Multi-layer Semi-Discrete Optimal Transport
for Texture Synthesis

Presentation   -   Papers   -   Slides   -   Source codes   -   Monolayer

Presentation

  We introduce a fast stochastic algorithm to approximate such a semi-discrete OT problem using a hierarchical multi-layer transport plan. This method allows for tractable computation in high-dimensional case and for large point-clouds, both during training and synthesis time. Experiments demonstrate its numerical advantage over multi-scale (or multi-level) methods. Applications to fast exemplar-based texture synthesis based on patch matching with two layers, also show stunning improvements over previous single layer approaches.

Paper

  The texture model is described in the paper

"A Fast Multi-Layer Approximation to Semi-Discrete Optimal Transport"
(Arthur Leclaire, Julien Rabin), accepted to the seventh International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), 2019. Hal preprint.

  The experiments shown in this paper can be reproduced using the codes available below.

Slides

  The slides of the presentation I gave at SSVM 2019 are available here.

Source codes (Matlab)

  The archive release_multilayer.zip contains source codes for texture synthesis with 2-layer patch optimal transport.

  This archive contains the main functions

• semi_discrete_ot_asgd_multilayer.m : compute 2-layer transport plan
• sample_transport_plan_multilayer.m : sample the 2-layer transport plan

  and also

• a script file multiscale_texsynth_multilayer_OT.m for the image experiments
• a script file expe_ssvm.m for the one-dimensional experiments
• a folder textures containing input texture images

  If you find some bugs or mistakes in those codes, you can report them by email to Arthur Leclaire.