40-Issue 5

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https://diglib.eg.org/handle/10.2312/2633079

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Browsing 40-Issue 5 by Subject "based models"

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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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    Stable and Efficient Differential Estimators on Oriented Point Clouds
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Lejemble, Thibault; Coeurjolly, David; Barthe, Loïc; Mellado, Nicolas; Digne, Julie and Crane, Keenan
    Point clouds are now ubiquitous in computer graphics and computer vision. Differential properties of the point-sampled surface, such as principal curvatures, are important to estimate in order to locally characterize the scanned shape. To approximate the surface from unstructured points equipped with normal vectors, we rely on the Algebraic Point Set Surfaces (APSS) [GG07] for which we provide convergence and stability proofs for the mean curvature estimator. Using an integral invariant viewpoint, this first contribution links the algebraic sphere regression involved in the APSS algorithm to several surface derivatives of different orders. As a second contribution, we propose an analytic method to compute the shape operator and its principal curvatures from the fitted algebraic sphere. We compare our method to the state-of-the-art with several convergence and robustness tests performed on a synthetic sampled surface. Experiments show that our curvature estimations are more accurate and stable while being faster to compute compared to previous methods. Our differential estimators are easy to implement with little memory footprint and only require a unique range neighbors query per estimation. Its highly parallelizable nature makes it appropriate for processing large acquired data, as we show in several real-world experiments.