2025‌​‌Activity reportProject-TeamTITANE​​

7.1.1 Module CGAL:​​ Parallel 3D Mesh Generation​​​‌ (Mesh 3)

• Keyword:
  3D‌
• Functional Description:
  Parallel generation‌​‌ of multi‑volume 3D meshes​​ from 3D images, or​​​‌ from a polyhedral or‌ implicit description of the‌​‌ boundaries.
• Contact:
  Pierre Alliez​​
• Participants:
  Clément Jamin, Mariette​​​‌ Yvinec

7.1.2 Generic tools‌ for presence detection on‌​‌ a mesh with CGAL​​

• Keywords:
  3D, Algorithm, C++,​​​‌ CGAL, Mesh, Mesh refinement,‌ Python, Point cloud, Anomaly‌​‌ detection
• Functional Description:
  A​​ set of generic tools​​​‌ for mesh pre-processing (conversion,‌ subdivision, ray tracing, reverse‌​‌ ray tracing), mesh face​​ detection (point-to-face association), and​​​‌ more general evaluation tasks‌ (classification, clustering, coloring) of‌​‌ a mesh with respect​​ to a point cloud​​​‌ registered onto it.
• Contact:‌
  Marie Aspro
• Participants:
  Marie‌​‌ Aspro, Erwan Amraoui, Pierre​​ Alliez, Ezio Malis

8.1.1 The P3 dataset:‌​‌ Pixels, Points and Polygons​​ for Multimodal Building Vectorization​​​‌

Participants: Raphael Sulzer,‌ Florent Lafarge, Liuyun‌​‌ Duan [Luxcarta Technology],​​ Nicolas Girard [Luxcarta Technology]​​​‌.

We present the‌ P3 dataset, a large-scale‌​‌ multimodal benchmark for building​​ vectorization, constructed from aerial​​​‌ LiDAR point clouds, high-resolution‌ aerial imagery, and vectorized‌​‌ 2D building outlines, collected​​ across three continents. The​​​‌ dataset contains over 10‌ billion LiDAR points with‌​‌ decimeter-level accuracy and RGB​​ (red green blue) images​​​‌ at a ground sampling‌ distance of 25 cm‌​‌ (see Figure 1).​​ While many existing datasets​​​‌ primarily focus on the‌ image modality, P 3‌​‌ offers a complementary perspective​​ by also incorporating dense​​​‌ 3D information. We demonstrate‌ that LiDAR point clouds‌​‌ serve as a robust​​ modality for predicting building​​​‌ polygons, both in hybrid‌ and end-to-end learning frameworks.‌​‌ Moreover, fusing aerial LiDAR​​ and imagery further improves​​​‌ accuracy and geometric quality‌ of predicted polygons. The‌​‌ P 3 dataset is​​ publicly available, along with​​​‌ code and pretrained weights‌ of three state-of-the-art models‌​‌ for building polygon prediction​​ here. A preprint​​​‌ manuscript has been uploaded‌ to arXiv 23.‌​‌

The image showcases satellite​​ mapping and data annotation​​​‌ for three regions: the‌ USA, Switzerland, and New‌​‌ Zealand. The map areas​​ are divided into training,​​​‌ validation, and testing sections.‌ Each section is shown‌​‌ with high-resolution satellite images​​ and corresponding annotated data​​​‌ points, which include various‌ tiles of aerial imagery‌​‌ and annotated features such​​​‌ as buildings and roads.​

8.1.2 Road network vectorization​​​‌ with geometric enforcement

Participants:​ Zhenyu Zhu, Florent​‌ Lafarge, Elena Di​​ Bernardino [LJAD, Université Côte​​​‌ d'Azur].

We present​ an automatic algorithm for​‌ graph-based road network extraction​​ from remote sensing images.​​​‌ While existing works mostly​ focus on improving accuracy,​‌ we address the problem​​ of the geometric quality​​​‌ of the output graphs.​ The state-of-the-art methods largely​‌ overlook this aspect by​​ generating graphs without strong​​​‌ geometric guarantees, regularity preservation​ and low complexity, which,​‌ at the end, reduce​​ their impact in many​​​‌ application scenarios. Our algorithm​ relies upon both foundation​‌ models that analyze road​​ networks with pixel-based representations​​​‌ and geometric algorithms and​ data structures in charge​‌ of connecting geometric primitives​​ into planar graphs (see​​​‌ Figure 2). This​ hybrid strategy allows us​‌ to strongly enforce the​​ geometric quality of the​​​‌ output graphs while bringing​ a high level of​‌ generalization. We show the​​ potential of our algorithm​​​‌ and its interest against​ existing methods on two​‌ datasets commonly-used in the​​ field using both the​​​‌ conventional accuracy metrics and​ new metrics introduced to​‌ measure the geometric quality​​ the output graphs.

Road​​​‌ network vectorization with geometric​ enforcement.

8.1.3 Illustrator's Depth:​ monocular layer index prediction​‌ for image decomposition

Participants:​​ Nissim Maruani, Pierre​​​‌ Alliez, Mathieu Desbrun​ [GEOMERIX Inria project-team],​‌ Peiying Zhang [CityUHK],​​ Siddhartha Chaudhuri [Adobe Research]​​​‌, Matthew Fisher [Adobe​ Research], Nanxuan Zhao​‌ [Adobe Research], Vladimir​​ Kim [Adobe Research],​​​‌ Wang Yifan [Adobe Research]​.

We introduced Illustrator's​‌ Depth, a novel definition​​ of depth that addresses​​​‌ a key challenge in​ digital content creation: decomposing​‌ flat images into editable,​​ ordered layers. Inspired by​​​‌ an artist's compositional process,​ Illustrator's Depth infers a​‌ layer index to each​​ pixel, forming an interpretable​​​‌ image decomposition through a​ discrete, globally consistent ordering​‌ of elements optimized for​​ editability (see Figure 3​​​‌). We also propose​ and train a neural​‌ network using a curated​​ dataset of layered vector​​​‌ graphics to predict layering​ directly from raster inputs.​‌ Our layer index inference​​ unlocks a range of​​​‌ powerful downstream applications. In​ particular, it significantly outperforms​‌ state-of-the-art baselines for image​​ vectorization while also enabling​​​‌ high-fidelity text-to-vector-graphics generation, automatic​ 3D relief generation from​‌ 2D images, and intuitive​​ depth-aware editing. By reframing​​ depth from a physical​​​‌ quantity to a creative‌ abstraction, Illustrator's Depth prediction‌​‌ offers a new foundation​​ for editable image decomposition.​​​‌ A preprint manuscript has‌ been uploaded to arXiv‌​‌ 21.

The image​​ shows three different illustrations​​​‌ processed through an "Illustrator's‌ Depth Estimation Model." The‌​‌ top row displays the​​ original images. The middle​​​‌ row displays depth estimation‌ results, with color gradients‌​‌ indicating depth, where darker​​ colors represent the background​​​‌ and lighter colors indicate‌ the foreground. The bottom‌​‌ section highlights applications of​​ this depth information, including​​​‌ image vectorization, 3D relief‌ fabrication, text to vector‌​‌ generation, as well as​​ depth-aware editing.

8.1.4 Progressive compression​​ of colored 3D point​​​‌ clouds

Participants: Armand Zampieri‌, Pierre Alliez,‌​‌ Guillaume Delarue [Samp AI]​​, Nachwa Abou Bakr​​​‌ [Samp AI].

Colored‌ 3D point clouds produced‌​‌ by modern sensor technologies​​ play an increasing role​​​‌ in enabling shared reality‌ experiences and in the‌​‌ development of digital twins.​​ As these point clouds​​​‌ become distributed and synchronized‌ across networked systems, there‌​‌ arises a need for​​ compression methods that progressively​​​‌ and efficiently transmit the‌ data. We explored a‌​‌ novel progressive compression technique​​ for static point cloud​​​‌ that transforms a colored‌ 3D point cloud into‌​‌ a sequence of incremental​​ updates, each enhancing spatial​​​‌ resolution and color fidelity‌ (see Figure 4).‌​‌ The compression process relies​​ on three tightly integrated​​​‌ data structures: a binary‌ space partition (BSP), an‌​‌ octree, and a palette​​ tree. The BSP encodes​​​‌ the spatial distribution of‌ point density, which is‌​‌ mapped over the octree​​ structure. Meanwhile, the palette​​​‌ tree incrementally refines a‌ color palette, tailored to‌​‌ each input point cloud,​​ which is then used​​​‌ to color the octree‌ point density function. Refinements‌​‌ of these data structures​​ are interleaved and encoded​​​‌ using entropy coding to‌ produce a compressed bitstream.‌​‌ Additionally, we contribute a​​ volume-based rendering algorithm designed​​​‌ for GPU execution, allowing‌ rapid visualization of the‌​‌ decompressed data. Focusing on​​ low-bitrate regimes (a critical​​​‌ priority for our target‌ applications), our method achieves‌​‌ superior rate-distortion efficiency compared​​ to MPEG G-PCC (Geometry-based​​​‌ Point Cloud Compression) and‌ Draco. This work has‌​‌ been submitted to the​​ Geometric Modeling and Processing​​​‌ 2026 conference.

