Learning intrinsic shape representations via spectral mesh convolutions

We introduce spectral-based convolutional operators embedded within Generalized Graph Neural Networks (G-GNNs). These operators enable deep learning on graphs through a learnable, energy-driven evolution process. This approach empowers us to impose specific properties on the graph convolutional kernel directly derived from the corresponding variational formulations. Our model incorporates both parameterized and non- parameterized graph Laplacian-based energies within the generalized graph convolutional layer to address features like smoothness, sharpness, and compact support. By making appropriate choices within our G-GNN framework, we pave the way for designing novel paradigms for 3D shape representation, reconstruction, and processing, while also enabling effective feature embeddings for intrinsic neural fields.