Fast mesh data augmentation via Chebyshev polynomial of spectral filtering.

Deep neural networks have recently been recognized as one of the powerful learning techniques in computer vision and medical image analysis. Trained deep neural networks need to be generalizable to new data that are not seen before. In practice, there is often insufficient training data available, which can be solved via data augmentation. Nevertheless, there is a lack of augmentation methods to generate data on graphs or surfaces, even though graph convolutional neural network (graph-CNN) has been widely used in deep learning. This study proposed two unbiased augmentation methods, Laplace-Beltrami eigenfunction Data Augmentation (LB-eigDA) and Chebyshev polynomial Data Augmentation (C-pDA), to generate new data on surfaces, whose mean was the same as that of observed data. LB-eigDA augmented data via the resampling of the LB coefficients. In parallel with LB-eigDA, we introduced a fast augmentation approach, C-pDA, that employed a polynomial approximation of LB spectral filters on surfaces. We designed LB spectral bandpass filters by Chebyshev polynomial approximation and resampled signals filtered via these filters in order to generate new data on surfaces. We first validated LB-eigDA and C-pDA via simulated data and demonstrated their use for improving classification accuracy. We then employed brain images of the Alzheimer's Disease Neuroimaging Initiative (ADNI) and extracted cortical thickness that was represented on the cortical surface to illustrate the use of the two augmentation methods. We demonstrated that augmented cortical thickness had a similar pattern to observed data. We also showed that C-pDA was faster than LB-eigDA and can improve the AD classification accuracy of graph-CNN.