SGP11: Eurographics Symposium on Geometry Processing
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An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes
(The Eurographics Association and Blackwell Publishing Ltd., 2011)We propose a robust 2D shape reconstruction and simplification algorithm which takes as input a defect-laden point set with noise and outliers. We introduce an optimal-transport driven approach where the input point set, ... -
Skeleton Computation of Orthogonal Polyhedra
(The Eurographics Association and Blackwell Publishing Ltd., 2011)Skeletons are powerful geometric abstractions that provide useful representations for a number of geometric operations. The straight skeleton has a lower combinatorial complexity compared with the medial axis. Moreover, ... -
A Multiscale Approach to Optimal Transport
(The Eurographics Association and Blackwell Publishing Ltd., 2011)In this paper, we propose an improvement of an algorithm of Aurenhammer, Hoffmann and Aronov to find a least square matching between a probability density and finite set of sites with mass constraints, in the Euclidean ... -
VASE: Volume-Aware Surface Evolution for Surface Reconstruction from Incomplete Point Clouds
(The Eurographics Association and Blackwell Publishing Ltd., 2011)Objects with many concavities are difficult to acquire using laser scanners. The highly concave areas are hard to access by a scanner due to occlusions by other components of the object. The resulting point scan typically ... -
On the Shape of a Set of Points and Lines in the Plane
(The Eurographics Association and Blackwell Publishing Ltd., 2011)Detailed geometric models of the real world are in increasing demand. LiDAR data is appropriate to reconstruct urban models. In urban scenes, the individual surfaces can be reconstructed and connected to form the scene ... -
As-Killing-As-Possible Vector Fields for Planar Deformation
(The Eurographics Association and Blackwell Publishing Ltd., 2011)Cartoon animation, image warping, and several other tasks in two-dimensional computer graphics reduce to the formulation of a reasonable model for planar deformation. A deformation is a map from a given shape to a new one, ... -
On Approximation of the Laplace-Beltrami Operator and the Willmore Energy of Surfaces
(The Eurographics Association and Blackwell Publishing Ltd., 2011)Discrete Laplace Beltrami operators on polyhedral surfaces play an important role for various applications in geometry processing and related areas like physical simulation or computer graphics. While discretizations of ... -
Multiscale Biharmonic Kernels
(The Eurographics Association and Blackwell Publishing Ltd., 2011)This paper introduces a general principle for constructing multiscale kernels on surface meshes, and presents a construction of the multiscale pre-biharmonic and multiscale biharmonic kernels. Our construction is based on ... -
A Complex View of Barycentric Mappings
(The Eurographics Association and Blackwell Publishing Ltd., 2011)Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two-dimensional ... -
Large-Scale Integer Linear Programming for Orientation Preserving 3D Shape Matching
(The Eurographics Association and Blackwell Publishing Ltd., 2011)We study an algorithmic framework for computing an elastic orientation-preserving matching of non-rigid 3D shapes. We outline an Integer Linear Programming formulation whose relaxed version can be minimized globally in ... -
Deformable 3D Shape Registration Based on Local Similarity Transforms
(The Eurographics Association and Blackwell Publishing Ltd., 2011)In this paper, a new method for deformable 3D shape registration is proposed. The algorithm computes shape transitions based on local similarity transforms which allows to model not only as-rigid-as-possible deformations ... -
An Optimization Approach to Improving Collections of Shape Maps
(The Eurographics Association and Blackwell Publishing Ltd., 2011)Finding an informative, structure-preserving map between two shapes has been a long-standing problem in geometry processing, involving a variety of solution approaches and applications. However, in many cases, we are given ... -
A Condition Number for Non-Rigid Shape Matching
(The Eurographics Association and Blackwell Publishing Ltd., 2011)Despite the large amount of work devoted in recent years to the problem of non-rigid shape matching, practical methods that can successfully be used for arbitrary pairs of shapes remain elusive. In this paper, we study the ... -
Coarse-to-Fine Combinatorial Matching for Dense Isometric Shape Correspondence
(The Eurographics Association and Blackwell Publishing Ltd., 2011)We present a dense correspondence method for isometric shapes, which is accurate yet computationally efficient. We minimize the isometric distortion directly in the 3D Euclidean space, i.e., in the domain where isometry ... -
A Hierarchical Grid Based Framework for Fast Collision Detection
(The Eurographics Association and Blackwell Publishing Ltd., 2011)We present a novel hierarchical grid based method for fast collision detection (CD) for deformable models on GPU architecture. A two-level grid is employed to accommodate the non-uniform distribution of practical scene ... -
A Multiscale Metric for 3D Mesh Visual Quality Assessment
(The Eurographics Association and Blackwell Publishing Ltd., 2011)Many processing operations are nowadays applied on 3D meshes like compression, watermarking, remeshing and so forth; these processes are mostly driven and/or evaluated using simple distortion measures like the Hausdorff ... -
Optimising Perceived Distortion in Lossy Encoding of Dynamic Meshes
(The Eurographics Association and Blackwell Publishing Ltd., 2011)Development of geometry data compression techniques in the past years has been limited by the lack of a metric with proven correlation with human perception of mesh distortion. Many algorithms have been proposed, but usually ... -
Localized Delaunay Refinement for Volumes
(The Eurographics Association and Blackwell Publishing Ltd., 2011)Delaunay refinement, recognized as a versatile tool for meshing a variety of geometries, has the deficiency that it does not scale well with increasing mesh size. The bottleneck can be traced down to the memory usage of ... -
All-Hex Mesh Generation via Volumetric PolyCube Deformation
(The Eurographics Association and Blackwell Publishing Ltd., 2011)While hexahedral mesh elements are preferred by a variety of simulation techniques, constructing quality all-hex meshes of general shapes remains a challenge. An attractive hex-meshing approach, often referred to as ... -
Rational Bi-cubic G2 Splines for Design with Basic Shapes
(The Eurographics Association and Blackwell Publishing Ltd., 2011)The paper develops a rational bi-cubic G<sup>2</sup> (curvature continuous) analogue of the non-uniform polynomial C<sup>2</sup> cubic B-spline paradigm. These rational splines can exactly reproduce ...
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