dataesr/scientific-paragraphs-categorization huggingface dataset:
Those participants who had 15% or more missing answers and did not fit the sample criteria (non-luxury buyers) were excluded from the dataset, leaving a usable sample of 1056 participants. We split the sample randomly (50:50) to form calibration and validation samples (  Diamantopoulos & Siguaw, 2000) , then we excluded any non-fashion luxury brands from both samples. In total, this left 390 responses in the calibration sample and 388 in the validation sample. We applied Exploratory Factor Analysis (EFA) (Study 2) to the calibration sample and Confirmatory Factor Analysis (CFA) (Study 3) to the validation sample, as well as another validation sample for structural model assessment with an additional 388 participants (Study 4). Table  2  presents the profile of the calibration sample (Study 2).
XFY/TEY mode XANES spectroscopy at Cr K-edge Cr K-edge XANES investigations of paint mock-ups were performed at the beamline BM08-LISA  [36]  and at the scanning X-ray microscope end station of beamline ID21 of the European Synchrotron Radiation Facility (ESRF, Grenoble, France)  [37, 38]. Measurements were carried out under 0. 5 atm He atmosphere with a Si(3 1 1) crystal at BM08-LISA and under vacuum using a Si(2 2 0) fixed exit double-crystal monochromator at ID21. At BM08-LISA, data were collected using an average beam size of ~70 × 100 µm 2 (h × v) and a fluence rate of ~10 4 ph/(s⋅μm 2 ). An appropriate sample holder  [39] , equipped with a collecting anode polarized at ~20 V and placed at about 10 mm from the sample, allowed performing simultaneously XANES measurements in two different detection modes: (i) TEY and (ii) XFY.
9892 keV. For normalization purposes, a photodiode upstream the sample was constantly monitoring the beam intensity. µ-XRF mapping was performed via raster scanning of the samples with 40 ms/pixel dwell time and using a 80 mm 2 collimated active area silicon drift diode detector (Xflash 5100, Bruker). Cr oxidation state maps acquired from K 2 CrO 4 mock-up were extracted by means of the PyMca software  [42] , after setting the energy of the incident X-ray beam at two energies: (i) at 5. 993 keV, for promoting the excitation of Cr VI -species, and (ii) at 6. 090 keV for collecting XRF signals of all Cr-species. Details about the procedure employed to extract the Cr oxidation state maps are described elsewhere  [43]. The ATHENA software package  [44]  was employed for the normalization and for the linear combination fitting (LCF) of the BM08-LISA and ID21 XANES spectra against a library of spectral profiles of Cr-reference powders.
Fig. 5 ) was obtained using the JGIXA software package  [46]. The sampling depth of the photoelectrons (predominantly originated by cascades of the Cr KLL Auger electrons at 4. 8 keV  [47] ) was estimated by following the procedure earlier reported in the literature  [21]. By following what we described in a previous study  [32] , a series of X-ray-induced damage tests at variable fluence conditions were performed on paint mock-ups both at BM08-LISA and ID21 to ensure that any Cr reduction process was not significantly impacting results.
Results To explore the capabilities of Cr K-edge TEY-XANES spectroscopy in performing selective surface Cr speciation investigations, we started with the study of fragments of Cr 0. 2 Y and K 2 CrO 4 paint mock-ups at beamline BM08-LISA. In line with previous studies  [27] [28] [29] 43] , the photoaging treatment of Cr 0. 2 Y and the natural aging of K 2 CrO 4 promote a significant darkening of the paint surface (Figs. 1A-2A ). Cr K-edge XANES spectroscopy data collected at the same time in XFY and TEY detection modes from unaged-Cr 0. 2 Y and 0 days-K 2 CrO 4 paint mock-ups reveal that only Cr VI -compounds are present (Figs. 1B-2B red lines; only the XFY spectra are reported as example). This is highlighted by the intense pre-edge peak at 5. 993 keV, attributed to a dipole-forbidden transition from the Cr 1s orbital into orbitals with Cr 3d character (t 2 symmetry).
