Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Iterative solution methods
Topics in optimization and sparse linear systems
Topics in optimization and sparse linear systems
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multigrid
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
SHAPE FROM SHADING: A METHOD FOR OBTAINING THE SHAPE OF A SMOOTH OPAQUE OBJECT FROM ONE VIEW
SHAPE FROM SHADING: A METHOD FOR OBTAINING THE SHAPE OF A SMOOTH OPAQUE OBJECT FROM ONE VIEW
Segmentation Given Partial Grouping Constraints
IEEE Transactions on Pattern Analysis and Machine Intelligence
Support Theory for Preconditioning
SIAM Journal on Matrix Analysis and Applications
Multilabel Random Walker Image Segmentation Using Prior Models
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
SIAM Journal on Matrix Analysis and Applications
Locally adapted hierarchical basis preconditioning
ACM SIGGRAPH 2006 Papers
Random Walks for Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
A linear work, O(n1/6) time, parallel algorithm for solving planar Laplacians
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Combinatorial and algebraic tools for optimal multilevel algorithms
Combinatorial and algebraic tools for optimal multilevel algorithms
Nonlocal Image and Movie Denoising
International Journal of Computer Vision
Real-time gradient-domain painting
ACM SIGGRAPH 2008 papers
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
IEEE Transactions on Pattern Analysis and Machine Intelligence
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Fourier Analysis of the 2D Screened Poisson Equation for Gradient Domain Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Efficient Nonlocal Means for Denoising of Textural Patterns
IEEE Transactions on Image Processing
Hierarchical Diagonal Blocking and Precision Reduction Applied to Combinatorial Multigrid
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
A breakthrough in algorithm design
Communications of the ACM
Multigrid and multilevel preconditioners for computational photography
Proceedings of the 2011 SIGGRAPH Asia Conference
The laplacian paradigm: emerging algorithms for massive graphs
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
A matrix hyperbolic cosine algorithm and applications
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Runtime guarantees for regression problems
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Spectral Image Segmentation Using Image Decomposition and Inner Product-Based Metric
Journal of Mathematical Imaging and Vision
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Linear systems and eigen-calculations on symmetric diagonally dominant matrices (SDDs) occur ubiquitously in computer vision, computer graphics, and machine learning. In the past decade a multitude of specialized solvers have been developed to tackle restricted instances of SDD systems for a diverse collection of problems including segmentation, gradient inpainting and total variation. In this paper we explain and apply the support theory of graphs, a set of of techniques developed by the computer science theory community, to construct SDD solvers with provable properties. To demonstrate the power of these techniques, we describe an efficient multigrid-like solver which is based on support theory principles. The solver tackles problems in fairly general and arbitrarily weighted topologies not supported by prior solvers. It achieves state of the art empirical results while providing robust guarantees on the speed of convergence. The method is evaluated on a variety of vision applications.