Sliced and Radon Wasserstein Barycenters of Measures

By Nicolas Bonneel, Julien Rabin, G. Peyr'e, Hanspeter Pfister. 2014

726 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

Generative Continual Concept Learning (2019, methodology): “In particular, we use Sliced Wasserstein Distance (SWD) [25] which is a suitable approximation for WD, while it can be computed efﬁciently using empirical samples, drawn from two distributions.”
Computational Optimal Transport (2018, methodology): “This approach is detailed in [Bonneel et al., 2015], following ideas from Marc Bernot.”
Demystifying Orthogonal Monte Carlo and Beyond (2020, methodology): “Sliced Wasserstein Distances [SWD]: Wasserstein Distances (WDs) are metrics in spaces of probabilistic distributions that have found several applications in deep generative models [5, 23].”
Latent Translation: Crossing Modalities by Bridging Generative Models (2019, methodology): “Sliced Wasserstein Distance (SWD) (Bonneel et al., 2015).”
Learning a Domain-Invariant Embedding for Unsupervised Domain Adaptation Using Class-Conditioned Distribution Alignment (2019, methodology): “This fact is used to approximate Wasserstein distance by SWD, which is a computationally efficient approximation and has recently drawn interest from the machine learning and computer vision communities [26], [1], [3], [8], [39].”
Learning Blind Video Temporal Consistency (2018, methodology): “We note that our approach is not limited to the above applications but can also be applied to tasks such as automatic white balancing [14], image harmonization [4] and image dehazing [13].”
Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptation (2019, methodology): “Our proposed SWD is essentially a variational version of original Wasserstein distance but at a fraction of its computational cost [4].”
SAR Image Classification Using Few-Shot Cross-Domain Transfer Learning (2019, background): “SWD approximates WD as sum of multiple Wasserstein distances of one-dimensional distributions which possess a closed-form solution [26, 1, 2, 16].”
Consistent estimation of a population barycenter in the Wasserstein space (2013, methodology): “For example, it has been successfully used for texture analysis in image processing [12, 28].”
Sliced Wasserstein Kernels for Probability Distributions (2015, methodology): “Rabin et al. [26] and Bonneel et al. [5] proposed to leverage the fact that these problems are easy to solve for one-dimensional distributions, and introduced an alternative distance called the Sliced Wasserstein distance.”
Stabilizing GAN Training with Multiple Random Projections (2017, background): “[17], who also use low-dimensional projections to deal with high-dimensional probability distributions.”
Empirical optimal transport on countable metric spaces: Distributional limits and statistical applications (2017, background): “Examples include Pele and Werman (2009); Shirdhonkar and Jacobs (2008); Bonneel et al. (2015) and the particularly successful entropically regularized transport distances (Cuturi, 2013; Solomon et al., 2015).”
Characterization of barycenters in the Wasserstein space by averaging optimal transport maps (2012, methodology): “For example, it has been successfully used for texture analysis in image processing [16, 36].”
Orthogonal Estimation of Wasserstein Distances (2019, methodology): “Firstly, the focus of sliced Wasserstein distance on one-dimensional marginals of probability distributions can lead to poorer quality results than true Wasserstein distance (Bonneel et al., 2015).”
Subspace Robust Wasserstein distances (2019, background): “The smallest eigenvalue is given for illustrative purposes only. barycenters (Bonneel et al., 2015) but also to train generative models (Kolouri et al., 2018; Deshpande et al., 2018).”
Optimal Mass Transport: Signal processing and machine-learning applications (2017, methodology): “The projection of high-dimensional PDFs is closely related to the well-known Radon transform in the imaging and image processing community [8], [25].”
Sliced Wasserstein Distance for Learning Gaussian Mixture Models (2017, methodology): “A formal measure theoretic definition of Radon transform for probability measures could be found in [6].”
Inference for empirical Wasserstein distances on finite spaces (2016, methodology): “Beyond this obvious modification it seems worthwhile to extend the methodology of directional differentiability in conjunction with a delta method to other functionals related to optimal transport, e.g. entropically regularized (Cuturi, 2013) or sliced Wasserstein distances (Bonneel et al., 2015).”