Browsing by Author "Ben-Chen, Mirela"

Now showing 1 - 4 of 4
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    BPM: Blended Piecewise Möbius Maps
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Rorberg, Shir; Vaxman, Amir; Ben-Chen, Mirela; Memari, Pooran; Solomon, Justin
    We propose a novel Möbius interpolator that takes as an input a discrete map between the vertices of two planar triangle meshes, and outputs a continuous map on the input domain. The output map interpolates the discrete map, is continuous between triangles, and has low quasi-conformal distortion when the input map is discrete conformal. Our map leads to considerably smoother texture transfer compared to the alternatives, even on very coarse triangulations. Furthermore, our approach has a closed-form expression, is local, applicable to any discrete map, and leads to smooth results even for extreme deformations. Finally, by working with local intrinsic coordinates, our approach is easily generalizable to discrete maps between a surface triangle mesh and a planar mesh, i.e., a planar parameterization. We compare our method with existing approaches, and demonstrate better texture transfer results, and lower quasi-conformal errors.
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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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    Hierarchical Functional Maps between Subdivision Surfaces
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Shoham‬‏, ‪Meged; Vaxman, Amir; Ben-Chen, Mirela; Bommes, David and Huang, Hui
    We propose a novel approach for computing correspondences between subdivision surfaces with different control polygons. Our main observation is that the multi-resolution spectral basis functions that are often used for computing a functional correspondence can be compactly represented on subdivision surfaces, and therefore can be efficiently computed. Furthermore, the reconstruction of a pointwise map from a functional correspondence also greatly benefits from the subdivision structure. Leveraging these observations, we suggest a hierarchical pipeline for functional map inference, allowing us to compute correspondences between surfaces at fine subdivision levels, with hundreds of thousands of polygons, an order of magnitude faster than existing correspondence methods. We demonstrate the applicability of our results by transferring high-resolution sculpting displacement maps and textures between subdivision models.
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    Robust Shape Collection Matching and Correspondence from Shape Differences
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Cohen, Aharon; Ben-Chen, Mirela; Panozzo, Daniele and Assarsson, Ulf
    We propose a method to automatically match two shape collections with a similar shape space structure, e.g. two characters in similar poses, and compute the inter-maps between the collections. Given the intra-maps in each collection, we extract the corresponding shape difference operators, and use them to construct an embedding of the shape space of each collection. We then align the two shape spaces, and use the knowledge gained from the alignment to compute the inter-maps. Unlike existing approaches for collection alignment, our method is applicable to small and large collections alike, and requires no parameter tuning. Furthermore, unlike most approaches for non-isometric correspondence, our method uses solely the variation within the collection to extract the inter-maps, and therefore does not require landmarks, descriptors or any additional input. We demonstrate that we achieve high matching accuracy rates, and compute high quality maps on non-isometric shapes, which compare favorably with automatic state-of-the-art methods for non-isometric shape correspondence.