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

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