Complex Functional Maps: a Conformal Link between Tangent Bundles

This repository contains Python implementation for complex functional maps and additionally provides code to reproduce the main figures of the paper

Complex Functional Maps
Nicolas Donati, Etienne Corman, Simone Melzi, Maks Ovsjanikov
In CGF 2022
PDF

Use Complex Functional Maps

All the necessary code for complex functional maps is in the Tools/ folder. Apart from the standard libraries (numpy, scipy), you will need python bindings for libigl, which can be installed for instance with:

conda install -c conda-forge igl

Also, to run some of the scripts we provide to reproduce some of the figures and tables of the paper, you will need meshplot, which can also be fetched with conda:

conda install -c conda-forge meshplot

With meshplot one can directly display shapes interactively for instance in a Jupyter cell, as shown in the next images below, where we represent a vector field transfer (in the script VF_transfer.ipynb) and a map obtained with our method (in the script SMAL_example.ipynb).

We provide jupyter notebooks and their corresponding python scripts to show how to use complex functional maps in the scenarii we propose in the paper. To that end, we provide FAUST re-meshed and SMAL re-meshed datasets in the data/ folder.

Namely, we show:

• how to perform vector field transfer using complex functional maps, and a visualization of the transfer.
  • in VF_transfer.ipynb we load two shapes of the FAUST re-meshed dataset, get an accurate complex functional map using a reduced ground-truth functional map and transfer vector fields in a low spectral basis.
  • in VF_table.ipynb we provide a script to compare our vector field transfer to that of Wang et al. and Azencot et al., as desribed in the paper.
• how to use bijective Zoomout with discrete Optimisation (from Ren et al., SGP 2021) with our complex functional maps modification.
  • in SMAL_example.ipynb we load two shapes of the SMAL re-meshed dataset and compute maps between them using these different Zoomout (complex or not) algoritms.
  • in SMAL_table.ipynb we report the script used to get Table 3 (and Figure 9) of the paper.

Citation

If you use our work, please cite our paper.

@article{donati2022CFMaps,
  title={Complex Functional Maps: a Conformal Link between Tangent Bundles},
  author={Donati, Nicolas and Corman, Etienne and Melzi, Simone and Ovsjanikov, Maks},
  journal={CGF},
  year={2022}
}

Contact

If you have any problem about this implementation, please feel free to contact via:

nicolas DOT donati AT polytechnique DOT edu