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54
A Multigrid Method Enhanced By Krylov Subspace Iteration For Discrete Helmholtz Equations
, 1999
"... Standard multigrid algorithms have proven ineffective for the solution of discretizations of Helmholtz equations. In this work we modify the standard algorithm by adding GMRES iterations at coarse levels and as an outer iteration. We demonstrate the algorithm's effectiveness through theoretical ..."
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Cited by 79 (4 self)
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Standard multigrid algorithms have proven ineffective for the solution of discretizations of Helmholtz equations. In this work we modify the standard algorithm by adding GMRES iterations at coarse levels and as an outer iteration. We demonstrate the algorithm's effectiveness through theoretical analysis of a model problem and experimental results. In particular, we show that the combined use of GMRES as a smoother and outer iteration produces an algorithm whose performance depends relatively mildly on wave number and is robust for normalized wave numbers as large as two hundred. For fixed wave numbers, it displays gridindependent convergence rates and has costs proportional to the number of unknowns.
A multigrid platform for realtime motion computation with discontinuitypreserving variational methods
 International Journal of Computer Vision
, 2006
"... Abstract. Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such ad ..."
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Cited by 57 (15 self)
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Abstract. Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for realtime performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that realtime performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude.
A Variational Framework for Retinex
, 2003
"... Retinex theory addresses the problem of separating the illumination from the reflectance in a given image and thereby compensating for nonuniform lighting. This is in general an illposed problem. In this paper we propose a variational model for the Retinex problem that unifies previous methods. Si ..."
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Cited by 56 (2 self)
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Retinex theory addresses the problem of separating the illumination from the reflectance in a given image and thereby compensating for nonuniform lighting. This is in general an illposed problem. In this paper we propose a variational model for the Retinex problem that unifies previous methods. Similar to previous algorithms, it assumes spatial smoothness of the illumination field. In addition, knowledge of the limited dynamic range of the reflectance is used as a constraint in the recovery process. A penalty term is also included, exploiting apriori knowledge of the nature of the reflectance image. The proposed formulation adopts a Bayesian view point of the estimation problem, which leads to an algebraic regularization term, that contributes to better conditioning of the reconstruction problem.
Efficient linear system solvers for mesh processing
 IMA CONFERENCE ON THE MATHEMATICS OF SURFACES. VOLUME 3604 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2005
"... The use of polygonal mesh representations for freeform geometry enables the formulation of many important geometry processing tasks as the solution of one or several linear systems. As a consequence, the key ingredient for efficient algorithms is a fast procedure to solve linear systems. A large c ..."
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Cited by 42 (4 self)
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The use of polygonal mesh representations for freeform geometry enables the formulation of many important geometry processing tasks as the solution of one or several linear systems. As a consequence, the key ingredient for efficient algorithms is a fast procedure to solve linear systems. A large class of standard problems can further be shown to lead more specifically to sparse, symmetric, and positive definite systems, that allow for a numerically robust and efficient solution. In this paper we discuss and evaluate the use of sparse direct solvers for such kind of systems in geometry processing applications, since in our experiments they turned out to be superior even to highly optimized multigrid methods, but at the same time were considerably easier to use and implement. Although the methods we present are well known in the field of high performance computing, we observed that they are in practice surprisingly rarely applied to geometry processing problems.
Towards Fast NonRigid Registration
 IN INVERSE PROBLEMS, IMAGE ANALYSIS AND MEDICAL IMAGING, AMS SPECIAL SESSION INTERACTION OF INVERSE PROBLEMS AND IMAGE ANALYSIS
, 2002
"... A fast multiscale and multigrid method for the matching of images in 2D and 3D is presented. Especially in medical imaging this problem  denoted as the registration problem  is of fundamental importance in the handling of images from multiple image modalities or of image time series. The paper res ..."
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Cited by 39 (15 self)
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A fast multiscale and multigrid method for the matching of images in 2D and 3D is presented. Especially in medical imaging this problem  denoted as the registration problem  is of fundamental importance in the handling of images from multiple image modalities or of image time series. The paper restricts to the simplest matching energy to be minimized, i.e., E[] = R jf 1 f2 j , where f1 , f2 are the intensity maps of the two images to be matched and is a deformation. The focus is on a robust and efficient solution strategy. Matching of
Geometric Modeling Based on Triangle Meshes
"... This course is designed to cover the entire geometry processing pipeline based on triangle meshes. We will present the latest concepts for mesh generation and mesh repair, for geometry and topology optimizations like mesh smoothing, decimation, and remeshing, for parametrization, segmentation, and s ..."
