SGP13: Eurographics Symposium on Geometry Processing (CGF 32-5)

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https://diglib.eg.org/handle/10.2312/14332

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Animation-Aware Quadrangulation
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Marcias, Giorgio; Pietroni, Nico; Panozzo, Daniele; Puppo, Enrico; Sorkine-Hornung, Olga; Yaron Lipman and Hao Zhang
Geometric meshes that model animated characters must be designed while taking into account the deformations that the shape will undergo during animation. We analyze an input sequence of meshes with point-to-point correspondence, and we automatically produce a quadrangular mesh that fits well the input animation. We first analyze the local deformation that the surface undergoes at each point, and we initialize a cross field that remains as aligned as possible to the principal directions of deformation throughout the sequence. We then smooth this cross field based on an energy that uses a weighted combination of the initial field and the local amount of stretch. Finally, we compute a field-aligned quadrangulation with an off-the-shelf method. Our technique is fast and very simple to implement, and it significantly improves the quality of the output quad mesh and its suitability for character animation, compared to creating the quad mesh based on a single pose. We present experimental results and comparisons with a state-of-the-art quadrangulation method, on both sequences from 3D scanning and synthetic sequences obtained by a rough animation of a triangulated model.
Discrete Line Congruences for Shading and Lighting
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Wang, Jun; Jiang, Caigui; Bompas, Philippe; Wallner, Johannes; Pottmann, Hellmut; Yaron Lipman and Hao Zhang
Two-parameter families of straight lines (line congruences) are implicitly present in graphics and geometry processing in several important ways including lighting and shape analysis. In this paper we make them accessible to optimization and geometric computing, by introducing a general discrete version of congruences based on piecewise-linear correspondences between triangle meshes. Our applications of congruences are based on the extraction of a so-called torsion-free support structure, which is a procedure analogous to remeshing a surface along its principal curvature lines. A particular application of such structures are freeform shading and lighting systems for architecture. We combine interactive design of such systems with global optimization in order to satisfy geometric constraints. In this way we explore a new area where architecture can greatly benefit from graphics.
Fast and Robust Approximation of Smallest Enclosing Balls in Arbitrary Dimensions
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Larsson, Thomas; Källberg, Linus; Yaron Lipman and Hao Zhang
In this paper, an algorithm is introduced that computes an arbitrarily fine approximation of the smallest enclosing ball of a point set in any dimension. This operation is important in, for example, classification, clustering, and data mining. The algorithm is very simple to implement, gives reliable results, and gracefully handles large problem instances in low and high dimensions, as confirmed by both theoretical arguments and empirical evaluation. For example, using a CPU with eight cores, it takes less than two seconds to compute a 1:001-approximation of the smallest enclosing ball of one million points uniformly distributed in a hypercube in dimension 200. Furthermore, the presented approach extends to a more general class of input objects, such as ball sets.
Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Paillé, Gilles-Philippe; Poulin, Pierre; Lévy, Bruno; Yaron Lipman and Hao Zhang
We propose a method for mapping polynomial volumes. Given a closed surface and an initial template volume grid, our method deforms the template grid by fitting its boundary to the input surface while minimizing a volume distortion criterion. The result is a point-to-point map distorting linear cells into curved ones. Our method is based on several extensions of Voronoi Squared Distance Minimization (VSDM) combined with a higher-order finite element formulation of the deformation energy. This allows us to globally optimize the mapping without prior parameterization. The anisotropic VSDM formulation allows for sharp and semi-sharp features to be implicitly preserved without tagging. We use a hierarchical finite element function basis that selectively adapts to the geometric details. This makes both the method more efficient and the representation more compact. We apply our method to geometric modeling applications in computer-aided design and computer graphics, including mixed-element meshing, mesh optimization, subdivision volume fitting, and shell meshing.
Noise-Adaptive Shape Reconstruction from Raw Point Sets
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Giraudot, Simon; Cohen-Steiner, David; Alliez, Pierre; Yaron Lipman and Hao Zhang
We propose a noise-adaptive shape reconstruction method specialized to smooth, closed shapes. Our algorithm takes as input a defect-laden point set with variable noise and outliers, and comprises three main steps. First, we compute a novel noise-adaptive distance function to the inferred shape, which relies on the assumption that the inferred shape is a smooth submanifold of known dimension. Second, we estimate the sign and confidence of the function at a set of seed points, through minimizing a quadratic energy expressed on the edges of a uniform random graph. Third, we compute a signed implicit function through a random walker approach with soft constraints chosen as the most confident seed points computed in previous step.
An Operator Approach to Tangent Vector Field Processing
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Azencot, Omri; Ben-Chen, Mirela; Chazal, Frédéric; Ovsjanikov, Maks; Yaron Lipman and Hao Zhang
