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 "Geometric algorithms"

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    Fast Planar Harmonic Deformations with Alternating Tangential Projections
    (The Eurographics Association and John Wiley & Sons Ltd., 2017) Hefetz, Eden Fedida; Chien, Edward; Weber, Ofir; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
    We present a planar harmonic cage-based deformation method with local injectivity and bounded distortion guarantees, that is significantly faster than state-of-the-art methods with similar guarantees, and allows for real-time interaction. With a convex proxy for a near-convex characterization of the bounded distortion harmonic mapping space from [LW16], we utilize a modified alternating projection method (referred to as ATP) to project to this proxy. ATP draws inspiration from [KABL15] and restricts every other projection to lie in a tangential hyperplane. In contrast to [KABL15], our convex setting allows us to show that ATP is provably convergent (and is locally injective). Compared to the standard alternating projection method, it demonstrates superior convergence in fewer iterations, and it is also embarrassingly parallel, allowing for straightforward GPU implementation. Both of these factors combine to result in unprecedented speed. The convergence proof generalizes to arbitrary pairs of intersecting convex sets, suggesting potential use in other applications. Additional theoretical results sharpen the near-convex characterization that we use and demonstrate that it is homeomorphic to the bounded distortion harmonic mapping space (instead of merely being bijective).
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    GWCNN: A Metric Alignment Layer for Deep Shape Analysis
    (The Eurographics Association and John Wiley & Sons Ltd., 2017) Ezuz, Danielle; Solomon, Justin; Kim, Vladimir G.; Ben-Chen, Mirela; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
    Deep neural networks provide a promising tool for incorporating semantic information in geometry processing applications. Unlike image and video processing, however, geometry processing requires handling unstructured geometric data, and thus data representation becomes an important challenge in this framework. Existing approaches tackle this challenge by converting point clouds, meshes, or polygon soups into regular representations using, e.g., multi-view images, volumetric grids or planar parameterizations. In each of these cases, geometric data representation is treated as a fixed pre-process that is largely disconnected from the machine learning tool. In contrast, we propose to optimize for the geometric representation during the network learning process using a novel metric alignment layer. Our approach maps unstructured geometric data to a regular domain by minimizing the metric distortion of the map using the regularized Gromov-Wasserstein objective. This objective is parameterized by the metric of the target domain and is differentiable; thus, it can be easily incorporated into a deep network framework. Furthermore, the objective aims to align the metrics of the input and output domains, promoting consistent output for similar shapes. We show the effectiveness of our layer within a deep network trained for shape classification, demonstrating state-of-the-art performance for nonrigid shapes.
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    Modeling and Exploring Co-variations in the Geometry and Configuration of Man-made 3D Shape Families
    (The Eurographics Association and John Wiley & Sons Ltd., 2017) Laga, Hamid; Tabia, Hedi; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
    We introduce co-variation analysis as a tool for modeling the way part geometries and configurations co-vary across a family of man-made 3D shapes. While man-made 3D objects exhibit large geometric and structural variations, the geometry, structure, and configuration of their individual components usually do not vary independently from each other but in a correlated fashion. The size of the body of an airplane, for example, constrains the range of deformations its wings can undergo to ensure that the entire object remains a functionally-valid airplane. These co-variation constraints, which are often non-linear, can be either physical, and thus they can be explicitly enumerated, or implicit to the design and style of the shape family. In this article, we propose a data-driven approach, which takes pre-segmented 3D shapes with known component-wise correspondences and learns how various geometric and structural properties of their components co-vary across the set. We demonstrate, using a variety of 3D shape families, the utility of the proposed co-variation analysis in various applications including 3D shape repositories exploration and shape editing where the propagation of deformations is guided by the co-variation analysis. We also show that the framework can be used for context-guided orientation of objects in 3D scenes.
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    A Parallel Approach to Compression and Decompression of Triangle Meshes using the GPU
    (The Eurographics Association and John Wiley & Sons Ltd., 2017) Jakob, Johannes; Buchenau, Christoph; Guthe, Michael; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
    Most state-of-the-art compression algorithms use complex connectivity traversal and prediction schemes, which are not efficient enough for online compression of large meshes. In this paper we propose a scalable massively parallel approach for compression and decompression of large triangle meshes using the GPU. Our method traverses the input mesh in a parallel breadth-first manner and encodes the connectivity data similarly to the well known cut-border machine. Geometry data is compressed using a local prediction strategy. In contrast to the original cut-border machine, we can additionally handle triangle meshes with inconsistently oriented faces. Our approach is more than one order of magnitude faster than currently used methods and achieves competitive compression rates.