Acknowledgments The research was financially supported by the  Horizon 2020  projects  IPERION-CH  ( H2020-INFRAIA-2014-2015 , GA no. 654028 ) and  IPERION-HS  ( H2020-INFRAIA-2019-1 , GA no. 871034 ) as well as by the  Italian  project  AMIS  ( Dipartimenti di Eccellenza   2018-2022 , funded by  MUR and Perugia University). For the beamtime grants received, we thank  ESRF  for the measurements performed at beamline ID21 (experiments no. HG-64, HG-129 and in-house beamtimes) and the  CERIC-ERIC Research Infrastructure  (proposal id:  20207042 ) for those carried out at beamline BM08-LISA of ESRF. LISA is financed by the  Consiglio Nazionale delle Ricerche , project N • DFM. AD006. 072. FWO (Brussels ) projects  G054719N  and  I001919N  are also acknowledged for support.
Remerciements 43 Les auteurs tiennent à remercier  Jean-David Moreau  ( université de Bourgogne ), qui a contribué, dans une autre étude, à l'analyse paléontologique des silex de Moragne, et  Pierre Miramand  ( université de La Rochelle ) qui a participé aux prospections de surface. Ils remercient également Éléna Paillet et Stéphan Hinguant pour leur travail de révision.
In the field of digital cultural heritage (DCH), 2D/3D digitization strategies are becoming more and more complex. The emerging trend of multimodal imaging (i. e. , data acquisition campaigns aiming to put in cooperation multi-sensor, multi-scale, multi-band and/or multi-epochs concurrently) implies several challenges in term of data provenance, data fusion and data analysis. Making the assumption that the current usability of multi-source 3D models could be more meaningful than millions of aggregated points, this work explores a "reduce to understand" approach to increase the interpretative value of multimodal point clouds. Starting from several years of accumulated digitizations on a single use-case, we define a method based on density estimation to compute a Multimodal Enhancement Fusion Index (MEFI) revealing the intricate modality layers behind the 3D coordinates.
This leads us to the first issue of exponentiality as the data are multiplying in number, size and mass, excluding the wealth of uninterpreted data. More recently, the DCH field has seen a shift towards multimodal approaches, aiming to explore the cooperation of the data collected with different modalities (i. e. , time, scale, dimension, etc. ). Multimodal datasets encompass the diversity and complexity of the data accumulated from several experts using different sensors at different times in variable contexts. Indeed, this type of multi-source documentation represents the large majority of the works presented by the scientific community nowadays. This leads us to the second issue of intricacy, as it becomes more complex to access and extract meaningful information out of the latent and cross-relations between numerous datasets.
These leads are relevant and interesting for CH studies; however, this paper does not deal directly with this. Instead, we introduce a method one step prior (i. e. , before the potential semantic extraction/exploration), following the belief that the multimodal datasets contain meaningful information that could possibly guide semantically driven approaches. This idea emerged while trying to exploit a substantial data collection made from digital surveys on a single heritage object. Like many other heritage sites or objects across the world, a multidisciplinary scientific team worked on a small chapel from the 15th century, having known recurrent data acquisition campaigns for the past few years. Facing the inability to record, understand and efficiently link our gathered data, we have begun this work improving the analysis of our multimodal dataset using a computational method.
The core problem emerged from the evidence that, after the registration and data merging, amounted to nothing more than hundreds of millions of unstructured geometric coordinates belonging to attributes stacked into a 3D space. The informative and interpretative values of such a massive and complex 3D dataset is in this primal state, close to zero. Furthermore, even a powerful workstation would deliver a poor experience in terms of visualization and interaction with the model. The hypothesis motivating this work was that the accumulation of data and more importantly its deviation, carried important information about how the model was completed and what it is composed of. To this end, we envisioned to create an indicative heat-map to reveal where the model has more information and where it is lacking.
This was used in our case to focus on over-and under-documented areas in the digitized model. Additionally, it could serve as a method to guide the understanding and interpretation of complex and heterogeneous datasets. As MEFI is correlated with data fusion issues, some outcomes are discussed towards innovative computational or InfoViz methods contributing to multimodal fusion strategies in CH application. This section has introduced MEFI into a more generic scientific reasoning and motivation. A state-of-the-art method is proposed in Section 2, in which discussion and value of the method are articulated among related works. In Section 3, the Notre-Dame des-Fontaînes data collection is presented as a use case in the context of the study. The complete methodology is detailed in Section 4, where stepby-step explanations and the MEFI pseudocode of is provided.
