Geometrical, topological and perceptual analysis of 3D meshes




Regular Centroidal Voronoi tessellations

We advocate the use of a regularity criterion to evaluate the quality of Centroidal Voronoi tessellations (CVTs). We propose a hierarchical algorithm that constructs more regular 3D CVTs than related work. We also propose an algorithm to compute CVTs from implicit volumetric forms and show that the resulting CVTs better approximate the input shape than voxel grids bounded with Marching Cubes or Delaunay tetrahedrizations, for a variety of criteria.

Context:  Li Wang's PhD thesis.
Co-workers:  Li Wang (PhD student), Edmond Boyer (research director, Inria).
More details:  CVT Generator software, [CGF'16], [ECCV'16].


Mesh repair with interactive topology control

We propose an algorithm to transform any kind of mesh (a triangle soup, for instance) into a 2-manifold, with an interactive control of the topology.

Context:  started during my postdoc at UPC, Barcelona.
Co-workers:  Carlos Andújar (associate professor, UPC), Pere Brunet (professor, UPC), Àlvar Vinàcua (associate professor, UPC), Stéphanie Rey (Ensimag intern).
More details:  [CAD'11].


Constriction computation on triangulated surfaces

Constrictions are locally shortest closed curves. Automatic detection of these curves can be of great interest for several applications in the area of surface understanding. I have developed several algorithms to do this. I have also investigated (not very successfully) their relation with the surface's local geometry (e.g., curvatures).

Context:  part of my PhD thesis.
Co-worker:  Dominique Attali (researcher, CNRS).
More details:  [VisSym'03], [Pacific Graphics'03 (short)], [Eurographics'05 (short)].




Computation of the homology of simplicial complexes

We propose an algorithm to compute the homology groups (of any dimension) of simplicial complexes. Our method is based on the theory of constructive homology.

Context:  IDEAL project.
Co-workers:  Dobrina Boltcheva (postdoc), Sara Merino Aceituno (Master student), Jean-Claude Léon (professor, Univ. Grenoble), Leila De Floriani (professor, Univ. Genova), David Canino (PhD student, Univ. Genova), Francis Sergeraert (professor, Univ. Grenoble).
More details:  [RR'10], [CAD/SPM'11].


Classification of non-manifold singularities in 3D models

This work aims at classifying possible topological singularities discarding a simplicial complex mesh to be a manifold.

Context:  IDEAL project.
Co-workers:  Jean-Claude Léon (professor, Univ. Grenoble), Leila De Floriani (professor, Univ. Genova).
More details:  [SMI'09].


Topological quadrangulation of 3D shapes

We propose a topological decomposition of a 3D shape (represented as a triangular mesh) into quadrangles.

Context:  part of my PhD thesis.
Co-workers:  Dominique Attali (researcher, CNRS).
More details:  [GMod'03].


Visual perception


Just-noticeable distortion profile for meshes

We analyse how much vertices of a mesh can move without the human eye to notice.

Context:  part of Georges Nader's PhD thesis and PADME project.
Co-workers:  Georges Nader (PhD student), Kai Wang (researcher, CNRS), Florent Dupont (professor, Univ. Lyon).
More details:  [TVCG'16], [PG'16].