An Elastic Basis for Spectral Shape Correspondence

This code accompanies the SIGGRAPH 2023 conference paper An Elastic Basis for Spectral Shape Correspondence, by Florine Hartwig, Josua Sassen, Omri Azencot, Martin Rumpf, Mirela Ben-Chen

In this paper we develop a spectral non-isometric correspondence method that aligns extrinsic features using a functional map approach. We propose a novel crease-aware spectral basis derived from the Hessian of an elastic thin shell energy and describe the necessary adaptations for using non-orthogonal basis functions in the functional map framework.

Requirements

This code uses python bindings for an implementation of the Discrete Shell Energy available here

• Thin shell energy

and the following packages

• numpy
• scipy.sparse
• scipy.spatial
• libigl
• polyscope (for visualization)
• tqdm
• matplotlib

Demo Scripts

We provide two example scripts which show the basis functionality of the code. For comparison, our code also provides the option to use the eigenfunctions of the Laplace Beltrami operator as a basis for the functional map approach. In this case our method reduces to ZoomOut.

• Cartoon.py script to compute correspondences between modified versions of a Homer and a Max-Planck bust model. The necessary data is stored in data/ . For creating the deformed mesh versions, we used an implementation of Computational caricaturization of surfaces by Sela, Matan, Yonathan Aflalo, and Ron Kimmel. Computer Vision and Image Understanding 141 (2015): 1-17.
• CatLion.py script to compute correspondences between a cat and lion shape available at http://people.csail.mit.edu/sumner/research/deftransfer/data.html. We provide a shell script which will automatically download and store the necessary data (cat-reference.obj and lion-reference.obj).

For more details and theoretic background have a look at our paper. If you should have any questions, feel free to reach out to Florine Hartwig!

Attribution

Please cite our paper when using this code. You can use the following bibtex

@inproceedings{HaSaAz23,
  title={An Elastic Basis for Spectral Shape Correspondence},
  author={Hartwig, Florine and Sassen, Josua and Azencot, Omri and Rumpf, Martin and Ben-Chen, Mirela},
  booktitle={ACM SIGGRAPH 2023 Conference Proceedings},
  year={2023},
  publisher = {Association for Computing Machinery},
  doi = {10.1145/3588432.3591518}
}