). Therefore, a dataset is considered as multimodal if its source data are composed of various sensors, scales, spectra, collected at different times, or by numerous experts and with the resultant combination being greater (from an informative point of view) than the sum of its elements. Prosaically speaking, data fusion ideally follows the leitmotif 1+1=3. Accordingly, several works from CH literature discuss the combination of imaging techniques, either in their spectral  [7] , scalar  [8]  or temporal  [9]  aspects, and extent synchronic  [5]  or diachronic  [10]  approaches. The novel works show a trend that the majority of ongoing practices and projects are integrating or moving towards multimodal imaging, outlining a critical direction for future research. Nevertheless, as reported in  [11, 12] , current multimodal scenarios are often restricted to dual cross-modalities, and most of the time a technique is subordinated to the other.
In many works, if not all, photogrammetry has been used as a bridging technique  [5, 7, [12] [13] [14] [15]. In this work, we tried to extend the capacity to manage cooperating modalities, intentionally variable in number and type. In this end, the dataset used mixes no less than 28 sources obtained with five main imaging techniques (see Section 3). That being said, combining this many sources was challenging, particularly in terms of data fusion issues. As reported by a few works addressing data fusion in the CH field  [16, 17] , difficulties lie in the fact that the merging of data can interfere at almost any step of the workflow with different dimension-based approaches; 2D-2D, 2D-3D or 3D-3D (the last one being the most used). Generally, among many methods  [18] , data registration is achieved by best-fit approaches derived from iterative closest point (ICP) algorithms for purely 3D data else with mutual information  [19]  when dealing with 2D/3D approaches.
Interestingly, even from a quick literature review, one can make a list of phenomena that degrade data fusion, many of which are highly representative of CH-oriented multimodal datasets (lack of ground truth, imperfection, outliers, heterogeneity, conflictual data, dimensionality, registration error, redundancy, operational time, or processing framework). Downstream, by the disposal of measure of performance (MoP) tools to evaluate the supposed superiority of the output, as depicted in Figure  1. Similar to  [11] , it is noticed that performing data fusion is usually restricted to rigid and formatted data. Unfortunately, this is far from the reality concerning CH applications, where methods and tools are as rich and heterogeneous as the heritage objects. This may explain the gap between the CH domain and its related fields (e.
For the same reason, MEFI hasn't been tested on highly damaged sites, but this interesting lead should be investigated further in future works. Some methodological choices have been made to align the requirements of the method with the issues exposed in the previous sections. The exponentiality issue has motivated the definition of a new method instead of relying on pair-wise limited metrics (e. g. , C2C, and M3C2) while preserving the ability to handle large datasets (i. e. , Octree resampling, etc. )  [13, 47]. The intricacy issue defined the prerequisite for the method to simultaneously manage several multimodal layers (i. e. , epoch, resolution, scale and/or spectral dimensions). On the other hand, we focused on 3D-oriented examination to simplify the formalization and development of the method, but also limit, at the current stage, the scope of the techniques supported.
Of course, the registration uncertainty must be compatible with the target analysis level, in our case the RMS was estimated to be below 1 cm error for all the point sets (while the analysis level is set to 4 cm). As shown in the overview of the 3D dataset (see Figure  3 ), not all the data are spatially connected and interlinked; hence, the interest of the overlapping and co-registration mapping proposed in Figure  6a, b. The methodology developed to build the multimodal fusion index is composed of the following main components: • Semantisation: The semantic labelling of each point cloud source is obtained beforehand thanks to the extensive MEMoS-based description. For a given naming value, matching is made between the name of the point cloud and the appellation attribute stored in the WHAT section.
• Octree computation and sampling: The multi-dimensional aspect of the sources (i. e. , the scale and resolution) imply the need to unify the scale-space of the 3D datasets. The Octree is used as an underlying spatial grid, enabling multiple in-depth levels of detail. The sampling, based on a given Octree level, helps to discretize the point clouds to a comparable resolution while preserving the spatial coherence (e. g. , Octree grid).