Progressive compression‌ of colored 3D point‌​‌ clouds.

8.1.5 NURBSFit:​‌ Robust fitting of NURBS​​ surfaces to point clouds​​​‌

Participants: Florent Lafarge,​ Lizeth Fuentes Perez [University​‌ of Zurich], Renato​​ Pajarola [University of Zurich]​​​‌.

NURBS surfaces are​ compact parametric representations widely​‌ used in Computer-Aided Design​​ (CAD) modeling. Decomposing raw​​​‌ 3D data measurements into​ a set of such​‌ elements is a challenging​​ problem that existing methods​​​‌ approach by learning from​ CAD databases to both​‌ segment synthetic data and​​ fit parametric shapes on​​​‌ each segment. Unfortunately, these​ methods generalize poorly to​‌ raw data measurements, with​​ low robustness to imperfect​​​‌ data and complex objects​ and low scalability. To​‌ address this issue, we​​ propose an algorithm that​​​‌ fits NURBS surfaces to​ unorganized 3D point clouds,​‌ such as those generated​​ by laser and photogrammetry​​​‌ acquisition systems (see Figure​ 5). Starting with​‌ a fine configuration of​​ planar patches that approximate​​​‌ the object geometry, our​ algorithm performs merging operations​‌ that progressively regroup pairs​​ of adjacent patches into​​​‌ fewer, more expressive NURBS​ surfaces. This process is​‌ designed to be both​​ robust and performant with​​​‌ a series of technical​ ingredients that include an​‌ energy that controls the​​ global quality of a​​​‌ configuration of NURBS surfaces​ and an efficient ordering​‌ of the merging operations​​ based on a cost-efficient​​​‌ quadric surface fitting analysis.​ We show the potential​‌ of our algorithm on​​ both synthetic and real-world​​​‌ data and its efficiency​ against existing primitive fitting​‌ methods with results both​​ simpler and geometrically more​​​‌ accurate. This work was​ presented at the International​‌ Conference on 3D Vision​​ (3DV) 17.

The​​​‌ image shows a 3D​ point cloud of a​‌ horse. Left: four images​​ of the horse point​​​‌ cloud taken from various​ angles, depicting the horse​‌ in a dynamic pose.​​ Right: colorful, smooth 3D​​​‌ model of the horse,​ segmented into different regions,​‌ each with distinct colors​​ for visual differentiation.

8.1.6 Bayesian experimental design​​​‌ via contrastive diffusions

Participants:​ Pierre Alliez, Jacopo​‌ Iollo [STATIFY Inria project-team]​​, Florence Forbes [STATIFY​​​‌ Inria project-team], Christophe​ Heinkelé [Cerema].

Bayesian​‌ Optimal Experimental Design (BOED)​​ is a powerful tool​​​‌ to reduce the cost​ of running a sequence​‌ of experiments. When based​​ on the Expected Information​​​‌ Gain (EIG), design optimization​ corresponds to the maximization​‌ of some intractable expected​​ contrast between prior and​​​‌ posterior distributions. Scaling this​ maximization to high dimensional​‌ and complex settings has​​ been an issue due​​​‌ to BOED inherent computational​ complexity. In this work,​‌ we introduce a pooled​​ posterior distribution with cost-effective​​​‌ sampling properties and provide​ a tractable access to​‌ the EIG contrast maximization​​ via a new EIG​​ gradient expression. Diffusion-based samplers​​​‌ are used to compute‌ the dynamics of the‌​‌ pooled posterior and ideas​​ from bi-level optimization are​​​‌ leveraged to derive an‌ efficient joint sampling-optimization loop,‌​‌ without resorting to lower​​ bound approximations of the​​​‌ EIG. The resulting efficiency‌ gain allows to extend‌​‌ BOED to the well-tested​​ generative capabilities of diffusion​​​‌ models. By incorporating generative‌ models into the BOED‌​‌ framework, we expand its​​ scope and its use​​​‌ in scenarios that were‌ previously impractical. Numerical experiments‌​‌ and comparison with state-of-the-art​​ methods show the potential​​​‌ of the approach. This‌ work was presented at‌​‌ the International Conference on​​ Machine Learning (ICML) 18​​​‌.

8.1.7 Curvature-guided optimal‌ transport for rigid point‌​‌ cloud registration

Participants: Roberto​​ Dyke, Pierre Alliez​​​‌, Mathijs Wintraecken [DATASHAPE‌ Inria project-team], Marie-Aurélie‌​‌ Chanut [Cerema].

We​​ present a novel approach​​​‌ for rigid point cloud‌ registration that leverages curvature‌​‌ estimation to guide an​​ unbalanced optimal transport (UOT)​​​‌ framework. By approximating the‌ underlying surface using jet‌​‌ fitting to extract principal​​ curvatures k1 and k2,​​​‌ we incorporate geometric cues‌ into a stochastic mini-batch‌​‌ optimization strategy. This method​​ utilizes a dual form​​​‌ of the transport problem‌ to selectively optimize subsets‌​‌ based on curvature bins​​ defined by the shape​​​‌ index and mean curvature,‌ effectively aligning source and‌​‌ target clouds via an​​ Iterative Closest Point (ICP)-like​​​‌ objective. We evaluate our‌ approach on the FAUST-partial‌​‌ v2 benchmark, where it​​ significantly outperforms existing state-of-the-art​​​‌ optimal transport-based methods, achieving‌ a registration success rate‌​‌ of 94.78% using a​​ point-to-plane metric. Our results​​​‌ indicate promising progress for‌ OT-based registration, rivaling the‌​‌ accuracy of leading nearest​​ neighbor-based techniques (see Figure​​​‌ 6). This work‌ was presented as a‌​‌ poster at the Symposium​​ on Geometry Processing (SGP)​​​‌ 24.

The image‌ shows a 3D model‌​‌ of a statue head​​ with different colors representing​​​‌ various surface types. A‌ legend on the left‌​‌ details these types: blue​​ for Planar, orange for​​​‌ Parabolic, green for Elliptic,‌ red for Hyperbolic, gray‌​‌ for Bin, and beige​​ for Neighbor. The model​​​‌ is color-coded to indicate‌ these surface characteristics across‌​‌ different parts of the​​ statue's surface.

8.1.8 Hierarchical‌​‌ Gaussian partitioning for semantic​​ segmentation of airborne LiDAR​​​‌ scenes

Participants: Moussa Bendjilali‌, Pierre Alliez.‌​‌

We present a novel​​ approach to semantic segmentation​​​‌ of airborne LiDAR point‌ clouds that integrates a‌​‌ hierarchical Gaussian Mixture Model​​ (hGMM) within the Superpoint​​​‌ Transformer (SPT) framework. The‌ hGMM constructs a coarse-to-fine‌​‌ representation of the scene​​ by recursively fitting Gaussian​​​‌ components to spatially coherent‌ subsets of the point‌​‌ cloud, resulting in a​​ hierarchical and structured decomposition​​​‌ that serves as a‌ structured token set for‌​‌ the segmentation objective. While​​​‌ Gaussian Mixture Models (GMMs)​ can virtually fit any​‌ distribution, we constrain their​​ use to structured suburban​​​‌ scenes, where their parametric​ form is naturally suited​‌ to represent planar and​​ ellipsoidal geometries, hence allowing​​​‌ parsimonious mixtures. Experimental results​ on the DALES benchmark​‌ demonstrate that our method​​ achieves competitive performance with​​​‌ respect to state-of-the-art approaches,​ with notable improvements on​‌ classes such as ground​​ and buildings. Results on​​​‌ indoor S3DIS (Stanford Large-Scale​ 3D Indoor Spaces Dataset)​‌ confirm the method's intended​​ specificity to outdoor environments​​​‌ (see Figure 7).​ These findings validate hGMM​‌ as a principled and​​ effective alternative to heuristic​​​‌ partitioning techniques, integrating stochastic​ modeling with transformer-based semantic​‌ reasoning in large-scale 3D​​ environments. This work has​​​‌ been accepted to the​ ISPR 2026 conference.

The​‌ image compares two methods,​​ SGT (ours) and SPT,​​​‌ in three columns: Clusters,​ Predictions, and Errors. Each​‌ row corresponds to one​​ method. In the Clusters​​​‌ column, colorful 3D maps​ depict clustered data. The​‌ Predictions column shows a​​ similar map with different​​​‌ color gradients. The Errors​ column highlights discrepancies in​‌ gray with red error​​ points. The SGT method​​​‌ appears to produce slightly​ more refined clusters and​‌ fewer errors compared to​​ the SPT method.