In this paper, we introduce a novel coordinate-free method for manipulating and analyzing vector fields on discrete surfaces. Unlike the commonly used representations of a vector field as an assignment of vectors to the faces of the mesh, or as real values on edges, we argue that vector fields can also be naturally viewed as operators whose domain and range are functions defined on the mesh. Although this point of view is common in differential geometry it has so far not been adopted in geometry processing applications. We recall the theoretical properties of vector fields represented as operators, and show that composition of vector fields with other functional operators is natural in this setup. This leads to the characterization of vector field properties through commutativity with other operators such as the Laplace-Beltrami and symmetry operators, as well as to a straight-forward definition of differential properties such as the Lie derivative. Finally, we demonstrate a range of applications, such as Killing vector field design, symmetric vector field estimation and joint design on multiple surfaces.
Practical Anisotropic Geodesy
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Campen, Marcel; Heistermann, Martin; Kobbelt, Leif; Yaron Lipman and Hao Zhang
The computation of intrinsic, geodesic distances and geodesic paths on surfaces is a fundamental low-level building block in countless Computer Graphics and Geometry Processing applications. This demand led to the development of numerous algorithms - some for the exact, others for the approximative computation, some focussing on speed, others providing strict guarantees. Most of these methods are designed for computing distances according to the standard Riemannian metric induced by the surface's embedding in Euclidean space. Generalization to other, especially anisotropic, metrics - which more recently gained interest in several application areas - is not rarely hampered by fundamental problems. We explore and discuss possibilities for the generalization and extension of well-known methods to the anisotropic case, evaluate their relative performance in terms of accuracy and speed, and propose a novel algorithm, the Short-Term Vector Dijkstra. This algorithm is strikingly simple to implement and proves to provide practical accuracy at a higher speed than generalized previous methods.
Semantizing Complex 3D Scenes using Constrained Attribute Grammars
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Boulch, Alexandre; Houllier, Simon; Marlet, Renaud; Tournaire, Olivier; Yaron Lipman and Hao Zhang
We propose a new approach to automatically semantize complex objects in a 3D scene. For this, we define an expressive formalism combining the power of both attribute grammars and constraint. It offers a practical conceptual interface, which is crucial to write large maintainable specifications. As recursion is inadequate to express large collections of items, we introduce maximal operators, that are essential to reduce the parsing search space. Given a grammar in this formalism and a 3D scene, we show how to automatically compute a shared parse forest of all interpretations - in practice, only a few, thanks to relevant constraints. We evaluate this technique for building model semantization using CAD model examples as well as photogrammetric and simulated LiDAR data.
Sparse Iterative Closest Point
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Bouaziz, Sofien; Tagliasacchi, Andrea; Pauly, Mark; Yaron Lipman and Hao Zhang
Rigid registration of two geometric data sets is essential in many applications, including robot navigation, surface reconstruction, and shape matching. Most commonly, variants of the Iterative Closest Point (ICP) algorithm are employed for this task. These methods alternate between closest point computations to establish correspondences between two data sets, and solving for the optimal transformation that brings these correspondences into alignment. A major difficulty for this approach is the sensitivity to outliers and missing data often observed in 3D scans. Most practical implementations of the ICP algorithm address this issue with a number of heuristics to prune or reweight correspondences. However, these heuristics can be unreliable and difficult to tune, which often requires substantial manual assistance. We propose a new formulation of the ICP algorithm that avoids these difficulties by formulating the registration optimization using sparsity inducing norms. Our new algorithm retains the simple structure of the ICP algorithm, while achieving superior registration results when dealing with outliers and incomplete data. The complete source code of our implementation is provided at http://lgg.epfl.ch/sparseicp.
Watertight Scenes from Urban LiDAR and Planar Surfaces
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Kreveld, Marc van; Lankveld, Thijs van; Veltkamp, Remco C.; Yaron Lipman and Hao Zhang
The demand for large geometric models is increasing, especially of urban environments. This has resulted in production of massive point cloud data from images or LiDAR. Visualization and further processing generally require a detailed, yet concise representation of the scene's surfaces. Related work generally either approximates the data with the risk of over-smoothing, or interpolates the data with excessive detail. Many surfaces in urban scenes can be modeled more concisely by planar approximations. We present a method that combines these polygons into a watertight model. The polygon-based shape is closed with free-form meshes based on visibility information. To achieve this, we divide 3-space into inside and outside volumes by combining a constrained Delaunay tetrahedralization with a graph-cut. We compare our method with related work on several large urban LiDAR data sets. We construct similar shapes with a third fewer triangles to model the scenes. Additionally, our results are more visually pleasing and closer to a human modeler's description of urban scenes using simple boxes.

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Browsing SGP13: Eurographics Symposium on Geometry Processing (CGF 32-5) by Subject "Computational Geometry and Object Modeling"

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