Wasserstein Barycenter and Its Application to Texture Mixing

By Julien Rabin, G. Peyr'e, Julie Delon, Marc Bernot. 2011

767 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Optimization

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Citations in the corpus

Progressive Growing of GANs for Improved Quality, Stability, and Variation (2017, methodology): “imate the statistical similarity by computing their sliced Wasserstein distance SWD(fxl i g;fyl i g), an efﬁciently computable randomized approximation to earthmovers distance, using 512 projections (Rabin et al., 2011). Intuitively a small Wasserstein distance indicates that the distribution of the”
Unsupervised Model Adaptation for Continual Semantic Segmentation (2020, methodology): “SWD approximates WD as a summation of WD between a number of random one-dimensional projections: D(p̂J , pT ) ≈ 1 L L∑ l=1 M∑ i=1 |〈γl, zppl[i]〉 − 〈γl, ψ(φ(x t tl[i] ))〉|2 (5) where γl ∈ Sf−1 is uniformly drawn random sample from the unit f -dimensional ball Sf−1, and pl[i] and tl[i] are the sorted ”
Designing an encoder for StyleGAN image manipulation (2021, methodology): “Note that FID and SWD measure perceptual quality for both reconstruction and editability.”
Sliced Score Matching: A Scalable Approach to Density and Score Estimation (2019, methodology): “Inspired by the idea of Sliced Wasserstein distance (Rabin et al., 2012), we consider projecting s d ( x ) and s m ( x ; θ ) onto some random direction v and propose to compare their average difference along that random direction.”
Computational Optimal Transport (2018, methodology): “They have been used for image processing [Rabin et al., 2011], in particular color modification [Solomon et al.”
Theoretical Analysis of Domain Adaptation with Optimal Transport (2016, methodology): “It turns out that the Wasserstein distance has been successfully used in various applications, for instance: computer vision [22], texture analysis [21], tomographic reconstruction [12] and clustering [9].”
Optimal Transport for Domain Adaptation (2014, background): “In this section, we present the general unsupervised domain adaptation problem and show how it can be addressed from an optimal transport perspective.”
Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm (2019, methodology): “In particular, Wasserstein barycenters have been successfully used in settings such as texture mixing [40], Bayesian inference [49], imaging [26], or model ensemble [18].”
Multi-marginal optimal transport: theory and applications (2014, methodology): “These include texture mixing in image processing, where the aim is to interpolate among several textures (encoded as measures) in order to synthesize a new one [69], and statistics, where the basic goal is to find an average among several distributions while preserving relevant features of them [6].”
Deep Transfer Learning for Few-Shot SAR Image Classification (2019, methodology): “In this paper, we use the Sliced Wasserstein Distance (SWD) to circumvent this challenge.”
Subspace Robust Wasserstein distances (2019, methodology): “The sliced approximation of OT (Rabin et al., 2011) consists in projecting two probability distributions on a given line, compute the optimal transport cost between these projected values, and then repeat this procedure to average these distances over several random lines.”
Fast Computation of Wasserstein Barycenters (2013, methodology): “Rabin et al. (2012) were to our knowledge the ﬁrst to consider practical approaches to compute Wasserstein barycen-ters between point clouds in R d .”
Data Augmentation for Deep-Learning-Based Electroencephalography. (2020, result): “All reviewed papers that used GAN as their DA technique Study Dataset Task information Input formulation Deep learning strategy Best Performance Augmented Size Accuracy (without DA) Accuracy (with DA) [61] BCI competition II dataset III 1 subject 280trials 3 channels 2 class Motor Imaginary EEG 7-15”
Low-Rank Subspaces in GANs (2021, methodology): “For metrics, we use Fréchet Inception Distance (FID) [16], Sliced Wasserstein Distance (SWD) [25], and masked Mean Squared Error (MSE).”
Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, methodology): “For the applications of barycenters in image processing, we refer to [256], where, for the sake of numerical computations, the distance W2 is replaced with SW2 (see Section 5.”
A Fast Proximal Point Method for Computing Wasserstein Distance (2018, background): “Wasserstein barycenter is widely used in machine learning and computer vision due to its nice property [5, 23].”