | A complete framework operating Spatially-Oriented RTI in a 3D/2D Cultural Heritage documentation and analysis tool[END_REF] detailing different combined modalities, this article presents recent advancements on automated co-registration of CH multimodal imaging. The development of TACO started and has been improved over the past few years on other joint research projects more especially focused on the documentation and follow-up of conservation-restoration works.

Multimodality in photogrammetric based workflows for CH documentation (see Figure 1) has involved some modifications from standard linear approaches, simplified hereafter as a synchronous Input and output (I/O) operation (Figure 1i). Nowadays, a presumed "final" output actually results from a complex operative chain involving scattered fusion and processing methods from multiple sources of data (Figure 1ii). During the co-registration of new data, we can face numerous issues for each step (shown in Figure 1iii); redundancy or compatibility with previous data (a), deprecated processing nodes (b), complexification and efficiency of fusion stage (c) or accumulation of disparate results (d). In this context, TACO aims to contribute to the creation of a stable and scalable method supporting incremental co-registration of CH resources over time (Figure 1iv). Diagram synthesizing CH oriented multimodal IBM workflows; conventional "one-shot" application (i), current state (ii) and issues (iii) and targeted approach (iv) using TACO.

Structure

The development of TACO has started on the assumption of the growing use of multimodal practices in the CH domain, introduced and defined above in Section 1. The next subsection interrogates TACO and related-works Section 1.2 in regard of IBM applications for data fusion purposes. Starting with a brief discussion on IBM framework, the Section 2 exposes all the components (in Section 2.1) and details the technical implementation for the Initial reconstruction (in Section 2.2) and Incremental registration (in Section 2.3) of multimodal image-sets. The results are presented and discussed in the Section 3, completed by our works in progress on interoperability problematic Section 3.1. Conclusion and perspectives on the methodological asset of TACO for CH data fusion are given in Section 4.

The Appendix A provides as an example, an operative implementation of TACO Appendix A within AIOLI web-service.

Related Literature

From the past decade, several domains such as the CH field target the digital replication as a mid-term scientific goal. This replica or "digital twin" of a CH artifact is facing two majors issues. The first one is the ability to build a digital replica as faithful and complete as possible and for which 3D scanning technologies provide great support. The second issue is the capacity of integrating seamlessly new data to keep the digital replica up to date according to the ever growing mass of digital documentation.

For the first issue, IBM is one of the techniques mainly used to generate a digital footprint of an object appearance at a given time. Affordable and considered as user-friendly, recent trends within both the scientific and not-expert community report on remarkable efforts to make it even more accessible and popular. The remote-computing applications (i.e., automatized and/or massive processing making accessible through a web-service) contributed to this goal since the early stage of digital photogrammetry [START_REF] Grussenmeyer | ARPENTEUR 3.0: Recent Developments in Web based Photogrammetry[END_REF][START_REF] Nilsson | The ARC 3D Webservice[END_REF][START_REF] Heller | 3D reconstruction from photographs by CMP SfM web service[END_REF][START_REF] Alliez | Culture 3D Cloud: A Cloud Computing Platform for 3D Scanning, Documentation, Preservation and Dissemination of Cultural Heritage[END_REF][START_REF] Nocerino | 3D reconstruction with a collaborative approach based on smartphones and a cloud-based server[END_REF]. Most of those works faced similar issues , i.e., the difficulty to reach a robust pipeline (meaning the ability to cope errors) and to define a versatile workflow, regardless of input data. Lately, the deployment of other web-services (e.g., WebODM, MiaW) have been eased with the automation degree included in FLOSS packages [START_REF] Moulon | Open multiple view geometry[END_REF][START_REF] Rupnik | MicMac-A free, open-source solution for photogrammetry[END_REF]. The development of photogrammetric Software as a Service (SaaS) has emerged concurrently with the upgrade of SfM solutions for massive processing. After decades of parallel development, the offer in IBM software remains fuzzy between SfM algorithms coming from Computer Vision community and more conventional photogrammetric methods [START_REF] Hartley | Relationship between photogrammmetry and computer vision. Integrating photogrammetric techniques with scene analysis and machine vision[END_REF][START_REF] Granshaw | Computer vision and photogrammetry: Interaction or introspection? Photogramm[END_REF]. As stated recent work [START_REF] Aicardi | Recent trends in cultural heritage 3D survey: The photogrammetric computer vision approach[END_REF], despite their similarities and differences both methods seem to converge toward an optimal and hybrid solution. Indeed, this so called "photogrammetric computer vision approach" might be a relevant solution to address the challenge of massive digitization of CH. On one side SfM has proven since the beginning its robustness and velocity to handle massive and unstructured dataset [START_REF] Snavely | Modeling the world from internet photo collections[END_REF]. On the other side, only the controlled environment of photogrammetric approaches can perform a global refinement [START_REF] Triggs | Bundle adjustment-A modern synthesis[END_REF] with demanding camera self-calibration models [START_REF] Remondino | Digital camera calibration methods: Considerations and comparisons[END_REF] to reach accurate measurements required for CH multi-source 3D dense reconstruction. In order to fully benefit of the assets belonging to each method, library or algorithm, the need of an interoperable process is raising. Some attempts have been recently made in this direction to release more handy tools [START_REF] Gonzalez-Aguilera | GRAPHOS-open-source software for photogrammetric applications[END_REF][START_REF] Gonzalez-Aguilera | PhotoMatch-An open-source multi-view and multi-modal feature matching tool for photogrammetric applications[END_REF]. Furthermore, the CH experts have high demand on preserving a data-provenance and data-quality continuum, hence the use of commercial solutions is frequently questioned in cross-comparison studies [START_REF] Remondino | Image-based 3D Modelling: A Review[END_REF][START_REF] Remondino | A critical review of automated photogrammetric processing of large datasets[END_REF][START_REF] Stathopoulou | Open-Source Image-Based 3d Reconstruction Pipelines: Review, Comparison and Evaluation[END_REF] in term of cost to performance ratio

