Locally adapted hierarchical basis preconditioning

By Richard Szeliski. 2006

124 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mechanics, Computational Theory and Mathematics, Optimization & Training

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Citations in the corpus

Deep Residual Learning for Image Recognition (2015, background): “It has been shown [3, 45, 46] that these solvers converge much faster than standard solvers that are unaware of the residual nature of the solutions.”
The Fast Bilateral Solver (2015, background): “Because of its bilateral nature, our preconditioner is inherently locally adapted and so resembles image-adapted preconditioners [21, 34].”
Joint bilateral upsampling (2007, methodology): “Although these systems are sparse and may be solved efﬁciently using multi-resolution solvers [Szeliski 2006], handling today’s multi-megapixel images remains a challenge: once the data exceeds the available physical memory, iteratively sweeping over the data results in thrashing.”
LIME: Low-Light Image Enhancement via Illumination Map Estimation (2017, background): “Since (I + ∑ d∈{u,v}D T d Diag(w̃d)Dd) is a symmetric positive definite Laplacian matrix, there are many techniques available for solving it, for example, [28], [29], [30], [31], [32].”
Fourier Analysis of the 2D Screened Poisson Equation for Gradient Domain Problems (2008, methodology): “A comparison of memory and run-time performance of our method (FS) to other state-of-the-art methods (QT [5], out-of-core SM [6], HB [21], LHAB) [27].”
ImageNet classification with deep convolutional neural networks (2012, unknown): “An alternative to Multigrid is hierarchical basis pre-conditioning [45, 46], which relies on variables that represent residual vectors between two scales.”
Local Laplacian filters: edge-aware image processing with a Laplacian pyramid (2011, methodology): “…1998], optimization-based methods, such as [Fattal et al. 2002; Farbman et al. 2008; Subr et al. 2009; Bhat et al. 2010], minimize a spatially inhomogeneous energy, and other approaches build dedicated basis functions for each new image, e.g., [Szeliski 2006; Fattal 2009; Fattal et al. 2009].”
Guided Image Filtering (2010, methodology): “Iterative solvers like the Jacobi method, Successive Over-Relaxation (SOR), and Conjugate Gradi-ents [40] are too slow to converge.”
A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors (2008, methodology): ““House” example is a convex energy minimization problem amenable to quadratic solvers; we include the results of HBF, the fast algorithm in [44].”
Joint Bi-layer Optimization for Single-Image Rain Streak Removal (2017, methodology): “Since a quadratic optimization with a quadratic regularization term can be optimized linearly [27, 20, 17], we solve the problem with the iterative re-weighted least squares (IRLS) technique [30].”
A Closed-Form Solution to Natural Image Matting (2006, background): “It should be noted that solving linear systems with this stru cture is a well studied problem [8], [16].”
Edge-avoiding wavelets and their applications (2009, background): “…N since subsampling is avoided [Fattal et al. 2007], solving multiple linear systems [Farbman et al. 2008], coping with the resulting poorly-conditioned systems [Szeliski 2006], or introducing additional dimensions and additional memory cost due to their discretization [Paris and Durand 2006].”
Learning Gaussian Conditional Random Fields for Low-Level Vision (2007, unknown): “Further improvements in speed may be possible by using a preconditioner suited for images, such as the preconditioner described in [15].”