8.2.1 ShapeShifter: 3D​​​‌ variations using multiscale and​ sparse point-voxel diffusion

Participants:​‌ Nissim Maruani, Pierre​​ Alliez, Mathieu Desbrun​​​‌ [GEOMERIX Inria project-team],​ Wang Yifan [Adobe Research]​‌, Matthew Fisher [Adobe​​ Research].

We introduced​​​‌ ShapeShifter, a new 3D​ generative model that learns​‌ to synthesize shape variations​​ based on a single​​​‌ reference model. While generative​ methods for 3D objects​‌ have recently attracted much​​ attention, current techniques often​​​‌ lack geometric details and/or​ require long training times​‌ and large resources. Our​​ approach remedies these issues​​​‌ by combining sparse voxel​ grids and point, normal,​‌ and color sampling within​​ a multiscale neural architecture​​​‌ that can be trained​ efficiently and in parallel.​‌ We show that our​​ resulting variations better capture​​​‌ the fine details of​ their original input and​‌ can handle more general​​ types of surfaces than​​​‌ previous SDF-based methods (Signed​ Distance Function). Moreover, we​‌ offer interactive generation of​​ 3D shape variants, allowing​​​‌ more human control in​ the design loop if​‌ needed (see Figure 8​​). This work was​​​‌ presented at the international​ conference on Computer Vision​‌ and Pattern Recognition (CVPR)​​ 19.

The image​​​‌ depicts a process for​ generating shapes using multiscale​‌ diffusion sampling. Starting with​​ input geometries (like a​​​‌ set of columns or​ an aerial view of​‌ a river), a training​​ phase is conducted. The​​​‌ trained model then generates​ new shapes through multiscale​‌ diffusion sampling. The process​​ includes normal distributions and​​ sampling points at varying​​​‌ scales, resulting in detailed‌ and varied generated shapes.‌​‌

8.2.2 KIBS: 3D‌ detection of planar roof‌​‌ sections from a single​​ satellite image

Participants: Florent​​​‌ Lafarge, Johann Lussange‌, Mulin Yu,‌​‌ Yuliya Tarabalka [Luxcarta Technology]​​.

Reconstructing urban areas​​​‌ in 3D from satellite‌ raster images has been‌​‌ a longstanding problem for​​ both academical and industrial​​​‌ research. While automatic methods‌ achieving this objective at‌​‌ a Level Of Detail​​ (LOD) 1 are mostly​​​‌ efficient today, producing LOD2‌ models is still a‌​‌ scientific challenge. In particular,​​ the quality and resolution​​​‌ of satellite data is‌ too low to infer‌​‌ accurately the planar roof​​ sections in 3D by​​​‌ using traditional plane detection‌ algorithms. Existing methods rely‌​‌ upon the exploitation of​​ both strong urban priors​​​‌ that reduce their applicability‌ to a variety of‌​‌ environments and multi-modal data,​​ including some derived 3D​​​‌ products such as Digital‌ Surface Models. In this‌​‌ work, we address this​​ issue with KIBS (Keypoints​​​‌ Inference By Segmentation), a‌ method that detects planar‌​‌ roof sections in 3D​​ from a single-view satellite​​​‌ image. By exploiting largescale‌ LOD2 databases produced by‌​‌ human operators with efficient​​ neural architectures, we manage​​​‌ to both segment roof‌ sections in images and‌​‌ extract keypoints enclosing these​​ sections in 3D to​​​‌ form 3D-polygons with a‌ low-complexity. The output set‌​‌ of 3D-polygons can be​​ used to reconstruct LOD2​​​‌ models of buildings when‌ combined with a plane‌​‌ assembly method. While conceptually​​ simple, our method manages​​​‌ to capture roof sections‌ as 3D-polygons with a‌​‌ good accuracy, from a​​ single satellite image only​​​‌ by learning indirect 3D‌ information contained in the‌​‌ image, in particular from​​ the view inclination, the​​​‌ distortion of facades, the‌ building shadows, roof peak‌​‌ and ridge perspective. We​​ demonstrate the potential of​​​‌ KIBS by reconstructing large‌ urban areas in a‌​‌ few minutes, with a​​ Jaccard index for the​​​‌ 2D segmentation of individual‌ roof sections of approximately‌​‌ 80% (see Figure 9​​). This work was​​​‌ published in the ISPRS‌ Journal of Photogrammetry and‌​‌ Remote Sensing 15.​​

3D detection of planar​​​‌ roof sections from a‌ single satellite image and‌​‌ building reconstruction.

8.2.3 MILo: Mesh-In-the-Loop​​ Gaussian Splatting for Detailed​​​‌ and Efficient Surface Reconstruction​

Participants: Nissim Maruani,​‌ Antoine Guédon [Ecole Polytechnique]​​, Diego Gomez [Ecole​​​‌ Polytechnique], Bingchen Gong​ [Ecole Polytechnique], George​‌ Drettakis [GraphDeco Inria project-team]​​, Maks Ovsjanikov [Ecole​​​‌ Polytechnique].

While recent​ advances in Gaussian Splatting​‌ have enabled fast reconstruction​​ of high-quality 3D scenes​​​‌ from images, extracting accurate​ surface meshes remains a​‌ challenge. Current approaches extract​​ the surface through costly​​​‌ post-processing steps, resulting in​ the loss of fine​‌ geometric details or requiring​​ significant time and leading​​​‌ to very dense meshes​ with millions of vertices.​‌ More fundamentally, the a​​ posteriori conversion from a​​​‌ volumetric to a surface​ representation limits the ability​‌ of the final mesh​​ to preserve all geometric​​​‌ structures captured during training.​ We present MILo, a​‌ novel Gaussian Splatting framework​​ that bridges the gap​​​‌ between volumetric and surface​ representations by differentiably extracting​‌ a mesh from the​​ 3D Gaussians. We design​​​‌ a fully differentiable procedure​ that constructs the mesh—including​‌ both vertex locations and​​ connectivity—at every iteration directly​​​‌ from the parameters of​ the Gaussians, which are​‌ the only quantities optimized​​ during training. Our method​​​‌ introduces three key technical​ contributions: (1) a bidirectional​‌ consistency framework ensuring both​​ representations—Gaussians and the extracted​​​‌ mesh—capture the same underlying​ geometry during training; (2)​‌ an adaptive mesh extraction​​ process performed at each​​​‌ training iteration, which uses​ Gaussians as differentiable pivots​‌ for Delaunay triangulation; (3)​​ a novel method for​​​‌ computing signed distance values​ from the 3D Gaussians​‌ that enables precise surface​​ extraction while avoiding geometric​​​‌ erosion. Our approach can​ reconstruct complete scenes, including​‌ backgrounds, with state-of-the-art quality​​ while requiring an order​​​‌ of magnitude fewer mesh​ vertices than previous methods​‌ (see Figure 10).​​ Due to their light​​​‌ weight and empty interior,​ our meshes are well​‌ suited for downstream applications​​ such as physics simulations​​​‌ and animation. This work​ was presented at the​‌ ACM SIGGRAPH Asia Conference​​ and published in ACM​​​‌ Transactions on Graphics 14​.

Mesh-in-the-Loop Gaussian Splatting.​‌

8.2.4​​ Geometric modeling of urban​​​‌ scenes with LOD2 formalism‌ from satellite images

Participants:‌​‌ Marion Boyer.

This​​ Ph.D. thesis funded by​​​‌ CNES and Airbus DS‌ was advised by Florent‌​‌ Lafarge.

Demand for urban​​ 3D models is increasing​​​‌ as their applications rise.‌ Although these models are‌​‌ usually created from LiDAR​​ point clouds or multiview​​​‌ images captured by aerial‌ acquisition, using satellite images‌​‌ would allow a better​​ coverage and a better​​​‌ acquisition frequency, while being‌ less costly. The new‌​‌ generation of satellite images​​ tends toward this objective​​​‌ with resolutions close to‌ those of the aerial‌​‌ images. However, reconstruction methods​​ for aerial data are​​​‌ not directly applicable on‌ satellite images, because of‌​‌ low facade visibility, reduced​​ number of image views​​​‌ and possible geometric distortions.‌ Designing methods suitable for‌​‌ satellite images is thus​​ an important scientific challenge.​​​‌ In this thesis, we‌ propose a pipeline for‌​‌ 3D reconstruction of buildings​​ from satellite images (see​​​‌ Figure 11). Unlike‌ state-of-the-art methods which begin‌​‌ by a semantic segmentation​​ and whose errors propagate​​​‌ through the rest of‌ the processing without the‌​‌ possibility of correction, we​​ propose to exploit semantic​​​‌ and geometric information at‌ the same level. The‌​‌ pipeline is composed of​​ two main algorithms. The​​​‌ first one aims at‌ extracting 2D geometric primitives‌​‌ from 2D point clouds​​ calculated from images. The​​​‌ second algorithm assembles these‌ primitives to build a‌​‌ structural representation of the​​ building roofs as a​​​‌ planar graph, called the‌ 2D wireframe. It relies‌​‌ on a semantic segmentation​​ of building roofs and​​​‌ 3D information of the‌ image, the Digital Surface‌​‌ Model. Both algorithms use​​ an energy minimization to​​​‌ balance the fidelity to‌ the data types used‌​‌ and the desired simplicity​​ of the output, which​​​‌ is necessary to represent‌ complex scenes. To demonstrate‌​‌ the efficiency of our​​ algorithms, we created a​​​‌ dataset comprising of extracts‌ of Pleiades Neo images.‌​‌ We also conducted experiments​​ on more varied datasets,​​​‌ which show the potential‌ of our algorithms 20‌​‌.

