Volume 37 (2018)

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Browsing Volume 37 (2018) by Subject "3D shape matching"

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    Localized Manifold Harmonics for Spectral Shape Analysis
    (© 2018 The Eurographics Association and John Wiley & Sons Ltd., 2018) Melzi, S.; Rodolà, E.; Castellani, U.; Bronstein, M. M.; Chen, Min and Benes, Bedrich
    The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback of such bases is their inherently global nature, as the Laplacian eigenfunctions carry geometric and topological structure of the entire manifold. In this paper, we introduce a new framework for local spectral shape analysis. We show how to efficiently construct localized orthogonal bases by solving an optimization problem that in turn can be posed as the eigendecomposition of a new operator obtained by a modification of the standard Laplacian. We study the theoretical and computational aspects of the proposed framework and showcase our new construction on the classical problems of shape approximation and correspondence. We obtain significant improvement compared to classical Laplacian eigenbases as well as other alternatives for constructing localized bases.The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback of such bases is their inherently global nature, as the Laplacian eigenfunctions carry geometric and topological structure of the entire manifold. In this paper, we introduce a new framework for local spectral shape analysis. We show how to efficiently construct localized orthogonal bases by solving an optimization problem that in turn can be posed as the eigendecomposition of a new operator obtained by a modification of the standard Laplacian.
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    Vector Field Map Representation for Near Conformal Surface Correspondence
    (© 2018 The Eurographics Association and John Wiley & Sons Ltd., 2018) Wang, Y.; Liu, B.; Zhou, K.; Tong, Y.; Chen, Min and Benes, Bedrich
    Based on a new spectral vector field analysis on triangle meshes, we construct a compact representation for near conformal mesh surface correspondences. Generalizing the functional map representation, our representation uses the map between the low‐frequency tangent vector fields induced by the correspondence. While our representation is as efficient, it is also capable of handling a more generic class of correspondence inference. We also formulate the vector field preservation constraints and regularization terms for correspondence inference, with function preservation treated as a special case. A number of important vector field–related constraints can be implicitly enforced in our representation, including the commutativity of the mapping with the usual gradient, curl, divergence operators or angle preservation under near conformal correspondence. For function transfer between shapes, the preservation of function values on landmarks can be strictly enforced through our gradient domain representation, enabling transfer across different topologies. With the vector field map representation, a novel class of constraints can be specified for the alignment of designed or computed vector field pairs. We demonstrate the advantages of the vector field map representation in tests on conformal datasets and near‐isometric datasets.Based on a new spectral vector field analysis on triangle meshes, we construct a compact representation for near conformal mesh surface correspondences. Generalizing the functional map representation, our representation uses the map between the low‐frequency tangent vector fields induced by the correspondence. While our representation is as efficient, it is also capable of handling a more generic class of correspondence inference. We also formulate the vector field preservation constraints and regularization terms for correspondence inference, with function preservation treated as a special case. A number of important vector field–related constraints can be implicitly enforced in our representation, including the commutativity of the mapping with the usual gradient, curl, divergence operators or angle preservation under near conformal correspondence.