Browsing by Author "Thiery, Jean-Marc"

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    Progressive Discrete Domains for Implicit Surface Reconstruction
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Zhao, Tong; Alliez, Pierre; Boubekeur, Tamy; Busé, Laurent; Thiery, Jean-Marc; Digne, Julie and Crane, Keenan
    Many global implicit surface reconstruction algorithms formulate the problem as a volumetric energy minimization, trading data fitting for geometric regularization. As a result, the output surfaces may be located arbitrarily far away from the input samples. This is amplified when considering i) strong regularization terms, ii) sparsely distributed samples or iii) missing data. This breaks the strong assumption commonly used by popular octree-based and triangulation-based approaches that the output surface should be located near the input samples. As these approaches refine during a pre-process, their cells near the input samples, the implicit solver deals with a domain discretization not fully adapted to the final isosurface. We relax this assumption and propose a progressive coarse-to-fine approach that jointly refines the implicit function and its representation domain, through iterating solver, optimization and refinement steps applied to a 3D Delaunay triangulation. There are several advantages to this approach: the discretized domain is adapted near the isosurface and optimized to improve both the solver conditioning and the quality of the output surface mesh contoured via marching tetrahedra.
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    Spectral Mesh Simplification
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Lescoat, Thibault; Liu, Hsueh-Ti Derek; Thiery, Jean-Marc; Jacobson, Alec; Boubekeur, Tamy; Ovsjanikov, Maks; Panozzo, Daniele and Assarsson, Ulf
    The spectrum of the Laplace-Beltrami operator is instrumental for a number of geometric modeling applications, from processing to analysis. Recently, multiple methods were developed to retrieve an approximation of a shape that preserves its eigenvectors as much as possible, but these techniques output a subset of input points with no connectivity, which limits their potential applications. Furthermore, the obtained Laplacian results from an optimization procedure, implying its storage alongside the selected points. Focusing on keeping a mesh instead of an operator would allow to retrieve the latter using the standard cotangent formulation, enabling easier processing afterwards. Instead, we propose to simplify the input mesh using a spectrum-preserving mesh decimation scheme, so that the Laplacian computed on the simplified mesh is spectrally close to the one of the input mesh. We illustrate the benefit of our approach for quickly approximating spectral distances and functional maps on low resolution proxies of potentially high resolution input meshes.