The second issue concerns the spatial registration of images which is the fundamental step prior to address the challenge of Data Fusion in the CH field. Several related works achieved to link or bridge imaging modalities by exploiting feature-based registration method combined with photogrammetric routines, in multi-band [START_REF] Barazzetti | Geometric and radiometric analysis of paintings[END_REF][START_REF] Nocerino | Mapping VIS and UVL imagery on 3D geometry for non-invasive, non-contact analysis of a vase[END_REF][START_REF] Grifoni | Construction and comparison of 3D multi-source multi-band models for cultural heritage applications[END_REF], multi-source [START_REF] Chane | Integration of 3D and multispectral data for cultural heritage applications: Survey and perspectives[END_REF][START_REF] Yeh | A streamlined photometric stereo framework for cultural heritage[END_REF][START_REF] Van Der Perre | Towards a combined use of IR, UV and 3D-Imaging for the study of small inscribed and illuminated artefacts[END_REF] and/or multi-scale [START_REF] Suwardhi | Digital 3D Borobudur-Integration of 3D surveying and modeling techniques[END_REF] approaches. As stated in a review article [START_REF] Ramos | Data fusion in cultural heritage a review[END_REF], the diversity of CH objects increases the complexity of defining and automating efficient or reproductible methods to reach satisfying data integration for CH purposes. One explanation of this complexity is the discrepancy of 2D and 3D data sources in the co-registration process compared to other domain like medical or satellite imaging where intermodality is better known and defined. For this purpose, TACO has been limited on image-based methods to avoid such technological gap and consequently improve the performances with photographic-based techniques widely used in CH documentation (e.g., photogrammetry, technical photography and computational photography). However, the extension of the co-registration scope to other techniques is planned and discussed in section Section 4.

This literature review underlines the current difficulty to build and handle the co-registration from several multimodal layers within a single and reproductible framework. This situation occurs because of the richness and the variety of heritage assets themselves as much as for the diversity of analysis methods required for their scientific documentations.

Totally Automated Co-Registration and Orientations

IBM is stated in the literature as a stable and reliable technique despite its relative uncertainty [START_REF] Remondino | Image-based 3D Modelling: A Review[END_REF]. As it remains an indirect measurement technique, the quality of the output is essentially related to the quality of the input data. In conventional applications the data processing is carried out by the same expert or institution, in charge of the adequacy and the control of data quality among the complete operative chain. The remote-computing and/or collaborative scenarios introduce a change of paradigm in that the data characteristics (i.e., size and/complexity, quality, acquisition strategy and purposes of the survey) are variable and mostly unknown. Moreover in CH applications sub-optimal circumstances in the acquisition stage are numerous: on-site conditions, bad lighting, object shape or material, lack of end-user experience. The occurrence of one or more of those elements proportionally increases complications in further processing stages. Therefore considering the unknown complexity of the input data it becomes harder to define a robust processing (i.e., minimizing bias, errors and failures) which requires to compromise between balance between versatility, velocity, accuracy and automation. Our approach is initialized with parameters prioritizing on the accuracy and progressively release constraints to gain in robustness against a sub-optimal condition. The counterpart is the potential increase of uncertainty-still better than a failure-and computational time (compensated with our computation server capacities).

