Search Results

Now showing 1 - 10 of 12
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    Deformation Transfer to Multi-Component Objects
    (The Eurographics Association and Blackwell Publishing Ltd, 2010) Zhou, Kun; Xu, Weiwei; Tong, Yiying; Desbrun, Mathieu
    We present a simple and effective algorithm to transfer deformation between surface meshes with multiple components. The algorithm automatically computes spatial relationships between components of the target object, builds correspondences between source and target, and finally transfers deformation of the source onto the target while preserving cohesion between the target s components. We demonstrate the versatility of our approach on various complex models.
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    ACM/EG Symposium on Computer Animation 2004
    (The Eurographics Association and Blackwell Publishing Ltd., 2004) Boulic, Ronan; Pai, Dinesh K.; Badler, Norman; Desbrun, Mathieu; Reveret, Lionel
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    Spectral Conformal Parameterization
    (The Eurographics Association and Blackwell Publishing Ltd, 2008) Mullen, Patrick; Tong, Yiying; Alliez, Pierre; Desbrun, Mathieu
    We present a spectral approach to automatically and efficiently obtain discrete free-boundary conformal parameterizations of triangle mesh patches, without the common artifacts due to positional constraints on vertices and without undue bias introduced by sampling irregularity. High-quality parameterizations are computed through a constrained minimization of a discrete weighted conformal energy by finding the largest eigenvalue/eigenvector of a generalized eigenvalue problem involving sparse, symmetric matrices. We demonstrate that this novel and robust approach improves on previous linear techniques both quantitatively and qualitatively.
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    Applied Geometry:Discrete Differential Calculus for Graphics
    (The Eurographics Association and Blackwell Publishing, Inc, 2004) Desbrun, Mathieu
    Geometry has been extensively studied for centuries, almost exclusively from a differential point of view. However, with the advent of the digital age, the interest directed to smooth surfaces has now partially shifted due to the growing importance of discrete geometry. From 3D surfaces in graphics to higher dimensional manifolds in mechanics, computational sciences must deal with sampled geometric data on a daily basis-hence our interest in Applied Geometry.In this talk we cover different aspects of Applied Geometry. First, we discuss the problem of Shape Approximation, where an initial surface is accurately discretized (i.e., remeshed) using anisotropic elements through error minimization. Second, once we have a discrete geometry to work with, we briefly show how to develop a full- blown discrete calculus on such discrete manifolds, allowing us to manipulate functions, vector fields, or even tensors while preserving the fundamental structures and invariants of the differential case. We will emphasize the applicability of our discrete variational approach to geometry by showing results on surface parameterization, smoothing, and remeshing, as well as virtual actors and thin-shell simulation.Joint work with: Pierre Alliez (INRIA) , David Cohen-Steiner (Duke U.), Eitan Grinspun (NYU), Anil Hirani (Caltech), Jerrold E. Marsden (Caltech), Mark Meyer (Pixar), Fred Pighin (USC), Peter Schroeder (Caltech), Yiying Tong (USC).
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    Spectral Affine-Kernel Embeddings
    (The Eurographics Association and John Wiley & Sons Ltd., 2017) Budninskiy, Max; Liu, Beibei; Tong, Yiying; Desbrun, Mathieu; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
    In this paper, we propose a controllable embedding method for high- and low-dimensional geometry processing through sparse matrix eigenanalysis. Our approach is equally suitable to perform non-linear dimensionality reduction on big data, or to offer non-linear shape editing of 3D meshes and pointsets. At the core of our approach is the construction of a multi-Laplacian quadratic form that is assembled from local operators whose kernels only contain locally-affine functions. Minimizing this quadratic form provides an embedding that best preserves all relative coordinates of points within their local neighborhoods. We demonstrate the improvements that our approach brings over existing nonlinear dimensionality reduction methods on a number of datasets, and formulate the first eigen-based as-rigid-as-possible shape deformation technique by applying our affine-kernel embedding approach to 3D data augmented with user-imposed constraints on select vertices.
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    Symmetry and Orbit Detection via Lie-Algebra Voting
    (The Eurographics Association and John Wiley & Sons Ltd., 2016) Shi, Zeyun; Alliez, Pierre; Desbrun, Mathieu; Bao, Hujun; Huang, Jin; Maks Ovsjanikov and Daniele Panozzo
    In this paper, we formulate an automatic approach to the detection of partial, local, and global symmetries and orbits in arbitrary 3D datasets. We improve upon existing voting-based symmetry detection techniques by leveraging the Lie group structure of geometric transformations. In particular, we introduce a logarithmic mapping that ensures that orbits are mapped to linear subspaces, hence unifying and extending many existing mappings in a single Lie-algebra voting formulation. Compared to previous work, our resulting method offers significantly improved robustness as it guarantees that our symmetry detection of an input model is frame, scale, and reflection invariant. As a consequence, we demonstrate that our approach efficiently and reliably discovers symmetries and orbits of geometric datasets without requiring heavy parameter tuning.
