Results 1  10
of
105
Least Squares Conformal Maps for Automatic Texture Atlas Generation
, 2002
"... A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded charts are packed in texture space. Existing texture atlas methods for triangulated surfaces suffer from ..."
Abstract

Cited by 329 (7 self)
 Add to MetaCart
(Show Context)
A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded charts are packed in texture space. Existing texture atlas methods for triangulated surfaces suffer from several limitations, requiring them to generate a large number of small charts with simple borders. The discontinuities between the charts cause artifacts, and make it difficult to paint large areas with regular patterns.
Surface Parameterization: a Tutorial and Survey
 In Advances in Multiresolution for Geometric Modelling, Mathematics and Visualization
, 2005
"... Summary. This paper provides a tutorial and survey of methods for parameterizing surfaces with a view to applications in geometric modelling and computer graphics. We gather various concepts from differential geometry which are relevant to surface mapping and use them to understand the strengths and ..."
Abstract

Cited by 243 (7 self)
 Add to MetaCart
Summary. This paper provides a tutorial and survey of methods for parameterizing surfaces with a view to applications in geometric modelling and computer graphics. We gather various concepts from differential geometry which are relevant to surface mapping and use them to understand the strengths and weaknesses of the many methods for parameterizing piecewise linear surfaces and their relationship to one another. 1
BigBang Simulation for Embedding Network Distances in Euclidean Space
, 2004
"... Embedding of a graph metric in Euclidean space efficiently and accurately is an important problem in general with applications in topology aggregation, closest mirror selection, and application level routing. We propose a new graph embedding scheme called BigBang Simulation (BBS), which simulates a ..."
Abstract

Cited by 152 (4 self)
 Add to MetaCart
(Show Context)
Embedding of a graph metric in Euclidean space efficiently and accurately is an important problem in general with applications in topology aggregation, closest mirror selection, and application level routing. We propose a new graph embedding scheme called BigBang Simulation (BBS), which simulates an explosion of particles under force field derived from embedding error. BBS is shown to be significantly more accurate, compared to all other embedding methods including GNP. We report an extensive simulation study of BBS compared with several known embedding schemes and show its advantage for distance estimation (as in the IDMaps project), mirror selection and topology aggregation.
Expressioninvariant 3D face recognition
, 2003
"... We present a novel 3D face recognition approach based on geometric invariants introduced by Elad and Kimmel. The key idea of the proposed algorithm is a representation of the facial surface, invariant to isometric deformations, such as those resulting from different expressions and postures of the ..."
Abstract

Cited by 108 (17 self)
 Add to MetaCart
(Show Context)
We present a novel 3D face recognition approach based on geometric invariants introduced by Elad and Kimmel. The key idea of the proposed algorithm is a representation of the facial surface, invariant to isometric deformations, such as those resulting from different expressions and postures of the face. The obtained geometric invariants allow mapping 2D facial texture images into special images that incorporate the 3D geometry of the face. These signature images are then decomposed into their principal components. The result is an efficient and accurate face recognition algorithm that is robust to facial expressions. We demonstrate the results of our method and compare it to existing 2D and 3D face recognition algorithms.
Greedy optimal homotopy and homology generators
 Proc. 16th Ann. ACMSIAM Symp. Discrete Algorithms
, 2005
"... Abstract We describe simple greedy algorithms to construct the shortest set of loops that generates either the fundamental group (with a given basepoint) or the first homology group (over any fixed coefficient field) of any oriented 2manifold. In particular, we show that the shortest set of loops t ..."
Abstract

Cited by 107 (11 self)
 Add to MetaCart
Abstract We describe simple greedy algorithms to construct the shortest set of loops that generates either the fundamental group (with a given basepoint) or the first homology group (over any fixed coefficient field) of any oriented 2manifold. In particular, we show that the shortest set of loops that generate the fundamental group of any oriented combinatorial 2manifold, with any given basepoint, can be constructed in O(n log n) time using a straightforward application of Dijkstra's shortest path algorithm. This solves an open problem of Colin de Verdi`ere and Lazarus.
Efficient Computation of IsometryInvariant Distances between Surfaces
"... We present an efficient computational framework for isometryinvariant comparison of smooth surfaces. We formulate the GromovHausdorff distance as a multidimensional scaling (MDS)like continuous optimization problem. In order to construct an efficient optimization scheme, we develop a numerical ..."
Abstract

