Image Analysis Using Multigrid Relaxation Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Surface Interpolation Using Hierarchical Basis Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hierarchical and variational geometric modeling with wavelets
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A multigrid tutorial: second edition
A multigrid tutorial: second edition
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Gradient domain high dynamic range compression
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Interpolation Using Wavelet Bases
IEEE Transactions on Pattern Analysis and Machine Intelligence
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
ACM SIGGRAPH 2003 Papers
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ACM SIGGRAPH 2004 Papers
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ACM SIGGRAPH 2004 Papers
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Locally adapted hierarchical basis preconditioning
ACM SIGGRAPH 2006 Papers
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ACM SIGGRAPH 2007 papers
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IEEE Transactions on Pattern Analysis and Machine Intelligence
Edge-preserving decompositions for multi-scale tone and detail manipulation
ACM SIGGRAPH 2008 papers
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ACM SIGGRAPH 2008 papers
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ACM SIGGRAPH 2009 papers
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ACM SIGGRAPH 2009 papers
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ACM SIGGRAPH Asia 2009 papers
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
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ACM Transactions on Graphics (TOG)
Efficient Multilevel Eigensolvers with Applications to Data Analysis Tasks
IEEE Transactions on Pattern Analysis and Machine Intelligence
A parallel multigrid Poisson solver for fluids simulation on large grids
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Domain transform for edge-aware image and video processing
ACM SIGGRAPH 2011 papers
A fast solver for a class of linear systems
Communications of the ACM
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ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Efficient preconditioning of laplacian matrices for computer graphics
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Large-scale flip-chip power grid reduction with geometric templates
Proceedings of the Conference on Design, Automation and Test in Europe
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This paper unifies multigrid and multilevel (hierarchical) preconditioners, two widely-used approaches for solving computational photography and other computer graphics simulation problems. It provides detailed experimental comparisons of these techniques and their variants, including an analysis of relative computational costs and how these impact practical algorithm performance. We derive both theoretical convergence rates based on the condition numbers of the systems and their preconditioners, and empirical convergence rates drawn from real-world problems. We also develop new techniques for sparsifying higher connectivity problems, and compare our techniques to existing and newly developed variants such as algebraic and combinatorial multigrid. Our experimental results demonstrate that, except for highly irregular problems, adaptive hierarchical basis function preconditioners generally outperform alternative multigrid techniques, especially when computational complexity is taken into account.