Semi-discrete Optimal Transport in Patch Space for Enriching Gaussian Textures

A bilevel texture model is proposed, based on a local transform of a Gaussian random field. The core of this method relies on the optimal transport of a continuous Gaussian distribution towards the discrete exemplar patch distribution. The synthesis then simply consists in a fast post-processing of a Gaussian texture sample, boiling down to an improved nearest-neighbor patch matching, while offering theoretical guarantees on statistical compliancy.

[1]  Eric Moulines,et al.  Non-Asymptotic Analysis of Stochastic Approximation Algorithms for Machine Learning , 2011, NIPS.

[2]  Marc Levoy,et al.  Fast texture synthesis using tree-structured vector quantization , 2000, SIGGRAPH.

[3]  Bruno Galerne,et al.  Texture Inpainting Using Efficient Gaussian Conditional Simulation , 2017, SIAM J. Imaging Sci..

[4]  Alexei A. Efros,et al.  Image quilting for texture synthesis and transfer , 2001, SIGGRAPH.

[5]  Gui-Song Xia,et al.  Synthesizing and Mixing Stationary Gaussian Texture Models , 2014, SIAM J. Imaging Sci..

[6]  Julien Rabin,et al.  Wasserstein Barycenter and Its Application to Texture Mixing , 2011, SSVM.

[7]  Quentin Mérigot,et al.  A Newton algorithm for semi-discrete optimal transport , 2016, ArXiv.

[8]  Irfan A. Essa,et al.  Graphcut textures: image and video synthesis using graph cuts , 2003, ACM Trans. Graph..

[9]  Franz Aurenhammer,et al.  Minkowski-Type Theorems and Least-Squares Clustering , 1998, Algorithmica.

[10]  Quentin Mérigot,et al.  A Multiscale Approach to Optimal Transport , 2011, Comput. Graph. Forum.

[11]  Baining Guo,et al.  Real-time texture synthesis by patch-based sampling , 2001, TOGS.

[12]  Yann Gousseau,et al.  Wasserstein Loss for Image Synthesis and Restoration , 2016, SIAM J. Imaging Sci..

[13]  Jean-Michel Morel,et al.  A Conditional Multiscale Locally Gaussian Texture Synthesis Algorithm , 2016, Journal of Mathematical Imaging and Vision.

[14]  Sylvain Lefebvre,et al.  State of the Art in Example-based Texture Synthesis , 2009, Eurographics.

[15]  Sylvain Lefebvre,et al.  Parallel controllable texture synthesis , 2005, ACM Trans. Graph..

[16]  Bruno Galerne,et al.  Optimal Patch Assignment for Statistically Constrained Texture Synthesis , 2017, SSVM.

[17]  Sung Yong Shin,et al.  On pixel-based texture synthesis by non-parametric sampling , 2006, Comput. Graph..

[18]  Bruno Galerne,et al.  Random Phase Textures: Theory and Synthesis , 2011, IEEE Transactions on Image Processing.

[19]  B. Lévy.  A Numerical Algorithm for L2 Semi-Discrete Optimal Transport in 3D , 2014, 1409.1279.

[20]  Gabriel Peyré,et al.  Stochastic Optimization for Large-scale Optimal Transport , 2016, NIPS.

[21]  Bruno Galerne,et al.  Texton Noise , 2017, Comput. Graph. Forum.

[22]  P. Bickel,et al.  Texture synthesis and nonparametric resampling of random fields , 2006, math/0611258.

[23]  C. Villani.  Topics in Optimal Transportation , 2003 .

[24]  Bruno Galerne,et al.  A texton for fast and flexible Gaussian texture synthesis , 2014, 2014 22nd European Signal Processing Conference (EUSIPCO).

[25]  Irfan Essa,et al.  Texture optimization for example-based synthesis , 2005, SIGGRAPH 2005.