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    Intrinsic Parameterizations of Surface Meshes
    (Blackwell Publishers, Inc and the Eurographics Association, 2002) Desbrun, Mathieu; Meyer, Mark; Alliez, Pierre
    Parameterization of discrete surfaces is a fundamental and widely-used operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute least-distorted parameterizations of large meshes. In this paper, we present new theoretical and practical results on the parameterization of triangulated surface patches. Given a few desirable properties such as rotation and translation invariance, we show that the only admissible parameterizations form a two-dimensional set and each parameterization in this set can be computed using a simple, sparse, linear system. Since these parameterizations minimize the distortion of different intrinsic measures of the original mesh, we call them Intrinsic Parameterizations. In addition to this partial theoretical analysis, we propose robust, efficient and tunable tools to obtain least-distorted parameterizations automatically. In particular, we give details on a novel, fast technique to provide an optimal mapping without fixing the boundary positions, thus providing a unique Natural Intrinsic Parameterization. Other techniques based on this parameterization family, designed to ease the rapid design of parameterizations, are also proposed.
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    Discrete 2-Tensor Fields on Triangulations
    (The Eurographics Association and John Wiley and Sons Ltd., 2014) Goes, Fernando de; Liu, Beibei; Budninskiy, Max; Tong, Yiying; Desbrun, Mathieu; Thomas Funkhouser and Shi-Min Hu
    Geometry processing has made ample use of discrete representations of tangent vector fields and antisymmetric tensors (i.e., forms) on triangulations. Symmetric 2-tensors, while crucial in the definition of inner products and elliptic operators, have received only limited attention. They are often discretized by first defining a coordinate system per vertex, edge or face, then storing their components in this frame field. In this paper, we introduce a representation of arbitrary 2-tensor fields on triangle meshes. We leverage a coordinate-free decomposition of continuous 2-tensors in the plane to construct a finite-dimensional encoding of tensor fields through scalar values on oriented simplices of a manifold triangulation. We also provide closed-form expressions of pairing, inner product, and trace for this discrete representation of tensor fields, and formulate a discrete covariant derivative and a discrete Lie bracket. Our approach extends discrete/finite-element exterior calculus, recovers familiar operators such as the weighted Laplacian operator, and defines discrete notions of divergence-free, curl-free, and traceless tensors-thus offering a numerical framework for discrete tensor calculus on triangulations. We finally demonstrate the robustness and accuracy of our operators on analytical examples, before applying them to the computation of anisotropic geodesic distances on discrete surfaces
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    Robust Pointset Denoising of Piecewise-Smooth Surfaces through Line Processes
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Wei, Jiayi; Chen, Jiong; Rohmer, Damien; Memari, Pooran; Desbrun, Mathieu; Myszkowski, Karol; Niessner, Matthias
    Denoising is a common, yet critical operation in geometry processing aiming at recovering high-fidelity models of piecewisesmooth objects from noise-corrupted pointsets. Despite a sizable literature on the topic, there is a dearth of approaches capable of processing very noisy and outlier-ridden input pointsets for which no normal estimates and no assumptions on the underlying geometric features or noise type are provided. In this paper, we propose a new robust-statistics approach to denoising pointsets based on line processes to offer robustness to noise and outliers while preserving sharp features possibly present in the data. While the use of robust statistics in denoising is hardly new, most approaches rely on prescribed filtering using data-independent blending expressions based on the spatial and normal closeness of samples. Instead, our approach deduces a geometric denoising strategy through robust and regularized tangent plane fitting of the initial pointset, obtained numerically via alternating minimizations for efficiency and reliability. Key to our variational approach is the use of line processes to identify inliers vs. outliers, as well as the presence of sharp features. We demonstrate that our method can denoise sampled piecewise-smooth surfaces for levels of noise and outliers at which previous works fall short.
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    Angle-Analyzer: A Triangle-Quad Mesh Codec
    (Blackwell Publishers, Inc and the Eurographics Association, 2002) Lee, Haeyoung; Alliez, Pierre; Desbrun, Mathieu