SGP18: Eurographics Symposium on Geometry Processing - Posters

Permanent URI for this collection

https://diglib.eg.org/handle/10.2312/2632599

Browse

Browsing SGP18: Eurographics Symposium on Geometry Processing - Posters by Issue Date

Filter results by year or month
Now showing 1 - 6 of 6
  • 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
    Out-of-core Resampling of Gigantic Point Clouds
    (The Eurographics Association, 2018) Bletterer, Arnaud; Payan, Frédéric; Antonini, Marc; Meftah, Anis; Ju, Tao and Vaxman, Amir
    Nowadays, LiDAR scanners are able to capture complex scenes of real life, leading to extremely detailed point clouds. However, the amount of points acquired (several billions) and their distribution raise the problem of sampling a surface optimally. Indeed, these point clouds finely describe the acquired scene, but also exhibit numerous defects in terms of sampling quality, and sometimes contain too many samples to be processed as they are. In this work, we introduce a local graph-based structure that enables to manipulate gigantic point clouds, by taking advantage of their inherent structure. In particular, we show how this structure allows to resample gigantic point clouds efficiently, with good blue-noise properties, whatever their size in a reasonable time.
  • Thumbnail Image
    Item
    Using Mathematical Morphology to Simplify Archaeological Fracture Surfaces
    (The Eurographics Association, 2018) ElNaghy, Hanan; Dorst, Leo; Ju, Tao and Vaxman, Amir
    It is computationally expensive to fit the high-resolution 3D meshes of abraded fragments of archaeological artefacts in a collection. Therefore, simplification of fracture surfaces while preserving the fitting essentials is required to guide and structure the whole reassembly process. Features of the scale spaces from Mathematical Morphology (MM) permit a hierarchical approach to this simplification, in a contact-preserving manner, while being insensitive to missing geometry. We propose a new method to focusing MM on the fracture surfaces only, by an embedding that uses morphological duality to compute the desired opening by a closing. The morphological scale space operations on the proposed dual embedding of archaeological fracture surfaces are computed in a distance transform treatment of voxelized meshes.
  • Thumbnail Image
    Item
    Solving PDEs on Deconstructed Domains
    (The Eurographics Association, 2018) Sellán, Silvia; Cheng, Herng Yi; Ma, Yuming; Dembowski, Mitchell; Jacobson, Alec; Ju, Tao and Vaxman, Amir
    When finding analytical solutions to Partial Differential Equations (PDEs) becomes impossible, it is useful to approximate them via a discrete mesh of the domain. Sometimes a robust triangular (2D) or tetrahedral (3D) mesh of the whole domain is a hard thing to accomplish, and in those cases we advocate for breaking up the domain in various different subdomains with nontrivial intersection and to find solutions for the equation in each of them individually. Although this approach solves one issue,it creates another, i.e. what constraints to impose on the separate solutions in a way that they converge to true solution on their union. We present a method that solves this problem for the most common second and fourth order equations in graphics.
  • Thumbnail Image
    Item
    Frontmatter: Symposium on Geometry Processing 2018 - Posters
    (The Eurographics Association, 2018) Ju, Tao; Vaxman, Amir; Ju, Tao and Vaxman, Amir
  • Thumbnail Image
    Item
    Denoising of Point-clouds Based on Structured Dictionary Learning
    (The Eurographics Association, 2018) Sarkar, Kripasindhu; Bernard, Florian; Varanasi, Kiran; Theobalt, Christian; Stricker, Didier; Ju, Tao and Vaxman, Amir
    We formulate the problem of point-cloud denoising in terms of a dictionary learning framework over square surface patches. Assuming that many of the local patches (in the unknown noise-free point-cloud) contain redundancies due to surface smoothness and repetition, we estimate a low-dimensional affine subspace that (approximately) explains the extracted noisy patches. This is achieved via a structured low-rank matrix factorization that imposes smoothness on the patch dictionary and sparsity on the coefficients. We show experimentally that our method outperforms existing denoising approaches in various noise scenarios.