PC-Gau: PCA basis of Scattered Gaussians for Shape Matching via Functional Maps

This repository contains the demo code for the paper: Colombo, M. and Boracchi, G. and Melzi, S., PC-Gau: PCA basis of Scattered Gaussians for Shape Matching via Functional Maps.

Code

The core function provided by the repository is compute_PC_Gau, which computes the atoms of PC-Gau basis given an input mesh and the necessary parameters.

There are also two demo scripts that show its usage.

Demo: point-wise maps

Run demo_p2p_map.m to display the atoms of PC-Gau basis and show a comparison between point-wise maps obtained using our basis and the standard LB basis. The output you should get is the following:

You can use both the gournd-truth correspondence and product preservation [NO17] to compute the functional map C, by setting the value of the parameter C_computation_method.

Demo: metrics

You can compute and plot the metrics presented in the paper for a demo shape, using both PC-Gau and LB. To do this, run demo_display_metrics.m. The output should look like the following figures:

Acknowledgements

Some of the code present in this repository is not ours. We would like to thank the authors of the following articles:

• Orthogonalized Fourier Polynomials for Signal Approximation and Transfer [paper] [code]
• Informative Descriptor Preservation via Commutativity for Shape Matching [paper] [code]