Fast mesh data augmentation via Chebyshev polynomial of spectral filtering

Area of Science:

• Computer Vision
• Medical Image Analysis
• Machine Learning

Background:

• Deep neural networks (DNNs) require extensive data for generalization.
• Data augmentation is crucial when training data is limited.
• Existing augmentation methods lack applicability to graph or surface data, despite the rise of graph convolutional neural networks (graph-CNNs).

Purpose of the Study:

• To propose novel, unbiased data augmentation techniques for surface data.
• To address the gap in augmentation methods for graph-based deep learning.
• To improve the generalizability and performance of DNNs on surface data.

Main Methods:

• Laplace-Beltrami eigenfunction Data Augmentation (LB-eigDA): Augments data by resampling Laplace-Beltrami coefficients.
• Chebyshev polynomial Data Augmentation (C-pDA): A faster approach using polynomial approximation of Laplace-Beltrami spectral filters for data generation on surfaces.
• Both methods generate data with the same mean as the observed data.

Main Results:

• LB-eigDA and C-pDA were validated using simulated data, showing improved classification accuracy.
• Application to Alzheimer's Disease Neuroimaging Initiative (ADNI) brain images demonstrated that augmented cortical thickness data retained a similar pattern to observed data.
• C-pDA proved faster than LB-eigDA and enhanced the classification accuracy of graph-CNNs for Alzheimer's Disease detection.

Conclusions:

• The proposed LB-eigDA and C-pDA methods effectively generate new surface data for deep learning.
• These techniques can enhance the performance of graph-CNNs in medical image analysis, as shown in AD classification.
• C-pDA offers a computationally efficient alternative for surface data augmentation.