SGP18: Eurographics Symposium on Geometry Processing - Posters

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

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Browsing SGP18: Eurographics Symposium on Geometry Processing - Posters by Subject "Computational Geometry and Object Modeling"

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    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.
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    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.