Browsing by Author "Hoppe, Hugues"

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    An Adaptive Multi‐Grid Solver for Applications in Computer Graphics
    (© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Kazhdan, Misha; Hoppe, Hugues; Chen, Min and Benes, Bedrich
    A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution is known to be ‘interesting’ (e.g. high frequency) only in localized regions. In this work, we propose an adaptive, finite elements, multi‐grid solver capable of efficiently solving such linear systems. Our solver is designed to be general‐purpose, supporting finite elements of different degrees, across different dimensions and supporting both integrated and pointwise constraints. We demonstrate the efficacy of our solver in applications including surface reconstruction, image stitching and Euclidean Distance Transform calculation.A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution is known to be ‘interesting’ (e.g. high frequency) only in localized regions. In this work, we propose an adaptive, finite elements, multi‐grid solver capable of efficiently solving such linear systems. Our solver is designed to be general‐purpose, supporting finite elements of different degrees, across different dimensions and supporting both integrated and pointwise constraints.
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    Poisson Surface Reconstruction with Envelope Constraints
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Kazhdan, Misha; Chuang, Ming; Rusinkiewicz, Szymon; Hoppe, Hugues; Jacobson, Alec and Huang, Qixing
    Reconstructing surfaces from scanned 3D points has been an important research area for several decades. One common approach that has proven efficient and robust to noise is implicit surface reconstruction, i.e. fitting to the points a 3D scalar function (such as an indicator function or signed-distance field) and then extracting an isosurface. Though many techniques fall within this category, existing methods either impose no boundary constraints or impose Dirichlet/Neumann conditions on the surface of a bounding box containing the scanned data. In this work, we demonstrate the benefit of supporting Dirichlet constraints on a general boundary. To this end, we adapt the Screened Poisson Reconstruction algorithm to input a constraint envelope in addition to the oriented point cloud. We impose Dirichlet boundary conditions, forcing the reconstructed implicit function to be zero outside this constraint surface. Using a visual hull and/or depth hull derived from RGB-D scans to define the constraint envelope, we obtain substantially improved surface reconstructions in regions of missing data.