Browsing by Author "Heeren, Behrend"

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    Elastic Correspondence between Triangle Meshes
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Ezuz, Danielle; Heeren, Behrend; Azencot, Omri; Rumpf, Martin; Ben-Chen, Mirela; Alliez, Pierre and Pellacini, Fabio
    We propose a novel approach for shape matching between triangular meshes that, in contrast to existing methods, can match crease features. Our approach is based on a hybrid optimization scheme, that solves simultaneously for an elastic deformation of the source and its projection on the target. The elastic energy we minimize is invariant to rigid body motions, and its non-linear membrane energy component favors locally injective maps. Symmetrizing this model enables feature aligned correspondences even for non-isometric meshes. We demonstrate the advantage of our approach over state of the art methods on isometric and non-isometric datasets, where we improve the geodesic distance from the ground truth, the conformal and area distortions, and the mismatch of the mean curvature functions. Finally, we show that our computed maps are applicable for surface interpolation, consistent cross-field computation, and consistent quadrangular remeshing of a set of shapes.
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    Solving Variational Problems Using Nonlinear Rotation-invariant Coordinates
    (The Eurographics Association, 2019) Sassen, Josua; Heeren, Behrend; Hildebrandt, Klaus; Rumpf, Martin; Bommes, David and Huang, Hui
    We consider Nonlinear Rotation-Invariant Coordinates (NRIC) representing triangle meshes with fixed combinatorics as a vector stacking all edge lengths and dihedral angles. Previously, conditions for the existence of vertex positions matching given NRIC have been established. We develop the machinery needed to use NRIC for solving geometric optimization problems. Moreover, we introduce a fast and robust algorithm that reconstructs vertex positions from close-to integrable NRIC. Our experiments underline that NRIC-based optimization is especially effective for near-isometric problems.