CGF20_waveletsOnShapes

This repository contains the code for the paper "Wavelet-based Heat Kernel Derivatives: towards Informative Localized Shape Analysis" by Maxime Kirgo, Simone Melzi, Giuseppe Patanè, Emanuele Rodolà and Maks Ovsjanikov.

In this paper, we propose a new construction for the Mexican hat wavelets on shapes with applications to partial shape matching. Our approach takes its main inspiration from the well-established methodology of diffusion wavelets. This novel construction allows us to rapidly compute a multiscale family of Mexican hat wavelet functions, by approximating the derivative of the heat kernel. We demonstrate that this leads to a family of functions that inherit many attractive properties of the heat kernel (e.g., local support, ability to recover isometries from a single point, efficient computation).

Main Functions

M = compute_normalized_shape(path_to_off_file, boundary_condition, normalization_factor);

% Input:
%   path_to_off_file: the shape on which the wavelets are computed.
%   boundary_condition: the boundary condition applied at the shape boundary ('neumann' or 'dirichlet').
%   normalization_factor: Normalization factor to apply when computing the shape.
%
% Output:
%   M: the mesh structure.

[sampM,sampN,sample_idx] = compute_samples_from_landmarks(N,nSamples,landmarks_M,landmarks_N,sampling_method);

% Input:
%   N: the shape on which the samples are selected (partial shape in the case of partial shape matching).
%   nSamples: the number of samples to compute.
%   landmarks_M: the set of available landmarks for the shape M.
%   landmarks_N: the set of available landmarks for the shape N.
%   sampling_method: the sampling method used to generate the samples ('FPS_EUCLIDEAN').
%
% Output:
%   sampM: list of nSamples on the shape M.
%   sampN: list of nSamples on the shape N.
%   sample_idx: list of indices that were used in landmarks_N.

[scales_M,scales_N,scales_other_M,scales_other_N] = compute_scales(M,N,nScales,ts_GT_max);

% Input:
%   M: the structure for shape M.
%   N: the structure for shape N.
%   nScales: the number of scales to compute.
%   ts_GT_max: the ts_GT_max parameter value, corresponding to the maximum diffusion allowed.
%
% Output:
%   scales_M: the list of scales for shape M for our method.
%   scales_N: the list of scales for shape N for our method.
%   scales_other_M: alternative list of scales for shape M.
%   scales_other_N: alternative list of scales for shape N.

dict_M = compute_wavelet_dict(M,sampM,scales_M);

% Input:
%   M: the shape on which the wavelets are computed.
%   sampM: the vertex ids where to compute the wavelets.
%   scales_M: the set of scales used to compute the wavelets.
%
% Output:
%   dict_M: an array containing the wavelets computed at the specified samples and scales.

Comments

• The script ex00_partial_shape_matching.m shows how to perform partial shape matching using our method.
• The script ex01_reproduce_fig07.m shows how to compute the data used to reproduce the Fig.7 of our paper.
• The script ex02_reproduce_fig07_plot.m plots the Fig.7 of our paper using the data produced with the script ex01_reproduce_fig07.m.
• If you have any question/comment about this work, please feel free to contact us: maximekirgo@gmail.com.

Acknowledgments

• This work was funded by EDF R&D and the ANRT as part of the CIFRE grant 2019/0433.
• The +MESH module was developped by Jing Ren.
• The bc and bd modules were developped by Emanuele Rodolà.

Citation

If this code contributes to academic work, please cite:

@inproceedings{kirgo2020wavelet,
  title={Wavelet-based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis},
  author={Kirgo, Maxime and Melzi, Simone and Patan{\`e}, Giuseppe and Rodol{\`a}, Emanuele and Ovsjanikov, Maks},
  booktitle={Computer Graphics Forum},
  year={2020},
  organization={Wiley Online Library}
}

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. For any commercial uses or derivatives, please contact us (maximekirgo@gmail.com, melzismn@gmail.com, patane@ge.imati.cnr.it, rodola@di.uniroma1.it, maks@lix.polytechnique.fr).