Geometric deep learning

After the registration of the facial images, each facial mesh has the same vertex number and edge connectivity. Thus, a 3D graph convolutional autoencoder can be applied to these facial meshes for dimensionality reduction. The low-dimensional representations are defined as endophenotypes. By decoding (one, or multiple) these endophenotype(s) via the docoder, the visual representation of endophenotype(s) can be shown with a faical heatmap, where red areas refer to inward changes while blue areas refer to outward changes of the face with respect to the geometric center of the head. Conventional statistical analysis can be applied to these endophenotypes, in scenarios of epidemiological or genetic studies.