Geometric modeling of​​ urban scenes with LOD2​​​‌ formalism.

8.2.5 Reference architecture‌​‌ and ontology framework for​​ digital twin construction

Participants:​​​‌ Kacper Pluta, Jonas‌ Schlenger [Technical University of‌​‌ Munich], Alwyn Mathew​​ [University of Cambridge],​​​‌ Timson Yeung [Technion],‌ Rafael Sacks [Technion],‌​‌ André Borrmann [Technical University​​ of Munich].

The​​​‌ application of digital twins‌ in building construction faces‌​‌ challenges due to limited​​ guidance on the necessary​​​‌ data management layers. This‌ work addresses this gap‌​‌ by investigating how the​​​‌ reference architecture for Digital​ Twin Construction (DTC) should​‌ be structured to manage​​ planning information, raw monitoring​​​‌ data, and derived knowledge,​ as well as its​‌ data schema to compare​​ project plans with status.​​​‌ By defining platform requirements​ and using Design Science​‌ Research Methodology, a solution​​ was implemented and validated​​​‌ using a case study​ based on the ConSLAM​‌ dataset. A plugin-based DTC​​ reference architecture employing multiple​​​‌ RDF (Resource Description Framework)​ graphs linked to specialized​‌ databases and the DTC​​ Ontology as the internal​​​‌ data schema are introduced.​ This architecture guides construction​‌ companies in data-driven decision-making​​ during execution. It establishes​​​‌ a foundation for managing​ digital twins and fosters​‌ the development of domain-specific​​ services that benefit from​​​‌ clear data structures, supporting​ a holistic digital twin​‌ adaptable to project-specific needs.​​ This work was published​​​‌ in the journal of​ Automation in Construction 16​‌.

8.3.1​​ Automatic hexahedral meshing using​​​‌ Dhondt cut algorithm

Participants:​ François Protais.

Automatic​‌ hexahedral meshing is an​​ active topic in research.​​​‌ The only current industrial​ approaches are octree-based methods.​‌ They provide a tool​​ that works reliably, but​​​‌ gives unstructured results. Recent​ works try to merge​‌ it with other approaches​​ to bring more structure​​​‌ to the generated mesh.​ The major blocking point​‌ is often the ability​​ to reproduce the state-of-the-art​​​‌ methods that rely on​ complex engineering. We propose​‌ an approach that gives​​ simple and reliable boundary​​​‌ management. We provide an​ open-source implementation that can​‌ generate hexahedral meshes without​​ any inverted elements (guaranteed,​​​‌ see Figure 12).​ Combined to other recent​‌ work, it provides a​​ complete octree-based hexahedral meshing​​​‌ pipeline. A preprint version​ of the work was​‌ published as an Inria​​ technical report 22.​​​‌

The image depicts a​ 3D grid or mesh​‌ structure, primarily in black​​ and red. Within the​​​‌ grid, there are several​ distorted, irregular shapes, also​‌ in red. Three zoomed-in​​ views highlight specific sections​​​‌ of these shapes, showcasing​ the detailed mesh patterns​‌ in greater clarity. The​​ hexahedral mesh is a​​​‌ complex network of interconnected​ lines forming the surface​‌ of the shapes. The​​ zoomed-in sections emphasize the​​​‌ intricate detailing and variations​ in the mesh structure.​‌

8.3.2​ Versatile Volume Fitting with​‌ Automatic Feature Preservation

Participants:​​ François Protais, Gianmarco​​​‌ Cherchi, Marco Livesu​, Maël Rouxel-Labbé.​‌

A vast amount of​​ applications require to operate​​​‌ on a volumetric mesh​ by editing its vertex​‌ positions so as to​​ fit to some geometric​​​‌ target while maintaining a​ good per element quality.​‌ Problems of this kind​​ arise in free-form deformation,​​​‌ remeshing, volume mapping, offsetting,​ feature recovery, and many​‌ others. Despite the fact​​ that each application poses​​​‌ its own technical and​ practical requirements, there are​‌ strong similarities between them.​​ To date, such similarity​​​‌ has not been fully​ exploited in the literature,​‌ which offers a fragmented​​ set of specialized tools​​ that are not flexible​​​‌ enough to embrace the‌ whole spectrum of applications.‌​‌ We introduce a highly​​ versatile volume deformation tool​​​‌ that, thanks to a‌ number of technical and‌​‌ practical contributions, naturally adapts​​ to a large variety​​​‌ of application needs, also‌ being faster and more‌​‌ scalable than existing specialized​​ solvers (see Figure 13​​​‌). We demonstrate its‌ capabilities in a large‌​‌ variety of applications and​​ release its source code​​​‌ to maximize its penetration‌ in the research and‌​‌ industrial communities. This work​​ was submitted. The software​​​‌ code is planned to‌ be part of a‌​‌ transfer to the CGAL​​ library, in collaboration with​​​‌ Geometry Factory.

The image‌ compares two methods for‌​‌ applying textures to a​​ 3D staircase model: standard​​​‌ alpha wrapping and an‌ enhanced version. Four columns‌​‌ show results with increasing​​ vertex counts (1.1K, 5.3K,​​​‌ 14.5K, and 31K). Each‌ column illustrates how texture‌​‌ quality improves with more​​ vertices; the enhanced method​​​‌ consistently produces smoother and‌ more detailed textures. Closer‌​‌ views highlight texture differences.​​ The parameter alpha (α)​​​‌ varies as D/20, D/40,‌ D/60, and D/80, affecting‌​‌ texture smoothness. The enhanced​​ method shows superior results​​​‌ across all vertex counts.‌

AlteIA‌​‌ - Cifre thesis

Participants:​​ Pierre Alliez, Moussa​​​‌ Bendjilali.

This Cifre‌ Ph.D. thesis project, entitled‌​‌ “From 3D Point Clouds​​ to Cognitive 3D Models”,​​​‌ started in September 2023,‌ for a total duration‌​‌ of 3 years. Digital​​ twinning of large-scale scenes​​​‌ and industrial sites requires‌ acquiring the geometry and‌​‌ appearance of terrains, large-scale​​ structures and objects. In​​​‌ this thesis, we assume‌ that the acquisition is‌​‌ performed by an aerial​​ laser scanner (LiDAR) attached​​​‌ to a helicopter (see‌ Figure 14). The‌​‌ generated 3D point clouds​​ record the point coordinates,​​​‌ intensities of reflectivity, and‌ possibly other attributes such‌​‌ as colors. These raw​​ measurement data can be​​​‌ massive, in the order‌ of 70 points per‌​‌ meter square, summing up​​ to several hundred million​​​‌ points for scenes extending‌ over kilometers. Analyzing large-scale‌​‌ scenes requires (1) enriching​​ these data with an​​​‌ abstraction layer, (2) understanding‌ the structure and semantics‌​‌ of the scenes, (3)​​ producing so-called cognitive 3D​​​‌ models that are searchable,‌ and (4) detecting the‌​‌ changes in the scenes​​ over time.

The input​​​‌ is assumed to be‌ a LiDAR 3D point‌​‌ cloud recording the point​​ coordinates and surface reflectivity​​​‌ intensity of a point‌ set sampled over a‌​‌ physical scene. We are​​ exploring novel algorithms for​​​‌ addressing semantic segmentation. More‌ specifically, we wish to‌​‌ retrieve the semantics of​​ the scene as well​​​‌ as the location, pose‌ and semantic classes of‌​‌ objects of interest. Ideally,​​ we seek for dense​​​‌ semantic segmentation, where the‌ class of each sample‌​‌ point is inferred in​​​‌ order to yield a​ complete description of the​‌ physical scene. We also​​ wish to distinguish each​​​‌ instance of a semantic​ class so that all​‌ objects of a scene​​ can be enumerated.

Large-scale​​​‌ scene of an electric​ infrastructure.

CNES​​ - Airbus

Participants: Marion​​​‌ Boyer, Florent Lafarge​.

