Browsing by Author "Kazhdan, Misha"

Now showing 1 - 6 of 6
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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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    Dense Point-to-Point Correspondences Between Genus-Zero Shapes
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Lee, Sing Chun; Kazhdan, Misha; Bommes, David and Huang, Hui
    We describe a novel approach that addresses the problem of establishing correspondences between non-rigidly deformed shapes by performing the registration over the unit sphere. In a pre-processing step, each shape is conformally parametrized over the sphere, centered to remove Möbius inversion ambiguity, and authalically evolved to expand regions that are excessively compressed by the conformal parametrization. Then, for each pair of shapes, we perform fast SO(3) correlation to find the optimal rotational alignment and refine the registration using optical flow. We evaluate our approach on the TOSCA dataset, demonstrating that our approach compares favorably to state-of-the-art methods.
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    Poisson Manifold Reconstruction - Beyond Co-dimension One
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Kohlbrenner, Maximilian; Lee, Singchun; Alexa, Marc; Kazhdan, Misha; Memari, Pooran; Solomon, Justin
    Screened Poisson Surface Reconstruction creates 2D surfaces from sets of oriented points in 3D (and can be extended to codimension one surfaces in arbitrary dimensions). In this work we generalize the technique to manifolds of co-dimension larger than one. The reconstruction problem consists of finding a vector-valued function whose zero set approximates the input points. We argue that the right extension of screened Poisson Surface Reconstruction is based on exterior products: the orientation of the point samples is encoded as the exterior product of the local normal frame. The goal is to find a set of scalar functions such that the exterior product of their gradients matches the exterior products prescribed by the input points. We show that this setup reduces to the standard formulation for co-dimension 1, and leads to more challenging multi-quadratic optimization problems in higher co-dimension. We explicitly treat the case of co-dimension 2, i.e., curves in 3D and 2D surfaces in 4D. We show that the resulting bi-quadratic problem can be relaxed to a set of quadratic problems in two variables and that the solution can be made effective and efficient by leveraging a hierarchical approach.
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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.
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    Polygon Laplacian Made Simple
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Bunge, Astrid; Herholz, Philipp; Kazhdan, Misha; Botsch, Mario; Panozzo, Daniele and Assarsson, Ulf
    The discrete Laplace-Beltrami operator for surface meshes is a fundamental building block for many (if not most) geometry processing algorithms. While Laplacians on triangle meshes have been researched intensively, yielding the cotangent discretization as the de-facto standard, the case of general polygon meshes has received much less attention. We present a discretization of the Laplace operator which is consistent with its expression as the composition of divergence and gradient operators, and is applicable to general polygon meshes, including meshes with non-convex, and even non-planar, faces. By virtually inserting a carefully placed point we implicitly refine each polygon into a triangle fan, but then hide the refinement within the matrix assembly. The resulting operator generalizes the cotangent Laplacian, inherits its advantages, and is empirically shown to be on par or even better than the recent polygon Laplacian of Alexa and Wardetzky [AW11] - while being simpler to compute.
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    Volumetric Video - Acquisition, Compression, Interaction and Perception
    (The Eurographics Association, 2021) Zell, Eduard; Castan, Fabien; Gasparini, Simone; Hilsmann, Anna; Kazhdan, Misha; Tagliasacchi, Andrea; Zarpalas, Dimitris; Zioulis, Nick; O'Sullivan, Carol and Schmalstieg, Dieter
    Volumetric video, free-viewpoint video or 4D reconstruction refer to the process of reconstructing 3D content over time using a multi-view setup. This method is constantly gaining popularity both in research and industry. In fact, volumetric video is more and more considered to acquire dynamic photorealistic content instead of relying on traditional 3D content creation pipelines. The aim of the tutorial is to provide an overview of the entire volumetric video pipeline. Furthermore, it presents existing projects that may serve as a starting point to this topic at the intersection of computer vision and graphics. The first part of the tutorial will focus on the process of computing 3D models from captured videos. Topics will include content acquisition with affordable hardware, photogrammetry, and surface reconstruction from point clouds. A remarkable contribution of the presenters to the graphics community is that they will not only provide an overview of their topic but have in addition open sourced their implementations. Topics of the second part will focus on usage and distribution of volumetric video, including data compression, streaming or post-processing like pose-modification or seamless blending. The tutorial will conclude with an overview of perceptual studies focusing on quality assessment of 3D and 4D content.