SGP09: Eurographics Symposium on Geometry Processing
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Separatrix Persistence: Extraction of Salient Edges on Surfaces Using Topological Methods
(The Eurographics Association and Blackwell Publishing Ltd, 2009)Salient edges are perceptually prominent features of a surface. Most previous extraction schemes utilize the notion of ridges and valleys for their detection, thereby requiring curvature derivatives which are rather sensitive ... -
Estimating the Laplace-Beltrami Operator by Restricting 3D Functions
(The Eurographics Association and Blackwell Publishing Ltd, 2009)We present a novel approach for computing and solving the Poisson equation over the surface of a mesh. As in previous approaches, we define the Laplace-Beltrami operator by considering the derivatives of functions defined ... -
Discrete Critical Values: a General Framework for Silhouettes Computation
(The Eurographics Association and Blackwell Publishing Ltd, 2009)Many shapes resulting from important geometric operations in industrial applications such as Minkowski sums or volume swept by a moving object can be seen as the projection of higher dimensional objects. When such a higher ... -
Approximating Gradients for Meshes and Point Clouds via Diffusion Metric
(The Eurographics Association and Blackwell Publishing Ltd, 2009)The gradient of a function defined on a manifold is perhaps one of the most important differential objects in data analysis. Most often in practice, the input function is available only at discrete points sampled from the ... -
Stability of Curvature Measures
(The Eurographics Association and Blackwell Publishing Ltd, 2009)We address the problem of curvature estimation from sampled compact sets. The main contribution is a stability result: we show that the Gaussian, mean or anisotropic curvature measures of the offset of a compact set K with ... -
Filtering Relocations on a Delaunay Triangulation
(The Eurographics Association and Blackwell Publishing Ltd, 2009)Updating a Delaunay triangulation when its vertices move is a bottleneck in several domains of application. Rebuilding the whole triangulation from scratch is surprisingly a very viable option compared to relocating the ... -
Feature preserving Delaunay mesh generation from 3D multi-material images
(The Eurographics Association and Blackwell Publishing Ltd, 2009)Generating realistic geometric models from 3D segmented images is an important task in many biomedical applications. Segmented 3D images impose particular challenges for meshing algorithms because they contain multi-material ... -
Isotropic Remeshing with Fast and Exact Computation of Restricted Voronoi Diagram
(The Eurographics Association and Blackwell Publishing Ltd, 2009)We propose a new isotropic remeshing method, based on Centroidal Voronoi Tessellation (CVT). Constructing CVT requires to repeatedly compute Restricted Voronoi Diagram (RVD), defined as the intersection between a 3D Voronoi ... -
Localized Quadrilateral Coarsening
(The Eurographics Association and Blackwell Publishing Ltd, 2009)In this paper we introduce a coarsening algorithm for quadrilateral meshes that generates quality, quad-only connectivity during level-of-coarsening creation. A novel aspect of this work is development and implementation ... -
Multi-objective shape segmentation and labeling
(The Eurographics Association and Blackwell Publishing Ltd, 2009)Shape segmentations designed for different applications show significant variation in the composition of their parts. In this paper, we introduce the segmentation and labeling of shape based on the simultaneous optimization ... -
Semi-regular Quadrilateral-only Remeshing from Simplified Base Domains
(The Eurographics Association and Blackwell Publishing Ltd, 2009)Semi-regular meshes describe surface models that exhibit a structural regularity that facilitates many geometric processing algorithms. We introduce a technique to construct semi-regular, quad-only meshes from input surface ... -
A Concise and Provably Informative Multi-Scale Signature Based on Heat Diffusion
(The Eurographics Association and Blackwell Publishing Ltd, 2009)We propose a novel point signature based on the properties of the heat diffusion process on a shape. Our signature, called the Heat Kernel Signature (or HKS), is obtained by restricting the well-known heat kernel to the ... -
Gromov-Hausdorff Stable Signatures for Shapes using Persistence
(The Eurographics Association and Blackwell Publishing Ltd, 2009)We introduce a family of signatures for finite metric spaces, possibly endowed with real valued functions, based on the persistence diagrams of suitable filtrations built on top of these spaces. We prove the stability of ... -
Isotopic Reconstruction of Surfaces with Boundaries
(The Eurographics Association and Blackwell Publishing Ltd, 2009)We present an algorithm for the reconstruction of a surface with boundaries (including a non-orientable one) in three dimensions from a sufficiently dense sample. It is guaranteed that the output is isotopic to the unknown ... -
Shape Analysis Using the Auto Diffusion Function
(The Eurographics Association and Blackwell Publishing Ltd, 2009)Scalar functions defined on manifold triangle meshes is a starting point for many geometry processing algorithms such as mesh parametrization, skeletonization, and segmentation. In this paper, we propose the Auto Diffusion ... -
Recovering Structure from r-Sampled Objects
(The Eurographics Association and Blackwell Publishing Ltd, 2009)For a surface in 3-space that is represented by a set S of sample points, we construct a coarse approximating polytope P that uses a subset of S as its vertices and preserves the topology of . In contrast to surface ... -
Smoothing of Partition of Unity Implicit Surfaces for Noise Robust Surface Reconstruction
(The Eurographics Association and Blackwell Publishing Ltd, 2009)We propose a novel method for smoothing partition of unity (PU) implicit surfaces consisting of sets of non-conforming linear functions with spherical supports. We derive new discrete differential operators and Laplacian ... -
Manifold Homotopy via the Flow Complex
(The Eurographics Association and Blackwell Publishing Ltd, 2009)It is known that the critical points of the distance function induced by a dense sample P of a submanifold ? of R?n are distributed into two groups, one lying close to ? itself, called the shallow, and the other close to ... -
Reconstruction of Multi-Label Domains from Partial Planar Cross-Sections
(The Eurographics Association and Blackwell Publishing Ltd, 2009)We present a novel algorithm for reconstructing a subdivision of the three-dimensional space (given arbitrarily-oriented slices of it) into labeled domains. The input to the algorithm is a collection of nonparallel planar ... -
Rotating Scans for Systematic Error Removal
(The Eurographics Association and Blackwell Publishing Ltd, 2009)Optical triangulation laser scanners produce errors at surface discontinuities and sharp features. These systematic errors are anisotropic. We examine the causes of these errors theoretically, and we study the correlation ...
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