Overview and Technical Description

The photogrammetric routine is composed of two main modules processing as follows: given I 0 the Initial set of images we want to find the set M 0 of point correspondences between overlapping images, the set of (intrinsic and extrinsic) calibrations C 0 , and the set D 0 of dense 3D points in the scene. For the Incremental processing, with I n the new set of images, we compute point correspondences M n between images in I 0 ∪ . . . ∪ I n , and then new calibrations C n . Considering this routine as a linear succession of I/O processes TACO introduces loops in the decisive steps and tries to resolve errors by incrementing some key parameters. The first node operates a robust Initial reconstruction described in Section 2.2 and Iter. 0 of Figure 2 with the ability to handle in one shot massive and complex image sets (including multiple sensors, focal). The second module allows a versatile Incremental co-registration to merge new image sets with previous iterations. The latter is divided into sub-modules deriving to different methods implemented and detailed in Section 2.3 and Iter. n of Figure 2. Optional modules are articulated to manage additional features like: absolute orientation based on coded-targets, interface to AIOLI or interoperable layers. TACO functions can be combined to build a fully automated pipeline suitable for remote-computing scenario. However modules and sub-modules can also be parameterized and used separately. As an example, options have been implemented to skip sub-steps of a process (e.g., avoid to recompute 2D image matching or disable 3D dense matching) so as to improve interactive uses. This modulative conception offers the flexibility to handle variable multimodal dataset requirements, as the framework dedicated to RTI fusion presented in a previous work [START_REF] Pamart | A complete framework operating Spatially-Oriented RTI in a 3D/2D Cultural Heritage documentation and analysis tool[END_REF].

The main dependence used as the core engine for photogrammetric reconstruction rely on MicMac, developed mainly at IGN since 2003 [START_REF] Rupnik | MicMac-A free, open-source solution for photogrammetry[END_REF]. Also known as the Pastis-Apero-Micmac toolchain it has the benefit of having been evaluated in a metrological context [START_REF] Toschi | On the evaluation of photogrammetric methods for dense 3D surface reconstruction in a metrological context[END_REF] contrary to FLOSS alternatives. However like all solution it suffers from bottlenecks such as latencies in 2D matching (Pastis) or the lack of parallelized bundle adjustment (Apero). Lately, interesting performances in features extraction and matching steps have been achieved (see Figures 9 and10) with OpenMVG [START_REF] Moulon | Open multiple view geometry[END_REF]. At short term, TACO aims to combine those two packages efficiently before looking forward the integration of new libraries in close future (COLMAP, THEIA, AliceVision). Our on-going developments on interoperable features between OpenMVG and TACO are discussed in Section 3.1. TACO has been coded in a generic iterative/recursive script running through a Python program to call commands available in IBM packages. An example of complete pipeline combining Initial and Incremental processes is structured as follows: (i) Culbuto is the module for automatic scaling and georeferencing (see Figures 3 and4

A Robust and Automated Initial Reconstruction for Complex Data Sets

The goal of this Initial process is to enhance the robustness, i.e., the ratio of successful computation, notwithstanding the type, the size, the complexity and the quality of the image set given in input. The Initial module passes through typical routine: 2D image matching from features extraction, internal self-calibration to relative orientation and absolute orientation until the sparse and dense cloud reconstruction. Beforehand, image meta-data are checked essentially to avoid missing EXIF (e.g., focal length) error or bias (e.g., image autorotation). A synthetic log is provided containing all meaningful camera settings for photogrammetry purposes (e.g., ISO, aperture, white balance etc). This approach is intended to guide the (re)processing strategy by EXIF grouping. Later on, it will facilitate the management, navigation and retrieval large oriented image-sets within AIOLI 2D/3D viewer (see Appendix A). Finally, this metadata aware process is requirement to strengthen the informative continuum in respect to data provenance scheme (semantic enrichment, CIDOC CRM etc.)

In (i), a module called Culbuto searches for 2D/3D coordinates files or tries to detect it from coded-targets within the images to compute absolute orientation in (iii). A first approach, is based on single QR-Code detection which embeds a metric dimension and where axes are derived from code corners (as supposed planar). It allows to approximate consistent scaling and orientation according to a user-defined coordinates system. This uncomplicated approach can be improved by using QR-code triplet as shown in Figure 3 devised for bigger object or scene. This method similar as using calibrated photogrammetric scale-bars still suffers from a lack of versatility and scalability for complex and/or large scale acquisitions. Lately, a second approach has been experimented to integrate free-from GCP's networks; by providing conventional space and images files coordinates, or in an automated way by coupling them with coded-targets sequential detection. With this method, the indexes contained in the targets are matched with 3D measurements (acquired by telemetric method, laser scanner similarly to total station). Interesting experiences using CCTag [START_REF] Calvet | Detection and accurate localization of circular fiducials under highly challenging conditions[END_REF] and AprilTag [START_REF] Wang | AprilTag 2: Efficient and robust fiducial detection[END_REF] have been lead to wield TACO in advanced multimodal data fusion scenario, see Figure 4.

