EBSW

Official PyTorch implementation for paper: Energy-Based Sliced Wasserstein Distance

Details of the model architecture and experimental results can be found in our papers.

@article{nguyen2023energy,
  title={Energy-Based Sliced Wasserstein Distance},
  author={Khai Nguyen and Nhat Ho},
  journal={Advances in Neural Information Processing Systems},
  year={2023},
  pdf={https://arxiv.org/pdf/2304.13586.pdf}
}

Please CITE our paper whenever this repository is used to help produce published results or incorporated into other software.

This implementation is made by Khai Nguyen.

Requirements

To install the required python packages, run

pip install -r requirements.txt

What is included?

• Implementation of EBSW
• Point-Cloud Gradient flow
• Color Transfer
• Deep Point-Cloud Reconstruction

Implementation of EBSW

We recommend IS-EBSW-e as the default implementation of EBSW. For other variants, we refer to our implementation in experiments.

import torch
def rand_projections(dim, num_projections=1000,device='cpu'):
    projections = torch.randn((num_projections, dim),device=device)
    projections = projections / torch.sqrt(torch.sum(projections ** 2, dim=1, keepdim=True))
    return projections

def one_dimensional_Wasserstein_prod(X,Y,theta,p):
    X_prod = torch.matmul(X, theta.transpose(0, 1))
    Y_prod = torch.matmul(Y, theta.transpose(0, 1))
    X_prod = X_prod.view(X_prod.shape[0], -1)
    Y_prod = Y_prod.view(Y_prod.shape[0], -1)
    wasserstein_distance = torch.abs(
        (
                torch.sort(X_prod, dim=0)[0]
                - torch.sort(Y_prod, dim=0)[0]
        )
    )
    wasserstein_distance = torch.sum(torch.pow(wasserstein_distance, p), dim=0,keepdim=True)
    return wasserstein_distance

def ISEBSW(X, Y, L=10, p=2, device="cpu"):
    dim = X.size(1)
    theta = rand_projections(dim, L,device)
    wasserstein_distances = one_dimensional_Wasserstein_prod(X,Y,theta,p=p)
    wasserstein_distances =  wasserstein_distances.view(1,L)
    weights = torch.softmax(wasserstein_distances,dim=1)
    sw = torch.sum(weights*wasserstein_distances,dim=1).mean()
    return  torch.pow(sw,1./p)

Point-Cloud Gradient flow

cd GradientFlow
python main_point.py

Color Transfer

cd ColorTransfer
python main.py --source [source image] --target [target image] --num_iter 2000 --cluster

Deep Point-cloud Reconstruction

Please read the README file in the PointcloudAE folder.

Acknowledgment

The structure of this repo is largely based on PointSWD. The structure of folder render is largely based on Mitsuba2PointCloudRenderer. The implementation of the Von Mises-Fisher distribution is taken from s-vae-pytorch.