Wasserstein Barycenter and its Application to Texture Mixing

This project is dedicated to the study of the paper "Wasserstein Barycenter and its Application to Texture Mixing". The objective is to reproduce the results from the paper, analyze its limitations, and propose solutions.

✅ Code

We attempted to code most of the functions from scratch. However, for the initial analyses, we used functions from the pot library for the sake of time. Later, we implemented our own functions for texture mixing. All outputs are generated using our own implementations.

🛠️ Project Structure

• data/: Contains all the necessary data (images) required to run the code.
• experiments/: Includes notebooks that replicate results, analyze limitations, and propose solutions. These notebooks are structured as follows:
  • Notebook 1: Basic functions from wasserstein distances, wasserstein barycenters and sliced approximations.
  • Notebook 2: Decomposition of the texture into wavelet coefficients.
  • Notebook 3: Reproduces the results of the paper for first order method and highlights the limitations.
  • Notebook 4: Implements potential solutions to address the identified limitations.
  • Notebook 5: Summarizes and visualizes the final results.
• outputs/: Stores the figures generated by running the notebooks.
• utils/: Contains helper functions used throughout the project.
• wasserstein/: Includes functions for calculating Wasserstein distances and barycenters, decomposing/recomposing the texture into coefficients etc.

🚀 How to Run the Project

1. Clone the repository:

   git clone https://github.com/your-name/Convolutional-Wasserstein-Distances.git
   cd Convolutional-Wasserstein-Distances
   

2. Install the dependencies:

   pip install -r requirements.txt
   

3. Run the notebooks in the experiments/ folder sequentially.

🔧 Code Architecture

Wasserstein-Barycenter-Project/  
├── data/                        
├── experiments/                 
│   ├── 1_projections_barycenter.ipynb       
│   ├── 2_wavelet_coefficients.ipynb         
│   ├── 3_texture_mixing_first_order.ipynb   
│   ├── 4_texture_mixing_with_reg.ipynb      
│   └── 5_high_dimensional_texture_mix.ipynb         
├── outputs/                     
├── utils/                                   
│   ├── basic_wasserstein.py    
│   ├── image_treatment.py      
│   └── projections.py                       
├── wasserstein/                 
│   ├── texture_mixing_new.py  
│   └── texture_mixing_with_reg.py             
├── requirements.txt             
└── README.md

🌟 Output examples

• Projection

• Texture mixing with 4 inputs

• Texture mixing with and without regularization

📝 License

This project was created by:

• Marion Chabrol
• Suzie Grondin
• Corentin Pernot

🔗 Links

• GitHub Repository: https://github.com/mchabrol/Convolutional-Wasserstein-Distances