37-Issue 5

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https://diglib.eg.org/handle/10.2312/2632598

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Browsing 37-Issue 5 by Subject "Line and curve generation"

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    Modular Latent Spaces for Shape Correspondences
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Ganapathi-Subramanian, Vignesh; Diamanti, Olga; Guibas, Leonidas J.; Ju, Tao and Vaxman, Amir
    We consider the problem of transporting shape descriptors across shapes in a collection in a modular fashion, in order to establish correspondences between them. A common goal when mapping between multiple shapes is consistency, namely that compositions of maps along a cycle of shapes should be approximately an identity map. Existing attempts to enforce consistency typically require recomputing correspondences whenever a new shape is added to the collection, which can quickly become intractable. Instead, we propose an approach that is fully modular, where the bulk of the computation is done on each shape independently. To achieve this, we use intermediate nonlinear embedding spaces, computed individually on every shape; the embedding functions use ideas from diffusion geometry and capture how different descriptors on the same shape inter-relate. We then establish linear mappings between the different embedding spaces, via a shared latent space. The introduction of nonlinear embeddings allows for more nuanced correspondences, while the modularity of the construction allows for parallelizable calculation and efficient addition of new shapes. We compare the performance of our framework to standard functional correspondence techniques and showcase the use of this framework to simple interpolation and extrapolation tasks.
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    Statistical Modeling of the 3D Geometry and Topology of Botanical Trees
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Wang, Guan; Laga, Hamid; Jia, Jinyuan; Xie, Ning; Tabia, Hedi; Ju, Tao and Vaxman, Amir
    We propose a framework for statistical modeling of the 3D geometry and topology of botanical trees. We treat botanical trees as points in a tree-shape space equipped with a proper metric that captures the geometric and the topological differences between trees. Geodesics in the tree-shape space correspond to the optimal sequence of deformations, i.e. bending, stretching, and topological changes, which align one tree onto another. In this way, the 3D tree modeling and synthesis problem becomes a problem of exploring the tree-shape space either in a controlled fashion, using statistical regression, or randomly by sampling from probability distributions fitted to populations in the tree-shape space. We show how to use this framework for (1) computing statistical summaries, e.g. the mean and modes of variations, of a population of botanical trees, (2) synthesizing random instances of botanical trees from probability distributions fitted to a population of botanical trees, and (3) modeling, interactively, 3D botanical trees using a simple sketching interface. The approach is fast and only requires as input 3D botanical tree models with a known upright orientation.