SGP: Eurographics Symposium on Geometry Processing

Permanent URI for this community

https://diglib.eg.org/handle/10.2312/434

Browse

Browsing SGP: Eurographics Symposium on Geometry Processing by Subject "3D Shape Matching"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    CustomCut: On-demand Extraction of Customized 3D Parts with 2D Sketches
    (The Eurographics Association and John Wiley & Sons Ltd., 2016) Guo, Xuekun; Lin, Juncong; Xu, Kai; Chaudhuri, Siddhartha; Jin, Xiaogang; Maks Ovsjanikov and Daniele Panozzo
    Several applications in shape modeling and exploration require identification and extraction of a 3D shape part matching a 2D sketch. We present CustomCut, an on-demand part extraction algorithm. Given a sketched query, CustomCut automatically retrieves partially matching shapes from a database, identifies the region optimally matching the query in each shape, and extracts this region to produce a customized part that can be used in various modeling applications. In contrast to earlier work on sketch-based retrieval of predefined parts, our approach can extract arbitrary parts from input shapes and does not rely on a prior segmentation into semantic components. The method is based on a novel data structure for fast retrieval of partial matches: the randomized compound k-NN graph built on multi-view shape projections. We also employ a coarse-to-fine strategy to progressively refine part boundaries down to the level of individual faces. Experimental results indicate that our approach provides an intuitive and easy means to extract customized parts from a shape database, and significantly expands the design space for the user. We demonstrate several applications of our method to shape design and exploration.
  • Thumbnail Image
    Item
    Functional Maps on Product Manifolds
    (The Eurographics Association, 2018) Rodolà, Emanuele; Lähner, Zorah; Bronstein, Alex M.; Bronstein, Michael M.; Solomon, Justin; Ju, Tao and Vaxman, Amir
    We consider the tasks of representing, analyzing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain. To apply these ideas in practice, we introduce localized spectral analysis of the product manifold as a novel tool for map processing.
  • Thumbnail Image
    Item
    Stable Region Correspondences Between Non-Isometric Shapes
    (The Eurographics Association and John Wiley & Sons Ltd., 2016) Ganapathi-Subramanian, Vignesh; Thibert, Boris; Ovsjanikov, Maks; Guibas, Leonidas; Maks Ovsjanikov and Daniele Panozzo
    We consider the problem of finding meaningful correspondences between 3D models that are related but not necessarily very similar. When the shapes are quite different, a point-to-point map is not always appropriate, so our focus in this paper is a method to build a set of correspondences between shape regions or parts. The proposed approach exploits a variety of feature functions on the shapes and makes use of the key observation that points in matching parts have similar ranks in the sorting of the corresponding feature values. Our algorithm proceeds in two steps. We first build an affinity matrix between points on the two shapes, based on feature rank similarity over many feature functions. We then define a notion of stability of a pair of regions, with respect to this affinity matrix, obtained as a fixed point of a nonlinear operator. Our method yields a family of corresponding maximally stable regions between the two shapes that can be used to define shape parts. We observe that this is an instance of the biclustering problem and that it is related to solving a constrained maximal eigenvalue problem. We provide an algorithm to solve this problem that mimics the power method. We show the robustness of its output to noisy input features as well its convergence properties. The obtained part correspondences are shown to be almost perfect matches in the isometric case, and also semantically appropriate even in non-isometric cases. We provide numerous examples and applications of this technique, for example to sharpening correspondences in traditional shape matching algorithms.