In (ii), an iterative multi-resolution 2D features extraction and matching approach has been implemented to find an optimum budget of key-points aiming to optimize further internal and external calibration steps. Based on the MicMac tool Tapioca, it is starting with a low pass intended to speed-up the computation and the sub-sampling is recursively increased to medium and high passes (respectively half and three quarters of the full size) until camera poses are determined successfully. As shown in Table 1, the average Reprojection Error (RE) is usually around 1 pixel. Optionally, some advanced options enable to modulate the image matching ratio [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF], to enhance local features [START_REF] Rosu | Coastal digital surface model on low contrast images[END_REF] in order to cope rebellious cases (e.g., texture less or low-overlapping). Exploiting this strategy called Manioc, TACO helps to converge to a successful bundle solution in the next calibration steps.

In (iii), the relative orientation is achieved by a combined use of MicMac tools to compute the initial value of orientation (Martini) and refine internal parameters and global orientation (Tapas) for each camera. Those tools are respectively using triplets with Tomasi-Kanabe method while the other solves a more conventional Bundle Block Adjustment with the Levenberg-Marquardt method. The main difference is that Tapas is mandatory as the only one computing internal self-calibration. TACO's contribution is to alternate logically between those complementary tools until the condition of global orientation of all pictures is satisfied. In case of failure the calibration model is progressively decreased (i.e., from Fraser Basic to Radial Basic), else a return to remaining image matching strategies is attempted. By the mean of this processing methodology, called AntiPasti, the chance to return a reliable (minimized residue) and consistent solution for cameras calibrations have significantly increased.

Finally in (iv) a 3D dense matching algorithm computes a dense point cloud. It is performed by the core algorithm of MicMac, but TACO gives access to all Per Image Matching automated tool to adapt strategies and density parameters (using a pyramidal approach). The gain of using TACO is related to the improvement mentioned which affect positively on the uncertainty of the reconstruction. The possibilities to use other algorithms will depends on interoperable bridges discussed below in Section 3.1.

Therefore, this first iteration of the pipeline constructs a stable and reliable initial geometric reference (see Table 1) pending for new images to be added during the next iterations. This dataset is serving as base for the following co-registration thus it is assumed to be controlled and complete as defining a master acquisition. It means that the camera positions and resulting point cloud are (at this stage of development) frozen (initially because of AIOLI requirement detailed in Appendix A). Nevertheless a more flexible methodology to release and or freeze constraints on camera calibration subsets is planned for future works. Indeed this global refinement strategy involved correlated metrics and has to be conducted jointly to the qualitative assessment of 3D dense reconstruction in multiple sources context. (*) refers to unillustrated dataset for copyright reasons but their names reveal their typologies.

A Versatile and Incremental Spatial Registration of New Images from Oriented Image Set

The collaborative and multidisciplinary framework of AIOLI platform detailed in Appendix A, has originally set the incremental registration of images as a priority. Furthermore, the specificity of CH studies requires to face the challenging variety of multimodal scenarios. The main difficulty to deal with, is the unknown overlapping ratio between iterations while images might have an high deviation in spatial or pixel resolution, radiometric consistency and changes within the scene or the object itself.

Just as for the Initial reconstruction, the enhancement of features extraction and matching approaches (i.e., strategy and resolution) in (v) has revealed as an essential steps to succeed the co-registration. In the case of single picture, a matching based on heuristic approach is trivial and time-consuming especially if the dataset exceeds hundred of images [START_REF] Hartmann | Recent developments in large-scale tie-point matching[END_REF]. In this context, our solution in consist of finding correspondences in a very low resolution to detect adjacent pictures to use as best-matches. In case of a new block of pictures, they are matched together before being matched with all or a subset of images from previous iterations. The Manioc strategy is repeated with the difference that the incremental sub-sampling benefit from past matches and a best-neighbours selection is used to speed-up computation. A lot of feature-based optimizations can be achieved at this stage. So far, some key-points filtering approaches have been experimented upon the findings of recent works [START_REF] Farella | Sparse point cloud filtering based on covariance features[END_REF].