• Visual enhancement: As the densities were highly variable, the distribution of the feature values could lead to some visualization issues. As MEFI is an indicative attribute, some transformations could be made on the scalar field to improve their interpretative value (e. g. , histogram equalization). This explains the bilateral smoothing applied in the last step to improve the distribution of values and decrease the impact of outliers and noise on the gradient. Once MEFI is computed, a colour map is created and fitted to the histogram. In the end a custom rainbow-based colour map is generated, but many others (diverging, wave, etc. ) could be used and adapted to better reveal the MEFI features. We chose to base the computation on the CloudCompare software  [48]  as it is an efficient, user-friendly and widely used tool in the CH community.
At the current stage of development, the process was made directly through the GUI, even though some steps are accessible with CLI. The automatization and generalization of the method, planned for future works (see Section 5. 2) and would be simplified by Python wrappers for Cloud-Compare (CloudCompy and the CloudCompare Python Plugin). The computational part is explained hereafter and detailed in pseudocode (see Algorithm A1 in Appendix A). Given a list of raw co-registered point clouds, the method returns a single point cloud subsampled according to a definite observation scale. The resulting point cloud is enriched with a scalar field called a Multimodal Enhancement Fusion Index (MEFI) derived from a single geometric features (density). The index is expressed for each point within a range between 0 and 255, associated with a histogram-fitted colour map  [49, 50].
At each level, the cell size is multiplied by two. Hence, for an mOS set to 0. 005 (e. g. , 5 mm) and equal to the minimum cell size, the respective sublevels are 0. 01, 0. 02, 0. 04, 0. 8, 0. 16 and so on. In this study, the level 18 equivalent to a 4 cm cell size has been defined as a suitable unit for the fOS. As mentioned in the software documentation, Octree is particularly suited for spatial indexing, to optimize comparison algorithms, and efficient extraction of nearest neighbours, all fundamental elements for the proposed method. Indeed, relying on Octree for MEFI provides many advantages as it ensures spatial consistency between all sources, allows multi-scale approaches and quicken density computation (based on nearest neighbours). In step two, for each point-cloud, data processing is initialized by a common Octree computation.
For visualization issues, the dataset was split corresponding to the inside and outside. The outdoor acquisitions consisted of only five point-sets with reduced overlap, making the MEFI less meaningful and interesting (see Figure  6 ). The main difficulty was found in the management of the density deviation in the point cloud that diverged in scale and resolution. As an indicator, the mean scaled density values varied between 229 for the less dense and 5340 for the most dense, with a standard deviation of 3861. Even though the MEFI acutely reveals where data are concentrated, it does not directly provide information about the modality present for each point. Thus, we used the original cloud index scalar field, computed during the fusion step, to match and retrieve information on the data sources stored in the MEMoS description.
Considering this, we wanted to develop a 3D web-viewer, due to the need for a dissemination solution allowing us to benefit from the MEFI as an additional texture without losing the initial colours of the point cloud, but also to experiment ways of combining 3D visualizations with local metadata/paradata visualizations. To do so, we used Potree. JS, a free open-source library offering a WebGL-based renderer for large point clouds  [59]. It is based on the prior generation of an Octree, performed using PotreeConverter 1. 7  [63]. From the input point cloud, PotreeConverter generates a binary file per node, as well as a JSON-formatted file specifying the properties of the point cloud, in particular its attributes. For the conversion, only the Euclidean coordinates of each point are required, but the software still supports some optional attributes (e.
From this point, we were able to implement new functions into the web-viewer to support these attributes and exploit them for visualization. The MEFI was mainly used in the shader, to create a new gradient texture (see Figure  11a ), which can, if necessary, be combined with others in a Potree composite texture. The MEFI numerical value corresponding to each point can be retrieved by the user with a point-picking tool. To query local metadata, we implemented a tool based on ray casting, allowing the real-time retrieval of all existing metadata and paradata concerning the hovered 3D point. Briefly, the principle is as follows: if we know the original cloud index value of a 3D point, then we can know which acquisition modality was used to generate it. It is then easy to query a JSON file containing the appropriate metadata, whether it is a local file or a document from an NoSQL database, to obtain the relevant information and display it directly in the viewer.
