A Multiscale Approach to Optimal Transport

By Quentin Mérigot. Computer graphics forum (Print), 2011

331 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b6df4592ca92531815fb82922ab0bf540666fe90

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Optimal Mass Transport: Signal processing and machine-learning applications (2017, methodology): “Recent advancements in numerical methods, including the work of Merigot [34] and Cuturi [14], among many others, have reinvigorated optimal transport-based distances as a feasible and appealing candidate for large-scale image-retrieval problems.”
Multivariate goodness-of-fit tests based on Wasserstein distance (2020, methodology): “, 2019), which implements the multi-scale algorithm in Mérigot (2011). • In all other cases (p = 1 or d = 5), we relied on our own C implementation of the SAG method as employed in Genevay et al. (2016).”
Iterative Bregman Projections for Regularized Transportation Problems (2014, background): “[44] Q Merigot, A Multiscale Approach to Optimal Transport, Computer Graphics Forum, 30 (2011), pp.”
Stochastic Wasserstein Barycenters (2018, positive): “Algorithms by Mérigot (2011) in 2D and Lévy (2015) in 3D use computational geometry to extract gradients for the dual semidiscrete problem; Kitagawa et al. (2016a) accelerate convergence via a second-order Newton method.”
Scaling Algorithms for Unbalanced Transport Problems (2016, methodology): “This problem, introduced by Alexandrov and Pogorelov as a theoretical tool, can be solved with geometric tools when using the squared Euclidean cost [4] (see also [52] for the development of eﬃcient algorithms using methods from computational geometry and [46] for 3-”
Sliced Wasserstein Kernels for Probability Distributions (2015, background): “Recent advances utilizing variational minimization [16, 9], particle approximation [44], multi-scale schemes [27, 29], and entropy regularization [11, 39, 4], have enabled transport metrics to be efficiently applied to machine learning and computer vision problems.”
Plugin estimation of smooth optimal transport maps (2021, background): “The optimization problem (16) is sometimes known as the semidiscrete optimal transport problem, for which efficient numerical solvers are well-studied (Mérigot, 2011; Levy and Schwindt, 2017).”
Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, methodology): “This is efficiently adressed in [233], where the problem is considered with a multi-resolution point of view.”
Stochastic Optimization for Large-scale Optimal Transport (2016, background): “The only known class of methods that can overcome this limitation are so-called semi-discrete solvers [1], that can be implemented efficiently using computational geometry primitives [12].”
{Euclidean, metric, and Wasserstein} gradient flows: an overview (2016, methodology): “For the applications to semi-discrete18 optimal transport problems, the results are now very fast (with discretizations with up to 106 points in some minutes, in 3D; the reader can have a look at [59,62,74] but also to Section6.”
Sliced and Radon Wasserstein Barycenters of Measures (2014, neutral): “Displacement interpolation has been employed for image warping and registration [18,23], to remove ﬂickering in old movies [11] and in computer graphics to perform manipulations on textures [21] and to interpolate reﬂectance for 3-”