Nowadays, 3D digitization systems generate numerical representations with high geometric accuracy. This accuracy involves massive - and often oversampled - point clouds, that are unsuitable for visualization, transmission and storage. The resulting meshes have the same limitations. Remeshing (to get structured data), and multiresolution coding are good ways to overcome these issues. Our research in geometry coding follows three ways:

**Reconstruction of Complex Scenes Captured by Terrestrial LiDARs**

In the context of the PhD of Arnaud Bletterer (2014-2018), and in collaboration with Cintoo3D, We work on the reconstruction of complex scenes captured by terrestrial LiDARs. Nowadays, LiDARs are able to generate tens of millions of points from a single acquisition. The main benefit of this considerable change lies in their capacity to capture extremely detailed surfaces. But this comes with a severe complexity in time and in memory, making the reconstruction very challenging, even sometimes impossible, with usual surface reconstruction approaches. The goal of our current work is to develop an algorithm that generates mesh surfaces from terrestrial LiDAR acquisitions, while preserving the topology of the captured reality. We already showed nice results from a single 360° terrestrial LiDAR acquisition of more than tens of millions of points.

**Semi-regular meshing and coding**.

During Jean-Luc Peyrot’s PhD (2011–2014), in collaboration with the Le2i laboratory of University of Burgundy, we proposed a framework for simplifiying the classical 3D digitization chain, first by improving the sampling of surfaces, and second by shortening the number of required treatments to obtain semi-regular meshes. More precisely, we integrated in a stereoscopic acquisition system:

- a blue noise sampling that preserves geometrical features [hal-01058835]. This technique ensures the fidelity to the initial shape while limiting the number of points. We proposed two versions: the first version handles meshes obtained by triangulation of the point clouds generated by the acquisition system, and generates the blue noise directly in the 3D space. The second version handles directly the stereoscopic images to get the final surface sampling. To the best of our knowledge, no prior work proposes such an approach, despite the advantage of controlling the number of sampling points at the beginning of the sampling/reconstruction process to avoid oversampled data as output;
- a semi-regular surface meshing [hal-01236999] that directly works on the stereoscopic 2D images and not on the triangulation of the point cloud generated by such acquisition systems. Our method can be seen as a parameterization based technique, as the remeshing process is driven by the connectivity of the stereoscopic images. Also, our reconstruction method processes the data as much as possible into the image domain, before embedding the surface in the 3D space. Our method is an alternative to the fastidious pipeline to get semi-regular meshes from physical objects.

**Hexahedral mesh coding**.

In collaboration with IFP-Energies Nouvelles, we also focus now on the compression of massive structured hexahedral meshes. Such meshes are common in geosciences and, as expected, their size is a drawback for storage, transmission, but also for numerical simulations (flow simulations for instance). Moreover, in this domain, meshes are generally based on a pillar grid structure. This structure has the advantage to give a regular connectivity to hexahedra, while allowing the modeling of geometrical discontinuities that may occur in the meshes coming from geosciences. These discontinuities describe mainly gaps in the physical terrains. Therefore we proposed a novel compression scheme for such data [hal-01315079]. Our scheme generates a hierarchy of meshes at increasing levels of resolution, while ensuring a geometrical coherency over the resolutions. Our main contribution is a lossless and reversible wavelet filtering that takes into account the geometrical discontinuities in order to preserve them whatever the resolution, but also manages the categorial properties that are generally associated with hexahedra in geosciences during analysis.