36-Issue 5

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https://diglib.eg.org/handle/10.2312/2631654

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Browsing 36-Issue 5 by Subject "Computational Geometry and Object Modelling"

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    The Shape Variational Autoencoder: A Deep Generative Model of Part-segmented 3D Objects
    (The Eurographics Association and John Wiley & Sons Ltd., 2017) Nash, Charlie; Williams, Chris K. I.; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
    We introduce a generative model of part-segmented 3D objects: the shape variational auto-encoder (ShapeVAE). The ShapeVAE describes a joint distribution over the existence of object parts, the locations of a dense set of surface points, and over surface normals associated with these points. Our model makes use of a deep encoder-decoder architecture that leverages the partdecomposability of 3D objects to embed high-dimensional shape representations and sample novel instances. Given an input collection of part-segmented objects with dense point correspondences the ShapeVAE is capable of synthesizing novel, realistic shapes, and by performing conditional inference enables imputation of missing parts or surface normals. In addition, by generating both points and surface normals, our model allows for the use of powerful surface-reconstruction methods for mesh synthesis. We provide a quantitative evaluation of the ShapeVAE on shape-completion and test-set log-likelihood tasks and demonstrate that the model performs favourably against strong baselines. We demonstrate qualitatively that the ShapeVAE produces plausible shape samples, and that it captures a semantically meaningful shape-embedding. In addition we show that the ShapeVAE facilitates mesh reconstruction by sampling consistent surface normals.
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    Stochastic Heat Kernel Estimation on Sampled Manifolds
    (The Eurographics Association and John Wiley & Sons Ltd., 2017) Aumentado-Armstrong, Tristan; Siddiqi, Kaleem; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
    The heat kernel is a fundamental geometric object associated to every Riemannian manifold, used across applications in computer vision, graphics, and machine learning. In this article, we propose a novel computational approach to estimating the heat kernel of a statistically sampled manifold (e.g. meshes or point clouds), using its representation as the transition density function of Brownian motion on the manifold. Our approach first constructs a set of local approximations to the manifold via moving least squares. We then simulate Brownian motion on the manifold by stochastic numerical integration of the associated Ito diffusion system. By accumulating a number of these trajectories, a kernel density estimation method can then be used to approximate the transition density function of the diffusion process, which is equivalent to the heat kernel. We analyse our algorithm on the 2-sphere, as well as on shapes in 3D. Our approach is readily parallelizable and can handle manifold samples of large size as well as surfaces of high co-dimension, since all the computations are local. We relate our method to the standard approaches in diffusion geometry and discuss directions for future work.