For the spatial registration in (vi), two alternative methods are integrated as sub-modules. They are both initialized from the results of the previous iterations (i.e., key-points, internal and external calibration or the dense point cloud). As formerly explained, the previous camera poses and corresponding geometries remain fixed for the ease development, but a more flexible global refinement module is planned. A first Bundle Block Adjustment (BBA) based approach is dedicated if a regular photogrammetric dataset-understood a sequence of overlapping images-is given in input. However according to the differences in the resolution (image size, focal length or distance to the object), radiometry (exposure, spectral band, illumination) or context (parasites, alterations) BBA could converge to sub-optimal, biased or erratic solution because of a lack of key-points (usually below 1000 matched features). In this case, a surrogated approach is based on a Spatial Resection approach [START_REF] Shih | A solution for space resection in closed form[END_REF] to calculate a single camera pose (or several processed sequentially), which also has the benefit of being robust to missing meta-data (non-photographic sensor, archive, analog photography). This alternative is based on 11 parameters Direct Linear Transformation (DLT) combined with RANSAC filtering (for outliers removal) to estimate both internal and external calibrations among a known set of camera poses. As no Ground Control Points are available, we use the key-points as 2D coordinates and their projection onto the depth-maps to retrieve corresponding 3D coordinates. This SR method can return an approximative solution, but enables to find a homographic relation with only tens of matching points when BBA is impossible.

For BBA and SR approach as well, the global accuracy and correctness is not related only to the number of key-points used for poses estimation but also in their redundancy and spatial distribution [START_REF] Farella | Sparse point cloud filtering based on covariance features[END_REF]. As a result, lower is key-points abundance and multiplicity, higher will be the uncertainty of the calibration and orientation computed with SR. Anyhow with both methods a result can converge to a false or odd solving for which some refinement methods will be investigate. For troubleshooting or optimization purposes different leads conduct to the incremental bundle adjustment of OpenMVG [START_REF] Moulon | Open multiple view geometry[END_REF][START_REF] Stathopoulou | Open-Source Image-Based 3d Reconstruction Pipelines: Review, Comparison and Evaluation[END_REF], the transition to an up-to-date perspective-three-point solver [START_REF] Larsson | Making minimal solvers for absolute pose estimation compact and robust[END_REF][START_REF] Ke | An efficient algebraic solution to the perspective-three-point problem[END_REF][START_REF] Persson | Lambda Twist: An Accurate Fast Robust Perspective Three Point (P3P) Solver[END_REF] or trying to refine registration with 2D/3D Mutual-Information [START_REF] Palma | Improving 2D-3D Registration by Mutual Information using Gradient Maps[END_REF].

Despite some possible improvements, current results (see Table 2) seem promising in regard of forthcoming evolution of TACO to endorse its aptitude to process complex multimodal CH imaging data sets. Overall results in term of quality, relative accuracy and versatility are discussed and illustrated in the next section.

Results and Discussions

Instead of using synthetic data, close to a hundred of datasets from MAP laboratory archives have been reprocessed to test the robustness and the versatility of TACO. This benchmark was composed of variated projects; from 5 up to 300 images, acquired different sensor sizes and resolutions (from smart-phones to full-frame DSLR) with a wide range of focal length (from 12 mm to 105 mm). TACO successfully completed 99% of those image sets made up of various qualities, scales, complexities and objects reflecting the reality of CH application. The main condition of success is the respect of basic rules of image capture. Since it has been integrated to the latest release of AIOLI, beta-testers feedbacks globally noticed less failing process or issues related to photogrammetric stages. An extract of pre-selected CH object typologies from this massive benchmark is given in Table 1 for the initial iteration. The results of incremental processing, depicting the following multimodal scenarios, are given in Table 2:

•

The Arbre-Serpents dataset (Figure 5) demonstrates the versatility to manage complex UAV-based data-acquisition.

•

The SA13 dataset (Figure 6) proves the ability to handle varied multi-focal acquisition.

•

The Vasarely dataset (Figure 7) highlight the capacity to deal with multi-scalar acquisition (14× GSD magnification).

•

The Old-Charity dataset (Figure 8) illustrate the velocity (40s of computing) to register an isolated picture on large image-set.

•

The Saint-Trophisme dataset (Figure A2) shows the robustness to integrate multi-temporal images including web-archive. The benchmark we present here have been processed using the computation server devised for AIOLI (Dell Power Edge R940, with a Intel Xeon CPU for a total of 144 cores of 3.0 GHz, 256 GB of RAM and 4 TB SSD storage). A virtual environment with Docker container [START_REF] Merkel | Lightweight Linux Containers for Consistent Development and Deployment[END_REF] is used to run processes on the server. Therefore, computational times given (in Table 1) may vary in case of server load or using a local workstation. The metrics for evaluating our benchmarking were the numbers oriented images and their theoretical precision in positioning which is assessed by an encouraging RMS reprojection error around 1 pixel. The necessary quality check and robustness evaluation will be verified in a further works by integrating a ground truth data comparisons to assess TACO performances.

