Fast Mesh Data Augmentation via Chebyshev Polynomial of Spectral filtering

Abstract

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 was not seen before. In practice, there is often insufficient training data available and augmentation is used to expand the dataset. Even though graph convolutional neural network (graph-CNN) has been widely used in deep learning, there is a lack of augmentation methods to generate data on graphs or surfaces. This study proposes 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 is the same as that of real data. LB-eigDA augments data via the resampling of the LB coefficients. In parallel with LB-eigDA, we introduce a fast augmentation approach, C-pDA, that employs a polynomial approximation of LB spectral filters on surfaces. We design LB spectral bandpass filters by Chebyshev polynomial approximation and resample signals filtered via these filters to generate new data on surfaces. We first validate LB-eigDA and C-pDA via simulated data and demonstrate their use for improving classification accuracy. We then employ the brain images of Alzheimer's Disease Neuroimaging Initiative (ADNI) and extract cortical thickness that is represented on the cortical surface to illustrate the use of the two augmentation methods. We demonstrate that augmented cortical thickness has a similar pattern to real data. Second, we show that C-pDA is much faster than LB-eigDA. Last, we show that C-pDA can improve the AD classification accuracy of graph-CNN.

References in corpus (12)

• A Survey on Deep Learning in Medical Image Analysis
• Semi-Supervised Classification with Graph Convolutional Networks
• Spectral Networks and Locally Connected Networks on Graphs
• Generative Adversarial Network in Medical Imaging: A Review
• Deep Convolutional Networks on Graph-Structured Data
• Convolutional Networks on Graphs for Learning Molecular Fingerprints
• Random Erasing Data Augmentation
• Deep Learning using Linear Support Vector Machines
• Gated Graph Sequence Neural Networks
• Learning Structural Node Embeddings Via Diffusion Wavelets
• Dataset Augmentation in Feature Space
• Distance Metric Learning using Graph Convolutional Networks: Application to Functional Brain Networks