The goal of​‌ this collaboration is to​​ design an automatic pipeline​​​‌ for modeling in 3D​ urban scenes under a​‌ CityGML LOD2 formalism using​​ the new generation of​​​‌ stereoscopic satellite images, in​ particular the 30cm resolution​‌ images offered by Pléiades​​ Néo satellites (see Figure​​​‌ 15). Traditional methods​ usually start with a​‌ semantic classification step followed​​ by a 3D reconstruction​​​‌ of objects composing the​ urban scene. Too often​‌ in traditional approaches, inaccuracies​​ and errors from the​​​‌ classification phase are propagated​ and amplified throughout the​‌ reconstruction process without any​​ possible subsequent correction. In​​​‌ contrast, our main idea​ consists in extracting semantic​‌ information of the urban​​ scene and in reconstructing​​​‌ the geometry of objects​ simultaneously. This project started​‌ in October 2022, for​​ a total duration of​​​‌ 3 years.

Pléiades Néo​ satellite images

Luxcarta​​​‌

Participants: Raphael Sulzer,​ Florent Lafarge.

The​‌ main goal of this​​ collaboration with Luxcarta is​​​‌ to develop new algorithms​ that improve the geometry​‌ and topology of 3D​​ models of buildings produced​​​‌ by the company. The​ algorithms should detect and​‌ enforce (i) geometric regularities​​ in 3D models, such​​​‌ as parallelism of roof​ edges or connection of​‌ polygonal facets at exactly​​ one vertex, and (ii)​​​‌ simplify models, e.g. by​ removing undesired facets or​‌ incoherent roof typologies. These​​ two objectives will have​​​‌ to be fulfilled under​ the constraint that the​‌ geometric accuracy of the​​ solution must remain close​​​‌ to the one of​ the input models. Assuming​‌ the input 3D models​​ are valid watertight polygon​​​‌ surface meshes, we will​ investigate metrics to quantify​‌ the geometric regularities and​​ the simplicity of the​​​‌ input models and will​ propose a formulation that​‌ allows both continuous and​​ discrete modifications. Continuous modifications​​​‌ will aim to better​ align vertices and edges,​‌ in particular to reinforce​​ geometric regularities. Discrete modifications​​​‌ will handle changes in​ roof topology with, for​‌ instance, removal or creation​​ of roof sections or​​​‌ new adjacencies between them.​ The output model will​‌ have to be valid​​ 2-manifold watertight polygon surface​​​‌ meshes. We will also​ investigate optimization mechanisms to​‌ explore the large solution​​ space of the problem​​ efficiently. This project started​​​‌ in November 2023, for‌ a total duration of‌​‌ 2.5 years.

Naval group​​

Participants: Pierre Alliez.​​​‌

This project is in‌ collaboration with the Acentauri‌​‌ project-team (two research engineers​​ are co-advised since November​​​‌ 2023). The context is‌ that of the factory‌​‌ of the future for​​ Naval Group, for submarines​​​‌ and surface ships. As‌ input, we have a‌​‌ digital model (e.g., a​​ frigate), the equipment assembly​​​‌ schedule and measurement data‌ (images or Lidar). We‌​‌ wish to monitor the​​ assembly site to compare​​​‌ the "as-designed" with the‌ "as-built" model. The main‌​‌ problem is a need​​ for coordination on the​​​‌ construction sites for decision‌ making and planning optimization.‌​‌ We wish to enable​​ following the progress of​​​‌ a real project and‌ to check its conformity‌​‌ with the help of​​ a digital twin. Currently,​​​‌ since Naval Group needs‌ to verify on site,‌​‌ rounds of visits are​​ required to validate the​​​‌ progress as well as‌ the equipment. These rounds‌​‌ are time consuming and​​ not to mention the​​​‌ constraints of the site,‌ such as the temporary‌​‌ absence of electricity or​​ the numerous temporary assembly​​​‌ and safety equipment. The‌ objective of the project‌​‌ is to automate the​​ monitoring, with sensor intelligence​​​‌ to validate the work.‌ Fixed sensor systems (cameras‌​‌ and LiDAR) are used,​​ with the addition of​​​‌ smartphones/tablets carried by operators‌ on site.

Samp AI‌​‌ - Cifre thesis

Participants:​​ Armand Zampieri, Pierre​​​‌ Alliez.

This project‌ (Cifre Ph.D. thesis) investigates‌​‌ algorithms for progressive, random​​ access compression of 3D​​​‌ point clouds for digital‌ twinning of industrial sites‌​‌ (see Figure 16).​​ The context is as​​​‌ follows. Laser scans of‌ industrial facilities contain massive‌​‌ amounts of 3D points​​ which are very reliable​​​‌ visual representations of these‌ facilities. These points represent‌​‌ the positions, color attributes​​ and other metadata about​​​‌ object surfaces. Samp turns‌ these 3D points into‌​‌ intelligent digital twins that​​ can be searched and​​​‌ interactively visualized on heterogeneous‌ clients, via streamed services‌​‌ on the cloud. The​​ 3D point clouds are​​​‌ first structured and enriched‌ with additional attributes such‌​‌ as semantic labels or​​ hierarchical group identifiers. Efficient​​​‌ streaming motivates progressive compression‌ of these 3D point‌​‌ clouds, while local search​​ or visualization queries call​​​‌ for random accessible capabilities.‌ Given an enriched 3D‌​‌ point cloud as input,​​ the objective is to​​​‌ generate as output a‌ compressed version with the‌​‌ following properties: (1) Random​​ accessible compressed (RAC) file​​​‌ format that provides random‌ access (not just sequential‌​‌ access) to the decompressed​​ content, so that each​​​‌ compressed chunk can be‌ decompressed independently, depending on‌​‌ the area in focus​​ on the client side.​​​‌ (2) Progressive compression: the‌ enriched point cloud is‌​‌ converted into a stream​​ of refinements, with an​​​‌ optimized rate-distortion tradeoff allowing‌ for early access to‌​‌ a faithful version of​​ the content during streaming.​​​‌ (3) Structure-preserving: all structural‌ and semantic information are‌​‌ preserved during compression, allowing​​ for structure-aware queries on​​​‌ the client. (4) Lossless‌ at the end: allows‌​‌ the original data to​​​‌ be perfectly reconstructed from​ the compressed data, when​‌ streaming is completed. The​​ PhD defense is planned​​​‌ January 26th 2026.

The​ image displays an industrial​‌ facility with complex piping​​ systems highlighted in various​​​‌ colors (green, yellow, red,​ blue) to denote different​‌ components. There is a​​ 3D scan overlay with​​​‌ a schematic diagram at​ the bottom showing equipment​‌ labels. The layout includes​​ a mix of valves,​​​‌ pipes, and machinery, with​ detailed markings and identifiers​‌ for maintenance or operational​​ purposes.

AI Verse​​

Participants: Pierre Alliez,​​​‌ Abir Affane.

In​ collaboration with Guillaume Charpiat​‌ (Tau Inria project-team, Saclay)​​ and AI Verse (Inria​​​‌ spin-off).

We pursued our​ collaboration with AI Verse​‌ on statistics for improving​​ sampling quality, applied to​​​‌ the parameters of a​ generative model for 3D​‌ scenes. The AI Verse​​ technology is devised to​​​‌ create infinitely random and​ semantically consistent 3D scenes.​‌ This creation is fast,​​ consuming less than 4​​​‌ seconds per labeled image.​ From these 3D scenes,​‌ the system is able​​ to build high quality​​​‌ synthetic images that come​ with rich labels that​‌ are unbiased unlike manually​​ annotated labels. As for​​​‌ real data, no metric​ exists to evaluate the​‌ performance of the synthetic​​ datasets to train a​​​‌ neural network. We thus​ tend to favor the​‌ photorealism of the images​​ but such a criterion​​​‌ is far from being​ the best. The current​‌ technology provides a means​​ to control a rich​​​‌ list of additional parameters​ (quality of lighting, trajectory​‌ and intrinsic parameters of​​ the virtual camera, selection​​​‌ and placement of assets,​ degrees of occlusion of​‌ the objects, choice of​​ materials, etc). Since the​​​‌ generation engine can modify​ all of these parameters​‌ at will to generate​​ many samples, we will​​​‌ explore optimization methods for​ improving the sampling quality.​‌ Most likely, a set​​ of samples generated randomly​​​‌ by the generative model​ does not cover well​‌ the whole space of​​ interesting situations, because of​​​‌ unsuited sampling laws or​ of sampling realization issues​‌ in high dimensions. The​​ main question is how​​​‌ to improve the quality​ of this generated dataset,​‌ that one would like​​ to be close somehow​​​‌ to the given target​ dataset (consisting of examples​‌ of images that one​​ would like to generate).​​​‌ For this, statistical analyses​ of these two datasets​‌ and of their differences​​ are required, in order​​​‌ to spot possible issues​ such as strongly under-represented​‌ areas of the target​​ domain. Then, sampling laws​​​‌ can be adjusted accordingly,​ possibly by optimizing their​‌ hyper-parameters, if any.