Toward the Interoperability Challenge

In spite of fully automated pipeline advantage, this solution isn't exempt from drawback. Consequently we tried to compensate the lack of interaction in both Initial (see Section 2.2) and Incremental (see Section 2.3) modes by the possibility to modify somehow the linearity of the algorithm (modules, submodules, skip/break point or different tweak and options) to expand its potential. This modular architecture of TACO was also in anticipation of our future work in terms of interoperability.

Data and information exchange in IBM is a great and open challenge arising. Currently the several conventions coexist in the SfM and photogrammetric softwares while reliable exchange file formats remain restricted. Therefore the definition of interoperable functions is a key notion to improve any IBM operative chain in term of velocity, robustness and relative accuracy by exploiting the best features of distinct solutions to reach an optimum result. It can be used to seize the opportunity to bridge photogrammetric community and SfM approach, and inversely. Nowadays there is no straightforward solution to combine a fast and robust initial poses estimation on a massive and unstructured image set globally refined with a precise compensation on GCP's with demanding internal calibration model. Finally, improving interoperative dialogue between key processes is also a leverage toward open-data and open-science as it can offers a viable and accessible alternative to commercial solutions but also creating a reciprocal data flows from FLOSS or to FLOSS reprocessing. Recently, attempts have been made to interlink TACO with Agisoft Metashape for complementary purposes rather than comparative reasons. Our work in progress focusing on the interoperability between algorithms, libraries and commercial software solutions revealed the importance to solve numerous exchange and conversion issues enumerated below:

•

A reversible tie-points format between single and multi-image observations.

•

A lossless intrinsic calibration model according to variable intrinsic parameters conventions.

•

A generic format for external calibration preserving uncertainty metrics.

•

A human/machine understandable format to manage 2D/3D coordinates of GCPs.

•

An enriched pointcloud format to compare and evaluate multi-source dense matching results.

For this purpose, two additional datasets are given as an example of the upcoming data conversion features offered by TACO. Those figures illustrate the benefit of a co-processing shared between OpenMVG and MicMac. The experimented pipeline (currently under development and implementation within TACO) uses OpenMVG until coarse initial orientation then data are converted and transferred to MicMac which performs a global refinement of intrinsic and extrinsic parameters and compute a dense cloud.

•

On Nettuno dataset (Figure 9) the interoperable process solved critical 2D matching issue between very low overlapping terrestrial and UAV acquisition.

•

On Lys model dataset (Figure 10) through the interoperable process a complex dataset composed of 841 was oriented with a single automated iteration.

The first example of Nettuno shows the limits of an approach based on a single solution. For this dataset, the MicMac-based attempts were failing among several iterations and optimisation trials while switching to OpenMVG unlock the situation. On the second example Lys model OpenMVG strongly speeded-up processing time while helping MicMac to reach trustworthy reprojection error (see avg. RE in Table 2) with a better camera model (Fraser Basic instead of Radial Basic). Therefore, the dense point cloud obtained was less noisy than the one processed straight from OpenMVG. Ideally, interoperability aim to achieve seamless conversion between all sub-processes to enrich and optimize operational chain leading upward to the highest output quality. Operating from open-source solutions and compatible with remote-computing scenarios, the first results seem promising because only two automated steps allow to calculate a first 3D reconstruction on large and or complex data sets intended to be enriched by incremental registration of other imaging resources.

Conclusions and Perspectives

The processing methodology implemented and deployable through TACO offers a significative gain of robustness and versatility from FLOSS photogrammetric automated routines. The Inital module has proved interesting results to handle variated data sets in terms of size and complexity. The complementarity of BBA+SR approaches of the Incremental nodes provide an efficient co-registration framework consequently offering a great support to multi-modal CH imaging applications (including simultaneous multi-scale, multi-sensor, multi-temporal or multi-spectral management).

Initially developed as generic solution dedicated to remote-computing purposes, TACO shows interesting flexibility and scalability toward mixed modalities. The main successful condition still remains the photogrammetric correspondences and consistency (i.e., spatial and resolution gaps, spectral or radiometric deviations, temporal or contextual variations) in between the initial set and further the incremental ones. The recent works on absolute orientation and the interoperable functions offer new perspectives. Different side-projects of TACO would focus on extended spatial 2D/3D registration methods by creating a possible link with other modeling techniques (range-based, primitive-based etc).

Nonetheless, new challenging issues arose from the current achievements and will require a special care to add new features and optimize existing ones. On one hand, the added value in term of versatility, robustness and interoperability appears promising to build and enrich a digital twin by gathering variated image sources. On the other hand, the transition to a consistent object/space coordinate system will enable metric evaluation with other data flows. However reconstructing a 3D model from multiple sources necessitates a qualitative evaluation system to consolidate persistently their respective geometries (various density, quality, uncertainty, temporal stage). Indeed, it would be counterproductive to co-register indefinitely cameras and geometries without considering their positive or negative impact on merged outputs. Consequently, the registration of several geometries coming from different sources also increase the complexity of analysis while it shall instead be able to guide our interpretative process (i.e., by associating a data source or a modality to the observations it allows). Exploiting TACO to this end could provide an effective support toward data fusion (with a noticeable added value linking geometric features to their semantic attributes).