The computation itself could be improved by relying on the Octree method, this time not only for the representation, but to generate and/or modulate the index directly in the spatial grid instead of the point clouds. This resulted from the choice to operate the first experiment on the GUI version of CloudCompare. The next steps will aim to improve reproducibility by testing and adapting the MEFI on other use-cases. Meanwhile, automation and generalization of the method will benefit from Python bindings to exploit different packages (CloudCompPy, PyMeshLab, PCL, Open3D). In this way, the MEFI 2. 0 could, for example, gain in computational cost and efficiency with prior overlap estimation based on oriented bounding boxes  [65]  and subsequent robust IoU estimation  [66]. In addition, during the development, using more weights (e.
Conclusions In this work, we presented a computational method providing an MEFI to 3D point clouds. We have developed a methodology to synthesize into a single point cloud a complex dataset obtained through multimodal 3D surveys. Their main issue of sparse resolutions and accuracies has been tackled by an Octree spatial grouping approach. This method can improve our understanding and therefore the interpretation of multi-source 3D models for CH-oriented studies. From a list of overlapping and registered point clouds, the proposed method returns, with reasonable and efficient computational cost, a density-based fusion index directly stored in point cloud attributes, easily readable by any 3D viewers. Combined with data-fitted colour maps, it acts similarly to a 3D heatmap to reveal the spatial variation between sparse and isolated or dense and redundant data, unveiling the multimodal digitization strategy deployed on heritage sites or objects.
These first MEFI results show interesting aptitudes to managing multi-modal datasets, i. e. , with simultaneous spatiotemporal layers. Interestingly, it is also robust to multi-resolution and multi-scale data thanks to the support of Octree spatial gridding. In this work, we also presented a lead for the data integration of semantic layers based on a descriptive capture metadata schema and CIDOC-CRM compliant format MEMoS  [4] , consequently contributing to improving data provenance in CH multimodal practices. In order to demonstrate the potential added-value to data analysis and interpretative prospects, a customized Potree viewer was developed to enhance the quantitative MEFI 3D features with qualitative and semantically enriched attributes. In conclusion, we hope that this work will contribute to CH-oriented studies towards intermodality (i.
Data Availability Statement: All data used for this study, including soft data (metadata) and hard data (point clouds) are accessible and shared under the Etalab Open License 2. 0. Pamart, Anthony (2023) « MEFI-Enriched 3D Multimodal Dataset of Notre Dame des Fontaines Chapel » (Dataset) NAKALA. https://doi. org/10. 34847/nkl. b09eh54s (Last accessed: 2 May 2023).
Acknowledgments:The authors would like to acknowledge the stakeholders of the case studies presented in this study, namely, the tourism department of the city of La Brigue for access provided to the Notre-Dame des Fontaines chapel. In addition, the authors would like to acknowledge all experts involved in the data acquisition campaigns, especially the ones mentioned in the WHO section of the MEMoS metadata description (see Figures4 and 5) who contributed to the creation of this multimodal dataset. Conflicts of Interest:The authors declare no conflict of interest.
ACKNOWLEDGEMENTS We thank  Dr Rossella Bedini  of the  Istituto Superiore di Sanità in Rome (IT)  for acquiring the CT scans of the skull. We thank  Dr Tania Ruspandini  of the  Department of Scienze della Terra, Sapienza, University of Rome (IT ) and  Dr Marco Albano  at  CNR in Rome (IT ) for SEM acquisitions. We wish to thank the two anonymous reviewers and the Editor for their valuable comments and suggestions. Source of support: "Population biology, diseases and mobility: Romans and Longobards in the post-classical era", Grande Progetto Sapienza 2018,  RG118164364E4CB5 ;  HORIZON EUROPE Marie Sklodowska-Curie Actions, B-CARED Osteobiographical investigation of disability and care in Medieval Europe ,  101061838. This study does not involve any modern human or animal subject. Open Access Funding provided by  Universita degli Studi di Roma La Sapienza  within the  CRUI-CARE Agreement.