Laplace-Beltrami eigenfunction Data Augmentation (LB-eigDA) and Chebyshev polynomial Data Augmentation (C-pDA)
(C) 2020 Shih-Gu Huang shihgu@gmail.com Anqi Qiu bieqa@nus.edu.sg National University of Singapore
This package contains codes implementing the Laplace-Beltrami eigenfunction Data Augmentation (LB-eigDA) and Chebyshev polynomial Data Augmentation (C-pDA) to generate new data on surfaces. The mathematical detail is given in [1].
REFERENCES: [1] Huang, S.-G., Chung, M.K., Qiu, A.: Fast Mesh Data Augmentation via Chebyshev Polynomial of Spectral filtering. arXiv:2010.02811, 2020.
[2] Hammond, D.K., Vandergheynst, P., Gribonval, R.: Wavelets on graphs via spectral graph theory. Applied and Computational Harmonic Analysis 30, 129-150, 2011
[3] Tan, M., Qiu, A.: Spectral Laplace-Beltrami wavelets with applications in medical images. IEEE Transactions on Medical Imaging 34, 1005-1017, 2015
DEMONSTRATIONS:
- EXAMPLE.m : This example performs LB-eigDA and C-pDA to generate augmented data from simulated data on a hippocampus surface mesh [1] and generate Figure 2 in [1].
FUNCTIONS:
-
eigDA.m : Laplace-Beltrami eigenfunction Data Augmentation (LB-eigDA)
-
CpDA.m : Chebyshev polynomial Data Augmentation (C-pDA). The recurrence relation is modified from the Spectral Graph Wavelet Transform (SGWT) [2].
-
LB/ : Folder containing some functions modified from Spectral Laplace-Beltrami Wavelets [3] for computing LB-operator
-
LB_operator.m : Discretization of Laplace-Beltrami operator
-
permutation.m : Generate random permutations for LB-eigDA and C-pDA
-
eigen.m : Compute all or the first K eigenfunctions for LB-eigDA
-
BP_chebyshev.m: Compute Chebyshev expansion coefficients of all bandpass filters in C-pDA
-
figure_trimesh.m : Visualization of surface data
-
hippocampus_l.mat: Left hippocampus surface mesh