A new layer might have to be integrated in or on top of the proposed methodology to keep a trace of the processing steps while extracting indexes and metric useful to evaluate informative and geometric gains (or loss) of incremental and multimodal data fusion. Our latest experiments explored filtering approaches to reduce the redundancy of aggregated data to optimize and increase at the same time the interpretative value of long term incremental scenarios. In the meantime, advancements in CH-oriented approaches in un/supervised machine learning might provide interesting lead for classification [START_REF] Aceto | Mobile encrypted traffic classification using multimodal deep learning[END_REF] and segmentation purposes upstream [START_REF] Anzid | Multimodal Images Classification using Dense SURF, Spectral Information and Support Vector Machine[END_REF] or downstream [START_REF] Belhi | Leveraging known data for missing label prediction in cultural heritage context[END_REF] TACO.

As a conclusion, if we anticipate the ongoing transition from accumulated one-shot applications toward a systemic approach of CH imaging, one might prevent the complexification of digital content management. In this scenario, the main challenge for the construction and the synchronism of CH-oriented digital twins will be our capacity to maintain methods and tools, enabling to manage and convey over-time, the growing richness of CH documentation.

Cooperative Development between TACO and AIOLI

Once logged into AIOLI platform, users access a workspace to create a project (with public, shared or private visibility) linked to an Heritage Asset. The user is invited to upload an image set to obtain an initial photogrammetric reconstruction, powered by the fully automated TACO's workflow illustrated in Figure 2. The Initial process detailed in Section 2.2 aims to solve the self-optimization of the processing strategy from unknown inputs so as to increase the robustness and the relative accuracy expected to enable and support the semantic enrichment. This core feature of AIOLI is performed the semi-automatic 2D/3D annotation framework and the geometric analysis tools described in [START_REF] Manuel | 2D/3D semantic annotation of spatialized images for the documentation and analysis of cultural heritage[END_REF][START_REF] Manuel | A semi-automatic 2D/3D annotation framework for the geometric analysis of heritage artefacts[END_REF]. However, image-based documentation is no longer a linear workflow, nor one shot application, neither a punctual work done by a single end-user, with the same equipment, experience and purposes. The TACO Incremental processing modules detailed in Section 2.3 aim to support the collaborative documentation of CH objects implied by the growing complexity of multimodal scenarios currently performed in CH domain. Therefore the possibility to add and merge new image-sets through several iterations is simultaneously implemented within AIOLI and TACO in a cooperative framework. However initial cameras and geometry are not refined else all the annotations and their attributes must be recomputed. A new feature like the automated scaling and orientation based on coded-target detections was also initiated from the need to compute consistent coordinate system of AIOLI scenes (i.e images, annotations and descriptors). An other feature specially developed within TACO for AIOLI purposes is internet archive registration shown in Figure 6. Finally, the ongoing works on interoperability aim to create AIOLI's import/export functions for expanding its accessibility and the potentialities of collaborative annotations from and to other solutions.

Figure 1 .

 1 Figure 1.Diagram synthesizing CH oriented multimodal IBM workflows; conventional "one-shot" application (i), current state (ii) and issues (iii) and targeted approach (iv) using TACO.

Figure 2 .

 2 Figure 2. Diagram showing the example of the fully automated TACO-based pipeline within AIOLI.

  ): it takes initial image set I 0 and outputs scaled image correspondences M S . (ii) Manioc is an automatic sub-sampling parametrization for 2D matching: it takes I 0 , and s max the largest dimension of the images in I 0 , subsampled at scale s ∈ {1000px . . . s max }, and outputs image correspondences M 0 . (iii) Antipasti is an adaptative self-calibration method: it takes M 0 , M S and outputs external and internal calibrations C 0 . (iv) The fully automatic Per Image Matching tools produces the dense cloud D 0 from I 0 , M 0 , C 0 . (v) During incremental registration, Manioc takes I 0 , I n new image set and and produces M n (correspondences with all image sets). It also gives the closest neighbours of I n : N n ⊂ I 0 . . . I n-1 . (vi) Finally, a robust and versatile incremental co-registration is performed given C n-1 , M n , N n , TACO computes C n , in the same spatial system as C 0 , either by Bundle Block Adjustment or Spatial Resection.

Figure 3 .

 3 Figure 3. Owl dataset : example of QR-code triplet based global orientation and scaling.

Figure 4 .