10.1.1​ Visits of international scientists​‌

10.2.1 3IA Côte d'Azur‌

Participants: Pierre Alliez,‌​‌ Nissim Maruani, François​​ Protais, Merve Asiler​​​‌.

Pierre Alliez holds‌ a chair from 3IA‌​‌ Côte d'Azur (Interdisciplinary Institute​​ for Artificial Intelligence). The​​​‌ topic of his chair‌ is “3D modeling of‌​‌ large-scale environments for the​​ smart territory”. In addition,​​​‌ he is the scientific‌ head of the fourth‌​‌ research axis entitled “AI​​ for smart and secure​​​‌ territories”. Two PhD thesis‌ students and two postdoctoral‌​‌ fellows have been funded​​ by this program: Tong​​​‌ Zhao (Ecole des Ponts‌ ParisTech, master MVA, now‌​‌ at Dassault Systemes Paris),​​ Nissim Maruani (Ecole Polytechnique,​​​‌ Master MVA, third year‌ PhD student), and François‌​‌ Protais (postdoctoral fellow from​​ December 2024 to September​​​‌ 2025) and Merve Asiler‌ (postdoctoral fellow from November‌​‌ 2025).

10.2.2 Inria challenge​​ ROAD-AI - with CEREMA​​​‌

Participants: Pierre Alliez,‌ Jacopo Iollo, Roberto‌​‌ Dyke.

The road​​ network is one of​​​‌ the most important elements‌ of public heritage. Road‌​‌ operators are responsible for​​ maintaining, operating, upgrading, replacing​​​‌ and preserving this heritage,‌ while ensuring careful management‌​‌ of budgetary and human​​ resources. Today, the infrastructure​​​‌ is being severely tested‌ by climate change (increased‌​‌ frequency of extreme events,​​ particularly flooding and landslides).​​​‌ Users are also extremely‌ attentive to issues of‌​‌ safety and comfort linked​​ to the use of​​​‌ infrastructure, as well as‌ to environmental issues relating‌​‌ to infrastructure construction and​​ maintenance. Roads and structures​​​‌ are complex systems: numerous‌ sub-systems, non-linear evolution of‌​‌ intrinsic characteristics, assets subject​​ to extreme events, strong​​​‌ changes in use or‌ constraints (e.g. climate change)‌​‌ due to their very​​ long lifespan. This Inria​​​‌ challenge takes into account‌ the following difficulties: volume‌​‌ and nature of data​​ (heterogeneity and incompleteness, multi-sources...​​​‌ ), multiple scales of‌ analysis (from the sub-systems‌​‌ of an asset to​​ the complete national network),​​​‌ prediction of very local‌ behaviors on the scale‌​‌ of a global network,​​ complexity of road objects​​​‌ due to their operation‌ and weather conditions, 3D‌​‌ modeling with semantization, and​​ expert knowledge modeling. This​​​‌ Inria challenge aims at‌ providing the scientific building‌​‌ blocks for upstream data​​ acquisition and downstream decision​​​‌ support. Cerema's use cases‌ for this challenge separate‌​‌ into four parts:

• Build​​ a dynamic “digital twin”​​​‌ of the road and‌ its environment on the‌​‌ scale of a complete​​ network;
• The behavioral "laws"​​​‌ of pavements and engineering‌ structures using data from‌​‌ surface monitoring or structure​​ visits, sensors and environmental​​​‌ data;
• Invent the concept‌ of connected bridges and‌​‌ tunnels on a system​​ scale;
• Define strategic investment​​​‌ and maintenance planning methods‌ (predictive, prescriptive and autonomous).‌​‌

We contributed to the​​ second axis of this​​​‌ challenge. The goal of‌ this axis was to‌​‌ model proteiform structures, by​​ investigating the following tasks:​​​‌ 1) Detection of structures‌ from cartographic data, 2)‌​‌ Recalibration and semantic segmentation​​​‌ of 3D data (external​ mapping) and 3) Internal​‌ 3D mapping.

The work​​ focused on monitoring cliffs​​​‌ and rocky slopes using​ periodic LiDAR scans and​‌ semantic segmentation of 3D​​ point clouds to detect​​​‌ precursors of rockfalls and​ large mass movements. Risk-prone​‌ areas were analyzed by​​ first classifying stable versus​​​‌ unstable zones and correcting​ inter-survey scanner misalignments. Vegetation,​‌ a major source of​​ geometric variability, was modeled​​​‌ through new multi-scale and​ topological descriptors estimating its​‌ intermediate fractal dimension, enabling​​ 98% detection and removal.​​​‌ The remaining terrain was​ then aligned through a​‌ robust partial registration method​​ based on optimal transport​​​‌ with relaxed mass conservation.​ A dedicated software module​‌ implementing these steps was​​ developed as a CGAL-based​​​‌ plugin integrated into CloudCompare.​ For internal 3D mapping,​‌ we have developed a​​ novel greedy Bayesian approach​​​‌ that optimizes the gain​ of information in image​‌ reconstruction. This has been​​ investigated in the context​​​‌ of Jacopo Iollo's PhD​ thesis.

10.2.3 Inria challenge​‌ GéoIAug - with BRGM​​

Participants: Florent Lafarge,​​​‌ Steve Fétiveau.

Accessing​ and manipulating multidimensional geotemporal​‌ data in contexts other​​ than the traditional desktop​​​‌ workstation remains challenging despite​ the variety of mobile​‌ devices available to users,​​ no matter their expertise.​​​‌ In collaboration with researchers​ at BRGM, this project​‌ aims to explore the​​ specific case of geologists​​​‌ when they work in​ the field but still​‌ need access to their​​ data and to tools​​​‌ that enable them to​ capture their observations, compare​‌ them with existing data,​​ and iteratively sketch terrain​​​‌ models. Our goal is​ to develop knowledge and​‌ tools to effectively support​​ the creation, long-term reuse​​​‌ and access to those​ data before, during and​‌ after field trips. The​​ project brings together researchers​​​‌ from multiple domains at​ Inria and multiple departments​‌ at BRGM.

In the​​ GéoIAug challenge, our team​​​‌ is involved in the​ geometric modeling of geological​‌ layers. One of the​​ key challenges in the​​​‌ field for interactive visualization​ and physical simulation is​‌ to digitalize the soil​​ and subsoil in 3D​​​‌ with explicit mesh-based representations.​ Acquired on site, geological​‌ knowledge is traditionally interpolated​​ with implicit functions that​​​‌ predict the shape in​ the 3D space of​‌ various geological objects such​​ as subsoil layers or​​​‌ faults. Mesh generation techniques​ are then used to​‌ create a mesh data​​ structure that conforms to​​​‌ the zero value of​ implicit functions. These mesh​‌ generation techniques however suffer​​ from several issues. They​​​‌ typically produce dense meshes,​ conform poorly to implicit​‌ surface intersections or discontinuities,​​ and scale poorly to​​​‌ large scenes. Our main​ objective is to design​‌ and implement solutions to​​ the mesh generation problems​​​‌ mentioned above. In particular,​ the PhD candidate will​‌ investigate efficient and scalable​​ algorithms that can produce​​​‌ lightweight 3D meshes whose​ cells conform to the​‌ implicit functions and their​​ intersections. One of the​​​‌ main challenges will be​ to minimize the number​‌ of implicit function evaluations,​​ as they often are​​​‌ computationally expensive. Several research​ axes will be studied.​‌

10.2.4 PEPR NumPex

Participants:​​ Pierre Alliez, Christos​​ Georgiadis.

The Digital​​​‌ PEPR for Computing at‌ the Exascale (NumPEx) aims‌​‌ to design and develop​​ the software components and​​​‌ tools that will equip‌ future exascale machines and‌​‌ to prepare the major​​ application domains to fully​​​‌ exploit the capabilities of‌ these machines. These major‌​‌ application domains include both​​ scientific research and the​​​‌ industrial sector. This project‌ therefore contributes to France's‌​‌ response to the next​​ EuroHPC call for expressions​​​‌ of interest (AMI) (Exascale‌ France Project), with a‌​‌ view to hosting one​​ of the two European​​​‌ exascale machines planned in‌ Europe by 2024. The‌​‌ French consortium has chosen​​ GENCI as its "Hosting​​​‌ Entity" and the CEA‌ TGCC as its "Hosting‌​‌ Center". This PEPR contributes​​ to the constitution of​​​‌ a set of tools,‌ software, applications but also‌​‌ training that will allow​​ France to remain one​​​‌ of the leaders in‌ the field by developing‌​‌ a national ecosystem for​​ Exascale coordinated with the​​​‌ European strategy.

