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• Methodology for a complete geometrical analysis of the vaults of Notre-Dame de Paris after the fire. • 2D image-based method for comparison before and after the fire. • 3D point cloud-based method for comparison before and after the fire. • New method for accurate alignment of very large point clouds. The work presented in this article was carried out following the fire (April 15, 2019) that ravaged Notre-Dame de Paris. The goal was to establish in a short and limited time-span the structural diagnosis of the remaining vaults of the cathedral. The analysis relied on 2D and 3D data acquired before and after the fire, and available at that time. Two complementary methods have been developed to estimate potential displacements from multi-temporal surveys. The first method is mainly based on the processing of image collections obtained with photogrammetric routines right after the fire. The second method, based on the processing of raw 3D data acquired with Terrestrial Laser Scanning, was developed afterward to refine and complete the analysis. Both methods have benefited from essential functionalities offered by two open-source solutions proven to enable "real-based" modeling in Cultural Heritage contexts, namely Micmac and CloudCompare. This paper presents the complementary use of these two software packages whilst detailing some procedural computing approaches to document and support structural diagnosis in an emergency situation. The limits and capabilities of each method are exposed and analyzed, toward the objective to develop 2.5D and 3D based geometrical analysis, respectively from photogrammetric and lasergrammetric sources. The results are presented and discussed regarding their potential usage for a quantitative and accurate diagnosis of vaults. [ABSTRACT FROM AUTHOR]

[Display omitted] Three-dimensional data have become increasingly present in earth observation over the last decades. However, many 3D surveys are still underexploited due to the lack of accessible and explainable automatic classification methods, for example, new topo-bathymetric lidar data. In this work, we introduce explainable machine learning for 3D data classification using Multiple Attributes, Scales, and Clouds under 3DMASC, a new workflow. This workflow introduces multi-cloud classification through dual-cloud features, encrypting local spectral and geometrical ratios and differences. 3DMASC uses classical multi-scale descriptors adapted to all types of 3D point clouds and new ones based on their spatial variations. In this paper, we present the performances of 3DMASC for multi-class classification of topo-bathymetric lidar data in coastal and fluvial environments. We show how multivariate and embedded feature selection allows the building of optimized predictor sets of reduced complexity, and we identify features particularly relevant for coastal and riverine scene descriptions. Our results show the importance of dual-cloud features, lidar return-based attributes averaged over specific scales, and of statistics of dimensionality-based and spectral features. Additionally, they indicate that small to medium spherical neighbourhood diameters (<7 m) are sufficient to build effective classifiers, namely when combined with distance-to-ground or distance-to-water-surface features. Without using optional RGB information, and with a maximum of 37 descriptors, we obtain classification accuracies between 91 % for complex multi-class tasks and 98 % for lower-level processing using models trained on less than 2000 samples per class. Comparisons with classical point cloud classification methods show that 3DMASC features have a significantly improved descriptive power. Our contributions are made available through a plugin in the CloudCompare software, allowing non-specialist users to create classifiers for any type of 3D data characterized by 1 or 2 point clouds (airborne or terrestrial lidar, structure from motion), and two labelled topo-bathymetric lidar datasets, available on https://opentopography.org/. [ABSTRACT FROM AUTHOR]