Barycenters in the Wasserstein space, SIAM Journal on Mathematical Analysis, vol.43, pp.904-924, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00637399
A fixed-point approach to barycenters in Wasserstein space, Journal of Mathematical Analysis and Applications, vol.441, pp.744-762, 2016. ,
On a Wasserstein-type distance between solutions to stochastic differential equations, Ann. Appl. Probab, vol.29, pp.1609-1639, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01636082
Sliced and Radon Wasserstein barycenters of measures, Journal of Mathematical Imaging and Vision, vol.51, pp.22-45, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00881872
Optimal Transport for Gaussian Mixture Models, IEEE Access, vol.7, pp.6269-6278, 2019. ,
Aggregated Wasserstein Distance and State Registration for Hidden Markov Models, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2019. ,
In this experiment, the top left image is modified in such a way that its color palette goes through the GW2-barycenters between the color palettes of the four corner images. Each color palette is represented as a mixture of 10 Gaussian components. The weights used for the barycenters are bilinear with respect to the four corners of the rectangle. and Video, pp.125-149, 2018. ,
Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society: Series B (Methodological), vol.39, pp.1-22, 1977. ,
The Fréchet distance between multivariate normal distributions, Journal of multivariate analysis, vol.12, pp.450-455, 1982. ,
POT Python Optimal Transport library, 2017. ,
Semi-discrete optimal transport in patch space for enriching Gaussian textures, International Conference on Geometric Science of Information, pp.100-108, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01560785
Optimal maps for the multidimensional Monge-Kantorovich problem, Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, vol.51, pp.23-45, 1998. ,
, Texture synthesis using convolutional neural networks, in NIPS, 2015.
High-dimensional mixture models for unsupervised image denoising (HDMI), SIAM Journal on Imaging Sciences, vol.11, pp.2815-2846, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01544249
, Computational optimal transport, Foundations and Trends R in Machine Learning, vol.11, pp.355-607, 2019.
Removing artefacts from color and contrast modifications, IEEE Transactions on Image Processing, vol.20, pp.3073-3085, 2011. ,
,
, International Conference on Scale Space and Variational Methods in Computer Vision, pp.435-446, 2011.
On the n-coupling problem, Journal of multivariate analysis, vol.81, pp.242-258, 2002. ,
, Optimal Transport for Applied Mathematicians, 2015.
Single-frame Image Denoising and Inpainting Using Gaussian Mixtures, ICPRAM, pp.283-288, 2015. ,
, Topics in Optimal Transportation Theory, vol.58, 2003.
, Optimal transport: old and new, vol.338, 2008.
, SURE Guided Gaussian Mixture Image Denoising, vol.6, pp.999-1034, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00785334
Synthesizing and mixing stationary Gaussian texture models, SIAM Journal on Imaging Sciences, vol.7, pp.476-508, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00988761
On the identifiability of finite mixtures, Ann. Math. Statist, vol.39, pp.209-214, 1968. ,
Solving inverse problems with piecewise linear estimators: from Gaussian mixture models to structured sparsity, IEEE Trans. Image Process, vol.21, pp.2481-99, 2012. ,
From learning models of natural image patches to whole image restoration, Conf. Comput. Vis., IEEE, pp.479-486, 2011. ,