Our team‌ is mainly involved in‌​‌ the first workpackage entitled​​ “Mesh generation at the​​​‌ Exascale”. The main motivation‌ is that geometric representations‌​‌ and their discrete counterparts​​ (such as meshes) are​​​‌ usually the starting point‌ for simulation. These include‌​‌ adaptive, possibly multiresolution, robust​​ to defects, and efficient​​​‌ parallel representations of large-scale‌ models. The physics-based models‌​‌ need to include multiple​​ phenomena, or process couplings​​​‌ at multiple scales in‌ space and time. Space‌​‌ and time adaptivity are​​ then mandatory. Time integration​​​‌ requires special care to‌ become more parallel, more‌​‌ asynchronous, and more accurate​​ for long-time simulations. The​​​‌ requirement of adaptivity in‌ geometry and physics creates‌​‌ an imbalance that needs​​ to be overcome. AI-driven,​​​‌ data-driven, reduced-order, and more‌ generally surrogate models are‌​‌ now mandatory and take​​ various forms. Data must​​​‌ be understood in a‌ broad sense: from observations‌​‌ of the real physical​​ system to synthetic data​​​‌ generated by the physical‌ models. Surrogates enable orders‌​‌ of magnitude faster model​​ evaluations through the extraction​​​‌ and compression of salient‌ features in a very‌​‌ intensive training/learning (supervised, unsupervised​​ or reinforced) phase. Research​​​‌ topics include: handling multiphysics‌ and multiscale coupling, learning‌​‌ parametric dependencies, differential operators​​ or underlying physical laws,​​​‌ mitigating intensive communications during‌ the compression process, and‌​‌ exploiting the underlying computer​​ and data architectures. Multi-fidelity​​​‌ models include hierarchies of‌ models to provide a‌​‌ multi-fidelity problem-solving approach to​​ address very intensive problems​​​‌ beyond the current computing‌ capabilities. The challenge is‌​‌ to switch between representations​​ to efficiently compute and​​​‌ handle bias in so-called‌ “many-query” problems, which include‌​‌ design, optimization and other​​ high dimensional PDE problems.​​​‌ For our team, this‌ project funded a postdoctoral‌​‌ fellow (Christos Georgiadis from​​ May 2024 to April​​​‌ 2025), in collaboration with‌ Strasbourg University.

10.2.5 PEPR‌​‌ IRiMa

Participants: Florent Lafarge​​, Zhenyu Zhu.​​​‌

The exploratory IRiMa PEPR‌ aims to formalize a‌​‌ "science of risk" to​​ contribute to the development​​​‌ of a new strategy‌ for the management of‌​‌ risks and disasters and​​ their impacts in the​​​‌ context of global change.‌ To achieve this, it‌​‌ implements a series of​​​‌ research projects and expert​ assessments (involving observation, analysis​‌ or decision support) to​​ accelerate the transition to​​​‌ a society capable of​ facing a range of​‌ threats (hydro-climatic, telluric, technological,​​ health-related, coupled), by adapting​​​‌ and becoming more resilient​ and sustainable. In order​‌ to face this challenge,​​ which is increased by​​​‌ climate change, it is​ necessary to consolidate, stimulate​‌ and coordinate the national​​ research effort. It will​​​‌ attempt to integrate knowledge​ from the fields of​‌ geoscience, engineering, biology, digital​​ technology and social sciences​​​‌ with a view to​ taking a systemic approach​‌ to the management of​​ natural and technological risks.​​​‌ It will propose new​ innovative tools to better​‌ detect, understand, quantify, anticipate​​ and manage risks and​​​‌ disasters. It will focus​ in particular on the​‌ issue of cascade effects​​ combining natural, environmental, technological,​​​‌ health and biological hazards.​

Our team is involved​‌ in the Intelligent Mapping​​ project of the IRiMa​​​‌ PEPR, for proposing innovative​ solutions in the object​‌ vectorization problems. Indeed a​​ central problem in the​​​‌ project is to describe​ objects of interest contained​‌ in the remote sensing​​ data, typically large-scale images,​​​‌ with vectorized representations such​ as polygons, planar graphs​‌ or networks of parametric​​ curves. These compact and​​​‌ parametrizable representations are important​ for understanding, analyzing and​‌ simulating natural risks. One​​ of the main difficulties​​​‌ in our context is​ that objects of interest​‌ can have various appearances​​ and geometric specificities. For​​​‌ instance, buildings are surface​ objects whose boundaries are​‌ piecewise-lineic while roads or​​ faults are curved line​​​‌ networks. In the literature,​ methods are usually specific​‌ to only one type​​ of vector representation. For​​​‌ our team, this project​ is funding a PhD​‌ student, Zhenyu Zhu, since​​ October 2024.

11.1.1 Scientific​​​‌ events: selection

11.1.2 Journal​​

11.1.3 Invited talks​

• Pierre Alliez gave an​‌ invited talk (Quadric Error​​ Metrics for Variational Reconstruction​​​‌ and Neural Mesh Representation)​ at the Front Workshop​‌ (Geometric and computational aspects​​ of front propagations) organized​​ as part of the​​​‌ ERC Synergy project X-MESH,‌ in Crete (September 2025).‌​‌
• François Protais gave four​​ invited talks: Intro' at​​​‌ Inria Center at Université‌ Côte d'Azur, while visiting‌​‌ University of Cagliari in​​ June 2025, while visiting​​​‌ Geomerix (Inria/CNRS/Lix) in June‌ 2025, and at the‌​‌ Front Workshop in Greece​​ in September 2025.

11.1.4​​​‌ Scientific expertise

• Pierre Alliez‌ was a reviewer for‌​‌ the German DFG programme​​ (Deutsche Forschungsgemeinschaft Datenschutz), and​​​‌ for the European commission‌ (call HORIZON-CL2-2024-HERITAGE-ECCCH-01 - A‌​‌ European Collaborative Cloud for​​ Cultural Heritage).
• Florent Lafarge​​​‌ was a reviewer for‌ the MESR (CRI -‌​‌ crédit impot recherche and​​ JEI - jeunes entreprises​​​‌ innovantes) and for the‌ COMEVAL commission (equivalent of‌​‌ the evaluation commission for​​ the researchers of the​​​‌ French Ministry of Sustainable‌ Development).

11.1.5 Research administration‌​‌

• Pierre Alliez has been​​ chairing the Inria Evaluation​​​‌ Committee since September 2023,‌ in collaboration with Christine‌​‌ Morin and Luce Brotcorne.​​ This role is a​​​‌ half-time position.
• Pierre Alliez‌ has been the president‌​‌ of the CST (comité​​ scientifique et technique) of​​​‌ IGN (French Mapping Agency)‌ since November 2024. The‌​‌ CST monitors developments in​​ geomatics, remote sensing, cartography,​​​‌ and related fields; evaluates‌ IGN's research, innovation programs,‌​‌ and major technical projects.​​ It also provides expert​​​‌ opinions to support decision-making‌ by the director general‌​‌ and the board. In​​ this role, Pierre Alliez​​​‌ is also a member‌ of the sub-committee on‌​‌ imaging led by Sébastien​​ Lefevre.
• Pierre Alliez has​​​‌ been the scientific head‌ of the Inria-DFKI partnership‌​‌ since September 2022.
• Pierre​​ Alliez is a member​​​‌ of the scientific committee‌ of the 3IA Côte‌​‌ d'Azur.
• Florent Lafarge is​​ a member of the​​​‌ NICE committee. The main‌ actions of the NICE‌​‌ committee are to verify​​ the scientific aspects of​​​‌ the files of postdoctoral‌ students, to give scientific‌​‌ opinions on candidates for​​ national campaigns for postdoctoral​​​‌ stays, delegations, secondments as‌ well as requests for‌​‌ long duration invitations.
• Florent​​ Lafarge is a member​​​‌ of the technical committee‌ of the Academy of‌​‌ Excellence "Space, Environment, Risk​​ and Resilience" from Univ.​​​‌ Côte d'Azur.

11.2.1 Teaching

• Master:​​​‌ Pierre Alliez (with Gaétan‌ Bahl and Céline Duguet),‌​‌ Deep Learning, 32h, M2,​​ Université Côte d'Azur, France.​​​‌
• Master: Pierre Alliez (with‌ Xavier Descombes, Marc Antonini‌​‌ and Laure Blanc-Féraud), advanced​​ machine learning, 12h, M2,​​​‌ Université Côte d'Azur, France.‌
• Master: Pierre Alliez (with‌​‌ Maël Rouxel-Labbé from Geometry​​ Factory), The CGAL library,​​​‌ two full-days of masterclass,‌ M2, Marseille university, France.‌​‌
• Master: Florent Lafarge, Applied​​ AI, 8h, M2, Université​​​‌ Côte d'Azur, France.
• Master:‌ Florent Lafarge (with Angelos‌​‌ Mantzaflaris), Numerical Interpolation, 45h,​​ M1, Université Côte d'Azur,​​​‌ France.

