Convolutional Neural Network on Semi-Regular Triangulated Meshes and its Application to Brain Image Data

We developed a convolution neural network (CNN) on semi-regular triangulated meshes whose vertices have 6 neighbours. The key blocks of the proposed CNN, including convolution and down-sampling, are directly defined in a vertex domain. By exploiting the ordering property of semi-regular meshes, the convolution is defined on a vertex domain with strong motivation from the spatial definition of classic convolution. Moreover, the down-sampling of a semi-regular mesh embedded in a 3D Euclidean space can achieve a down-sampling rate of 4, 16, 64, etc. We demonstrated the use of this vertex-based graph CNN for the classification of mild cognitive impairment (MCI) and Alzheimer's disease (AD) based on 3169 MRI scans of the Alzheimer's Disease Neuroimaging Initiative (ADNI). We compared the performance of the vertex-based graph CNN with that of the spectral graph CNN.