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Deep neural networks have recently been recognized as one of the powerfullearning techniques in computer vision and medical image analysis. Trained deepneural networks need to be generalizable to new data that was not seen before.In practice, there is often insufficient training data available andaugmentation is used to expand the dataset. Even though graph convolutionalneural network (graph-CNN) has been widely used in deep learning, there is alack of augmentation methods to generate data on graphs or surfaces. This studyproposes two unbiased augmentation methods, Laplace-Beltrami eigenfunction DataAugmentation (LB-eigDA) and Chebyshev polynomial Data Augmentation (C-pDA), togenerate new data on surfaces, whose mean is the same as that of real data.LB-eigDA augments data via the resampling of the LB coefficients. In parallelwith LB-eigDA, we introduce a fast augmentation approach, C-pDA, that employs apolynomial approximation of LB spectral filters on surfaces. We design LBspectral bandpass filters by Chebyshev polynomial approximation and resamplesignals filtered via these filters to generate new data on surfaces. We firstvalidate LB-eigDA and C-pDA via simulated data and demonstrate their use forimproving classification accuracy. We then employ the brain images ofAlzheimer's Disease Neuroimaging Initiative (ADNI) and extract corticalthickness that is represented on the cortical surface to illustrate the use ofthe two augmentation methods. We demonstrate that augmented cortical thicknesshas a similar pattern to real data. Second, we show that C-pDA is much fasterthan LB-eigDA. Last, we show that C-pDA can improve the AD classificationaccuracy of graph-CNN.

Fast Mesh Data Augmentation via Chebyshev Polynomial of Spectral filtering