Browsing by Author "Marin, Diana"

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    Parameter-Free and Improved Connectivity for Point Clouds
    (The Eurographics Association, 2023) Marin, Diana; Ohrhallinger, Stefan; Wimmer, Michael; Singh, Gurprit; Chu, Mengyu (Rachel)
    Determining connectivity in unstructured point clouds is a long-standing problem that is still not addressed satisfactorily. In this poster, we propose an extension to the proximity graph introduced in [MOW22] to three-dimensional models. We use the spheres-of-influence (SIG) proximity graph restricted to the 3D Delaunay graph to compute connectivity between points. Our approach shows a better encoding of the connectivity in relation to the ground truth than the k-nearest neighborhood (kNN) for a wide range of k values, and additionally, it is parameter-free. Our result for this fundamental task offers potential for many applications relying on kNN, e.g., improvements in normal estimation, surface reconstruction, motion planning, simulations, and many more.
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    SIGDT: 2D Curve Reconstruction
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Marin, Diana; Ohrhallinger, Stefan; Wimmer, Michael; Umetani, Nobuyuki; Wojtan, Chris; Vouga, Etienne
    Determining connectivity between points and reconstructing their shape boundaries are long-standing problems in computer graphics. One possible approach to solve these problems is to use a proximity graph. We propose a new proximity graph computed by intersecting the to-date rarely used proximity-based graph called spheres-of-influence graph (SIG) with the Delaunay triangulation (DT). We prove that the resulting graph, which we name SIGDT, contains the piece-wise linear reconstruction for a set of unstructured points in the plane for a sampling condition superseding current bounds and capturing well practical point sets' properties. As an application, we apply a dual of boundary adjustment steps from the CONNECT2D algorithm to remove the redundant edges. We show that the resulting algorithm SIG-CONNECT2D yields the best reconstruction accuracy compared to state-of-the-art algorithms from a recent comprehensive benchmark, and the method offers the potential for further improvements, e.g., for surface reconstruction.