SGP19: Eurographics Symposium on Geometry Processing - Posters

Permanent URI for this collection

https://diglib.eg.org/handle/10.2312/2632798

Browse

Browsing SGP19: Eurographics Symposium on Geometry Processing - Posters by Title

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Adaptive Block Coordinate Descent for Distortion Minimization
    (The Eurographics Association, 2019) Naitsat, Alexander; Zeevi, Yehoshua Y.; Bommes, David and Huang, Hui
    We present a new unified algorithm for optimizing geometric energies and computing positively oriented simplicial mappings. Its major improvements over the state-of-the-art are: adaptive partition of vertices into coordinate blocks with the blended local-global strategy, introduction of new distortion energies for repairing inverted and degenerated simplices, modification of standard rotation-invariant measures, introduction of displacement norm for improving convergence criteria and for controlling the proposed local-global blending. Together these improvements form the basis for Adaptive Block Coordinate Descent (ABCD) algorithm aimed at robust geometric optimization. Our algorithm achieves state-of-the-art results in distortion minimization, even with highly distorted invalid initializations that contain thousands of inverted and degenerated elements. We show over a wide range of 2D and 3D problems that ABCD is more robust than existing techniques in locally injective mappings.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    Symposium on Geometry Processing 2019 – Posters: Frontmatter
    (Eurographics Association, 2019) Bommes, David; Huang, Hui; Bommes, David and Huang, Hui
  • Thumbnail Image
    Item
    Visual Assessments of Functional Maps
    (The Eurographics Association, 2019) Melzi, S.; Marin, R.; Musoni, P.; Castellani, U.; Tarini, M.; Bommes, David and Huang, Hui
    Shape-matching is one central topic in Geometry Processing, with numerous important applications in Computer Graphics and shape analysis, such as shape registration, shape interpolation, modeling, information transfer and many others. A recent and successful class of shape-matching methods is based on the functional maps framework [OBCS*12] where the correspondences between the two surfaces is described in terms of a mapping between functions. Several effective approaches have been proposed to produce accurate and reliable functional maps, leading to need for a way to assess the quality of a given solution. In particular, standard quantitative evaluation methods focus mainly on the global matching error disregarding the annoying effects of wrong correspondences along the surface details. Therefore, in this context, it is very important to pair quantitative numeric evaluations with a visual, qualitative assessment. Although this is usually not recognized as a problem, the latter task is not trivial, and we argue that the commonly employed solutions suffer from important limitations. In this work, we offer a new visual evaluation method which is based on the transfer of the object-space normals across the two spaces and then visualize the resulting lighting. In spite of its simplicity, this method produces readable images that allow subtleties of the mapping to be discerned, and improve direct comparability of alternative results.