Real-world examples:

The following are the examples of denoising on real-world scans of Monument a Napoleon (Cherbourg) and Niki's serpent. First, non-squared data fidelity is used to remove the strong spatial outliers, and then isotropic TV filtering is used on the color channels. The time taken to process Napoleon pointcloud (500k points) is 37 seconds on NVIDIA 1080Ti.

Graph_Signal_Processing

• This project implements Total Variation and Tikhonov regularization on graphs to process pointclouds.
• 
• It uses torch_geometric for fast processing on gpu.
• It is recommended to render the notebooks here.

Installation

• One needs faiss for the graph construction.
• One needs torch_geometric for processing the signal on the graphs.
• Start by installing Miniconda.
• Activate the conda base environment using conda activate.
• Install pytorch and faiss in the conda environment using

(base) $ conda install pytorch torchvision cudatoolkit=10.2 -c pytorch
(base) $ conda install -c pytorch faiss-gpu cudatoolkit=10.2

• You may need to change the cudatookit version. More details on above step are here and here.
• The next two steps are important.
• Install torch_geometric inside the conda environment using the pip command, Not the conda install command. Just follow the steps here.
• To render the pointclouds locally, one needs open3d. Again, it is recommended to install open3d using the pip command Not the conda-install command.

(base) $ pip install open3d

Cite

• The Primal-Dual algo implemented in this repo is the same as the one used to produce the results in the Section2 of this paper.
• The paper argues that some variational-methods can be formulated as a Message Passing Networks which allows the use of graph machine learning libraries (like torch_geo, dgl) to solve inverse problems on graphs.

@misc{azad2021variational,
      title={Variational models for signal processing with Graph Neural Networks}, 
      author={Amitoz Azad and Julien Rabin and Abderrahim Elmoataz},
      year={2021},
      eprint={2103.16337},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}