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Cited by 18 (0 self)
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This course is designed to cover the entire geometry processing pipeline based on triangle meshes. We will present the latest concepts for mesh generation and mesh repair, for geometry and topology optimizations like mesh smoothing, decimation, and remeshing, for parametrization, segmentation, and shape editing. In addition to describing and discussing the related algorithms, we will also give valuable implementation hints and provide source code for most of the covered topics. The course assumes only very basic knowledge on geometric concepts in general, but does not require specific knowledge on polygonal meshes and how to discretize the respective problems for those. It is intended for computer graphics researchers, software developers and engineers from CAGD, computer games, or the movie industry, who are interested in geometry processing
Cascadic multiresolution methods for image deblurring
 SIAM J. Imag. Sci
"... Abstract. This paper investigates the use of cascadic multiresolution methods for image deblurring. Iterations with a conjugate gradienttype method are carried out on each level, and terminated by a stopping rule based on the discrepancy principle. Prolongation is carried out by nonlinear edgepres ..."
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Cited by 15 (7 self)
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Abstract. This paper investigates the use of cascadic multiresolution methods for image deblurring. Iterations with a conjugate gradienttype method are carried out on each level, and terminated by a stopping rule based on the discrepancy principle. Prolongation is carried out by nonlinear edgepreserving operators, which are defined via PDEs associated with Perona–Malik or total variationtype models. Computed examples demonstrate the effectiveness of the methods proposed.
Multigrid methods for obstacle problems
"... Abstract. In this review, we intend to clarify the underlying ideas and the relations between various multigrid methods ranging from subset decomposition, to projected subspace decomposition and truncated multigrid. In addition, we present a novel globally convergent inexact active set method which ..."
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Cited by 14 (2 self)
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Abstract. In this review, we intend to clarify the underlying ideas and the relations between various multigrid methods ranging from subset decomposition, to projected subspace decomposition and truncated multigrid. In addition, we present a novel globally convergent inexact active set method which is closely related to truncated multigrid. The numerical properties of algorithms are carefully assessed by means of a degenerate problem and a problem with a complicated coincidence set. 1.
A Parallel Algebraic Multigrid Solver on Graphics Processing Units ⋆
"... Abstract. The paper presents a multiGPU implementation of the preconditioned conjugate gradient algorithm with an algebraic multigrid preconditioner (PCGAMG) for an elliptic model problem on a 3D unstructured grid. An efficient parallel sparse matrixvector multiplication scheme underlying the PCG ..."
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Cited by 13 (1 self)
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Abstract. The paper presents a multiGPU implementation of the preconditioned conjugate gradient algorithm with an algebraic multigrid preconditioner (PCGAMG) for an elliptic model problem on a 3D unstructured grid. An efficient parallel sparse matrixvector multiplication scheme underlying the PCGAMG algorithm is presented for the manycore GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster and a multiGPU configuration with eight GPUs is about 100 times faster than a typical server CPU core. 1
Sensitive Couture for Interactive Garment Modeling and Editing
"... Figure 1: “2D or not 2D? ” This timeless question is rendered moot by Sensitive Couture, our tool for simultaneous, synchronized modeling and editing of both a 2D garment pattern (top) and its corresponding 3D drape (bottom). We present a novel interactive tool for garment design that enables, for t ..."
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Cited by 12 (3 self)
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Figure 1: “2D or not 2D? ” This timeless question is rendered moot by Sensitive Couture, our tool for simultaneous, synchronized modeling and editing of both a 2D garment pattern (top) and its corresponding 3D drape (bottom). We present a novel interactive tool for garment design that enables, for the first time, interactive bidirectional editing between 2D patterns and 3D highfidelity simulated draped forms. This provides a continuous, interactive, and natural design modality in which 2D and 3D representations are simultaneously visible and seamlessly maintain correspondence. Artists can now interactively edit 2D pattern designs and immediately obtain stable accurate feedback online, thus enabling rapid prototyping and an intuitive understanding of complex drape form.