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
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Texture Synthesis by Non-Parametric Sampling
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
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
Convex Optimization
SIAM Journal on Matrix Analysis and Applications
Locally adapted hierarchical basis preconditioning
ACM SIGGRAPH 2006 Papers
Graph Partitioning by Spectral Rounding: Applications in Image Segmentation and Clustering
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
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
Analysis of Aggregation-Based Multigrid
SIAM Journal on Scientific Computing
Real-time gradient-domain painting
ACM SIGGRAPH 2008 papers
Faster approximate lossy generalized flow via interior point algorithms
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Non-local Regularization of Inverse Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
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
Generalizing the Nonlocal-means to super-resolution reconstruction
IEEE Transactions on Image Processing
Approaching Optimality for Solving SDD Linear Systems
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Efficient Nonlocal Means for Denoising of Textural Patterns
IEEE Transactions on Image Processing
A fast solver for a class of linear systems
Communications of the ACM
Efficient preconditioning of laplacian matrices for computer graphics
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
A simple, combinatorial algorithm for solving SDD systems in nearly-linear time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Several algorithms for problems including image segmentation, gradient inpainting and total variation are based on solving symmetric diagonally dominant (SDD) linear systems. These algorithms generally produce results of high quality. However, existing solvers are not always efficient, and in many cases they operate only on restricted topologies. The unavailability of reliably efficient solvers has arguably hindered the adoptability of approaches and algorithms based on SDD systems, especially in applications involving very large systems. A central claim of this paper is that SDD-based approaches can now be considered practical and reliable. To support our claim we present Combinatorial Multigrid (CMG), the first reliably efficient SDD solver that tackles problems in general and arbitrary weighted topologies. The solver borrows the structure and operators of multigrid algorithms, but embeds into them powerful and algebraically sound combinatorial preconditioners, based on novel tools from support graph theory. In order to present the derivation of CMG, we review and exemplify key notions of support graph theory that can also guide the future development of specialized solvers. We validate our claims on very large systems derived from imaging applications. Finally, we outline two new reductions of non-linear filtering problems to SDD systems and review the integration of SDD systems into selected algorithms.