Cited by 94 (25 self)
 Add to MetaCart
(Show Context)
We present an efficient computational framework for isometryinvariant comparison of smooth surfaces. We formulate the GromovHausdorff distance as a multidimensional scaling (MDS)like continuous optimization problem. In order to construct an efficient optimization scheme, we develop a numerical tool for interpolating geodesic distances on a sampled surface from precomputed geodesic distances between the samples. For isometryinvariant comparison of surfaces in the case of partially missing data, we present the partial embedding distance, which is computed using a similar scheme. The main idea is finding a minimumdistortion mapping from one surface to another, while considering only relevant geodesic distances. We discuss numerical implementation issues and present experimental results that demonstrate its accuracy and efficiency.
Boundeddistortion piecewise mesh paramterization
 IEEE Visualization’02
, 2002
"... ..."
(Show Context)
Mesh parameterization methods and their applications
 FOUNDATIONS AND TRENDSÂŐ IN COMPUTER GRAPHICS AND VISION
, 2006
"... We present a survey of recent methods for creating piecewise linear mappings between triangulations in 3D and simpler domains such as planar regions, simplicial complexes, and spheres. We also discuss emerging tools such as global parameterization, intersurface mapping, and parameterization with co ..."
Abstract

Cited by 69 (1 self)
 Add to MetaCart
(Show Context)
We present a survey of recent methods for creating piecewise linear mappings between triangulations in 3D and simpler domains such as planar regions, simplicial complexes, and spheres. We also discuss emerging tools such as global parameterization, intersurface mapping, and parameterization with constraints. We start by describing the wide range of applications where parameterization tools have been used in recent years. We then briefly review the pertinent mathematical background and terminology, before proceeding to survey the existing parameterization techniques. Our survey summarizes the main ideas of each technique and discusses its main properties, comparing it to other methods available. Thus it aims to provide guidance to researchers and developers when assessing the suitability of different methods for various applications. This survey focuses on the practical aspects of the methods available, such as time complexity and robustness and shows multiple examples of parameterizations generated using different methods, allowing the reader to visually evaluate and compare the results.
Fast computation of weighted distance functions and geodesics on implicit hypersurfaces
 J. Comput. Phys
"... An algorithm for the computationally optimal construction of intrinsic weighted distance functions on implicit hypersurfaces is introduced in this paper. The basic idea is to approximate the intrinsic weighted distance by the Euclidean weighted distance computed in a band surrounding the implicit h ..."
Abstract

Cited by 64 (9 self)
 Add to MetaCart
(Show Context)
An algorithm for the computationally optimal construction of intrinsic weighted distance functions on implicit hypersurfaces is introduced in this paper. The basic idea is to approximate the intrinsic weighted distance by the Euclidean weighted distance computed in a band surrounding the implicit hypersurface in the embedding space, thereby performing all the computations in a Cartesian grid with classical and efficient numerics. Based on work on geodesics on Riemannian manifolds with boundaries, we bound the error between the two distance functions. We show that this error is of the same order as the theoretical numerical error in computationally optimal, Hamilton–Jacobibased, algorithms for computing distance functions in Cartesian grids. Therefore, we can use these algorithms, modified to deal with spaces with boundaries, and obtain also for the case of intrinsic distance functions on implicit hypersurfaces a computationally efficient technique. The approach can be extended to solve a more general class of Hamilton–Jacobi equations defined on the implicit surface, following the same idea of approximating their solutions by the solutions in the embedding Euclidean space. The framework here introduced thereby allows for the computations to be performed on a Cartesian grid with computationally optimal algorithms, in spite of the fact that the distance and Hamilton–Jacobi equations are intrinsic to the implicit hypersurface. c ○ 2001 Academic Press Key Words: implicit hypersurfaces; distance functions; geodesics; Hamilton– Jacobi equations; fast computations.