Regularization of inverse visual problems involving discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
The connection machine
Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
On the multi-level splitting of finite element spaces
Numerische Mathematik
Image Analysis Using Multigrid Relaxation Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Visual reconstruction
The Computation of Visible-Surface Representations
IEEE Transactions on Pattern Analysis and Machine Intelligence
ECCV 90 Proceedings of the first european conference on Computer vision
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Optimal surface reconstruction from planar contours
Communications of the ACM
Finite element solution of boundary value problems: theory and computation
Finite element solution of boundary value problems: theory and computation
Bayesian Modeling of Uncertainty in Low-Level Vision
Bayesian Modeling of Uncertainty in Low-Level Vision
The Massively Parallel Processor
The Massively Parallel Processor
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Surface Reconstruction Preserving Discontinuities
Surface Reconstruction Preserving Discontinuities
Information-based complexity in nonlinear equations and computer vision (multivariate splines, optimal algorithms, zero-finding)
Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of Illuminant Direction, Albedo, and Shape from Shading
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Hierarchical and variational geometric modeling with wavelets
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Fast Scalable Algorithm for Discontinuous Optical Flow Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
A fast Gibbs sampler for synthesizing constrained fractals
Proceedings of the 7th conference on Visualization '96
Motion Estimation with Quadtree Splines
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spline-Based Image Registration
International Journal of Computer Vision
Physically Based Adaptive Preconditioning for Early Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
Scattered Data Interpolation with Multilevel B-Splines
IEEE Transactions on Visualization and Computer Graphics
A Fast Gibbs Sampler for Synthesizing Constrained Fractals
IEEE Transactions on Visualization and Computer Graphics
The L/sub 2/-Polynomial Spline Pyramid
IEEE Transactions on Pattern Analysis and Machine Intelligence
Interpolation Using Wavelet Bases
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Surface Interpolation using Multiresolution Wavelet Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the 10th International Workshop on Theoretical Foundations of Computer Vision: Multi-Image Analysis
Keyframe-based tracking for rotoscoping and animation
ACM SIGGRAPH 2004 Papers
3D reconstruction of single picture
VIP '05 Proceedings of the Pan-Sydney area workshop on Visual information processing
Ink Normalization and Beautification
ICDAR '05 Proceedings of the Eighth International Conference on Document Analysis and Recognition
Locally adapted hierarchical basis preconditioning
ACM SIGGRAPH 2006 Papers
Modelling with implicit surfaces that interpolate
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Anatomic modeling from unstructured samples using variational implicit surfaces
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Efficient gradient-domain compositing using quadtrees
ACM SIGGRAPH 2007 papers
Image alignment and stitching: a tutorial
Foundations and Trends® in Computer Graphics and Vision
Image and video matting: a survey
Foundations and Trends® in Computer Graphics and Vision
Contour line thinning and multigrid generation of raster-based digital elevation models
International Journal of Geographical Information Science
Scattered data reconstruction by regularization in B-spline and associated wavelet spaces
Journal of Approximation Theory
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 2
Diffusion maps for edge-aware image editing
ACM SIGGRAPH Asia 2010 papers
Proceedings of the 2011 SIGGRAPH Asia Conference
Multigrid and multilevel preconditioners for computational photography
Proceedings of the 2011 SIGGRAPH Asia Conference
Approximation of minimum energy surfaces using optimal twists
Mathematical and Computer Modelling: An International Journal
Efficient preconditioning of laplacian matrices for computer graphics
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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An alternative to multigrid relaxation that is much easier to implement and more generally applicable is presented. Conjugate gradient descent is used in conjunction with a hierarchical (multiresolution) set of basis functions. The resultant algorithm uses a pyramid to smooth the residual vector before the direction is computed. Simulation results showing the speed of convergence and its dependence on the choice of interpolator, the number of smoothing levels, and other factors are presented. The relationship of this approach to other multiresolution relaxation and representation schemes is also discussed.