11.2.2 Supervision

• PhD‌ defended in May 2025:‌​‌ Jacopo Iollo, Sequential Bayesian​​ Optimal Design, funded​​​‌ by Inria challenge ROAD-AI,‌ in collaboration with CEREMA,‌​‌ since January 2022, co-advised​​ by Florence Forbes (Inria​​​‌ Grenoble), Christophe Heinkele (CEREMA)‌ and Pierre Alliez.
• PhD‌​‌ defended in December 2025:​​ Marion Boyer, Geometric modeling​​​‌ of urban scenes with‌ LOD2 formalism from satellite‌​‌ images 20, funded​​​‌ by CNES and Airbus,​ advised by Florent Lafarge.​‌
• PhD in progress: Nissim​​ Maruani, Learnable representations for​​​‌ 3D shapes, funded by​ 3IA, since November 2022,​‌ co-advised by Pierre Alliez​​ and Mathieu Desbrun (Geomerix​​​‌ Inria project-team, Inria Saclay),​ and in collaboration with​‌ Maks Ovsjanikov (Ecole Polytechnique​​ and Deepmind).
• PhD in​​​‌ progress: Armand Zampieri, Compression​ and visibility of 3D​‌ point clouds, Cifre thesis​​ with Samp AI, since​​​‌ December 2022, co-advised by​ Pierre Alliez and Guillaume​‌ Delarue (Samp AI).
• PhD​​ in progress: Moussa Bendjilali,​​​‌ From 3D point clouds​ to cognitive 3D models,​‌ Cifre thesis with AlteIA,​​ since September 2023, co-advised​​​‌ by Pierre Alliez and​ Nicola Luminari (AlteIA).
• PhD​‌ in progress: Zhenyu Zhu,​​ Object vectorization from remote​​​‌ sensing data, funded by​ PEPR IRiMa, since October​‌ 2024, co-advised by Florent​​ Lafarge and Elena Di​​​‌ Bernardino (LJAD).
• PhD in​ progress: Steve Fétiveau, Concise​‌ meshing of geological structures,​​ funded by the Inria-BRGM​​​‌ GéoIAug challenge, since November​ 2025, advised by Florent​‌ Lafarge.

11.2.3 Juries

• Pierre​​ Alliez was a reviewer​​​‌ for the PhD of​ Hendrik Brückler (University of​‌ Paderborn, Germany), Grégoire Grzeczkowicz​​ (IGN) and Sergio Salinas​​​‌ (Universidad de Chile).
• Pierre​ chaired the PhD committee​‌ of Marion Boyer (Inria​​ TITANE project-team, CNES and​​​‌ Airbus) and Matteo Azzini​ (Inria).
• Pierre Alliez was​‌ a member of the​​ "Comité de Suivi Doctoral"​​​‌ for the PhD thesis​ of Arnaud Gueze (Ecole​‌ Polytechnique), Raphaël Razafindralambo (Inria​​ MAASAI project-team), Davide Adamo​​​‌ (Université Côte d'Azur and​ MAASAI project-team) and Baptiste​‌ Genest (Université Lyon 1).​​
• Florent Lafarge was a​​​‌ reviewer for the PhD​ of Florent Geniet (University​‌ of Paris Est), Shubhendu​​ Jena (Univerity of Rennes)​​​‌ and Lizeth Fuentes (University​ of Zurich, Switzerland).
• Florent​‌ Lafarge chaired the PhD​​ thesis committee of Stefan​​​‌ Larsen (University Côte d'Azur).​
• Florent Lafarge was a​‌ member of the "Comité​​ de Suivi Doctoral" for​​​‌ the PhD thesis of​ Amine Ouasfi (Mimetic Inria​‌ project-team) and Henro Kriel​​ (University Côte d'Azur).

11.3.1 Others science​ outreach relevant activities

• Pierre​‌ Alliez gave a talk​​ at “C@fé ADSTIC" in​​​‌ December, for PhD students​ of the doctoral school​‌ ADSTIC.
• In December, Florent​​ Lafarge hosted a half-day​​​‌ workshop introducing geometric modeling​ to middle-school students enrolled​‌ in a Terra Numerica​​ internship..

International journals

• 14​​​‌ articleA.Antoine Guédon‌, D.Diego Gomez‌​‌, N.Nissim Maruani​​, B.Bingchen Gong​​​‌, G.George Drettakis‌ and M.Maks Ovsjanikov‌​‌. MILo: Mesh-In-the-Loop Gaussian​​​‌ Splatting for Detailed and​ Efficient Surface Reconstruction.​‌ACM Transactions on Graphics​​December 2025HALback​​​‌ to text
• 15 article​J.Johann Lussange,​‌ M.Mulin Yu,​​ Y.Yuliya Tarabalka and​​​‌ F.Florent Lafarge.​ KIBS: 3D detection of​‌ planar roof sections from​​ a single satellite image​​​‌.ISPRS Journal of​ Photogrammetry and Remote Sensing​‌2025HALback to​​ text
• 16 articleJ.​​​‌Jonas Schlenger, K.​Kacper Pluta, A.​‌Alwyn Mathew, T.​​Timson Yeung, R.​​​‌Rafael Sacks and A.​André Borrmann. Reference​‌ architecture and ontology framework​​ for digital twin construction​​​‌.Automation in Construction​174June 2025,​‌ 106111HALDOIback​​ to text

International peer-reviewed​​​‌ conferences

• 17 inproceedingsL.​ J.Lizeth J Fuentes​‌ Perez, F.Florent​​ Lafarge and R.Renato​​​‌ Pajarola. NURBSFit: Robust​ Fitting of NURBS Surfaces​‌ to Point Clouds.​​International Conference on 3D​​​‌ Vision (3DV)Vancouver, Canada​2026HALback to​‌ text
• 18 inproceedingsJ.​​Jacopo Iollo, C.​​​‌Christophe Heinkelé, P.​Pierre Alliez and F.​‌Florence Forbes. Bayesian​​ Experimental Design via Contrastive​​​‌ Diffusions.Internation Conference​ on Learning RepresentationsICLR​‌ 2025 - International Conference​​ on Learning RepresentationsSingapore,​​​‌ Singapore2025, 1-24​HALback to text​‌
• 19 inproceedingsN.Nissim​​ Maruani, W.Wang​​​‌ Yifan, M.Matthew​ Fisher, P.Pierre​‌ Alliez and M.Mathieu​​ Desbrun. ShapeShifter: 3D​​​‌ Variations Using Multiscale and​ Sparse Point-Voxel Diffusion.​‌CVPR 2025 - IEEE/CVF​​ Conference on Computer Vision​​​‌ and Pattern RecognitionNashville​ (Tenessee), United StatesJune​‌ 2025HALback to​​ text

Doctoral dissertations and​​​‌ habilitation theses

• 20 thesis​M.Marion Boyer.​‌ Geometric modeling of urban​​ scenes with LOD2 formalism​​​‌ from satellite images.​Université Côte d'AzurDecember​‌ 2025HALback to​​ textback to text​​​‌

Reports & preprints

• 21​ miscN.Nissim Maruani​‌, P.Peiying Zhang​​, S.Siddhartha Chaudhuri​​​‌, M.Matthew Fisher​, N.Nanxuan Zhao​‌, V.Vladimir Kim​​, P.Pierre Alliez​​​‌, M.Mathieu Desbrun​ and W.Wang Yifan​‌. Illustrator's Depth: Monocular​​ Layer Index Prediction for​​​‌ Image Decomposition.2025​HALDOIback to​‌ text
• 22 reportF.​​François Protais. Automatic​​​‌ hexahedral meshing using Dhondt's​ cut algorithm.Inria​‌ - Sophia AntipolisJanuary​​ 2025HALback to​​​‌ text
• 23 miscR.​Raphael Sulzer, L.​‌Liuyun Duan, N.​​Nicolas Girard and F.​​​‌Florent Lafarge. The​ P3 dataset: Pixels, Points​‌ and Polygons for Multimodal​​ Building Vectorization.May​​​‌ 2025HALback to​ text

Other scientific publications​‌

• 24 inproceedingsR. M.​​Roberto M Dyke,​​​‌ M.Mathijs Wintraecken,​ M.-A.Marie-Aurélie Chanut and​‌ P.Pierre Alliez.​​ Curvature-Guided Optimal Transport for​​​‌ Rigid Point Cloud Registration​.SGP 2025 -​‌ Symposium on Geometry Processing​​Bilbao, SpainJuly 2025​​​‌HALback to text​

Software

• 25 softwareD.​‌David Coeurjolly, B.​​Bastien Doignies, J.-O.​​​‌Jacques-Olivier Lachaud, B.​Bertrand Kerautret, K.​‌Kacper Pluta and T.​​Tristan Roussillon. DGtal​​ 2.0.2.0July​​​‌ 2025 lic: GNU Lesser‌ General Public License v3.0‌​‌ or later.HAL​​Software HeritageVCS