 4 Figure 4. Example of automated scaling and orientation of wood painting base on experimental double sided coded-targets fusion.

Figure 5 .

 5 Figure 5. Arbre-Serpents dataset : fusion result of two UAV-based blocks of acquisition (before and after restoration).

Figure 6 .

 6 Figure 6. SA13 dataset : example of complex multi-focal processing (each color represents a new iteration).

Figure 7 .

 7 Figure 7. Vasarely dataset : data fusion with high scaling deviation (Initial iteration in green and Incremental set in blue.

Figure 8 .

 8 Figure 8. Old-Charity dataset : isolated single picture registration using Spatial Resection.

Figure 9 .

 9 Figure 9. Nettuno dataset : successful interoperable OpenMVG+MicMac process on low overlapping UAV and terrestrial.

Figure 10 .

 10 Figure 10. Lys model dataset : current "best-score" of TACO fully automated process on single iteration.The aim of the proposed methodology is to contribute to photogrammetric-based documentation and analysis of CH objet providing a user-friendly tool (easily accessible through all-in-one command).

Figure A2 .

 A2 Figure A2. Saint-Trophisme dataset : spatial-Resection of a web-based archives.

Table 1 .

 1 Composition and results of initial data sets extracted from the global benchmarking.

	Dataset	Initial nb. of Images	Computational Sparse Cloud Dense Cloud Initial Avg. RE Time (k)Points (M)Points in (px)
	SA13	8	2 min	102	2.35	1.08
	Fragment *	21	4 min	60	1.34	0.47
	Saint-Trophisme	26	7 min	94	3.13	0.54
	Owl	40	7 min	108	2.68	0.93
	Vasarely	65	7 min	127	1.76	0.74
	Excavation site *	95	43 min	641	1.34	0.49
	Small temple *	134	120 min	1850	4.04	0.74
	Old-charity	181	170 min	224	1.14	0.73
	Arbre-serpents	273	390 min	1468	5.62	1.26
	Nettuno	256	Nc.	2806	9.87	0.43
	Lys model	841	Nc.	20,989	44.4	0.66

Table 2 .

 2 Details of multimodal dataset enrichment and results of incremental processing.

	Dataset	Added Number of Number of Images Iterations Sensors	Number of Focal Length	Final Avg. RE in(px)
	SA13	+107	12	1	6	1.54
	Saint-Trophisme	+4	4	4	4	0.6 *
	Vasarely	+6	3	1	2	0.80
	Old-charity	+1	1	1	1	1.12 *
	Arbre-serpents	+259	3	1	1	1.65
	Nettuno	Na	1	2	2	0.59
	Lys model	Na	1	2	3	1.21

(*) refers to values including images oriented with Spatial Resection.

Funding: This research was partially funded supported by the ANR SUMUM project, grant Référence ANR-17-CE38-0004 of the French Agence Nationale de la Recherche.

Acknowledgments:

The authors would like to acknowledge the stakeholders of the case-studies illustrating this paper, respectively the Vasarely and Arbre-serpents data sets correspond to the Zett painting of Victor Vasarely from the Fondation Vasarely d'Aix-en-Provence and the sculpture of Niki de Saint Phalle from the Musée des Beaux-arts d'Angers. The authors would also like to acknowledge their colleagues of FBK-3DOM in Trento and MAP-ARIA from Lyon for sharing respectively their data sets Nettuno and Lys model used and illustrated in this publication. A special acknowledgment to Éloi Gattet, president of the Mercurio start-up behind the idea and the draft of Culbuto module handling the QR code-based automatic scaling.

Data sets presented in this paper are available and shareable on request, in case there is no conflict with the right-holders of the artworks

Author Contributions: Conceptualization, A.P. and F.M.; methodology, A.P. ; software, F.M.; formal analysis, A.P. and F.M. ; writing-original draft preparation, A.P.; writing-review and editing, A.P., F.M., L.d.L. and P.V.; visualization, A.P. ; supervision, L.d.L. and P.V. All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest:

The authors declare no conflict of interest.

Appendix A. AIOLI

AIOLI is a reality-based 3D annotation platform designed for a multidisciplinary CH community to construct semantically enriched descriptions of heritage assets from photogrammetric reconstruction and spatial labelling. This platform aims to impulse an innovative framework for the massive and large-scale collaborative CH documentation by linking features like Image-based modeling, 2D-3D spreading and correlation of semantic annotations, multi-layered analysis of qualitative and quantitative attributes. The service is deployed through a cloud-like infrastructure to make processing, visualization and annotation processes simply accessible via multi-device responsive web interfaces (PCs, tablets and smartphones) on-line and on-site. For more information on updates or to join beta-testing program, visit the website (http:www.aioli.cloud/).