MDNF: Multi-Diffusion-Nets for Neural Fields on Meshes
This work addresses the challenge of learning complex neural fields on meshes for applications like texture mapping and geometry processing, though it appears incremental as it builds upon existing methods like Neural Fourier Filter Bank.
The authors tackled the problem of representing neural fields on triangle meshes by proposing a multi-resolution framework that decomposes spatial and frequency domains, achieving high accuracy and robustness to discontinuities, exponential scale variations, and mesh modifications.
We propose a novel framework for representing neural fields on triangle meshes that is multi-resolution across both spatial and frequency domains. Inspired by the Neural Fourier Filter Bank (NFFB), our architecture decomposes the spatial and frequency domains by associating finer spatial resolution levels with higher frequency bands, while coarser resolutions are mapped to lower frequencies. To achieve geometry-aware spatial decomposition we leverage multiple DiffusionNet components, each associated with a different spatial resolution level. Subsequently, we apply a Fourier feature mapping to encourage finer resolution levels to be associated with higher frequencies. The final signal is composed in a wavelet-inspired manner using a sine-activated MLP, aggregating higher-frequency signals on top of lower-frequency ones. Our architecture attains high accuracy in learning complex neural fields and is robust to discontinuities, exponential scale variations of the target field, and mesh modification. We demonstrate the effectiveness of our approach through its application to diverse neural fields, such as synthetic RGB functions, UV texture coordinates, and vertex normals, illustrating different challenges. To validate our method, we compare its performance against two alternatives, showcasing the advantages of our multi-resolution architecture.