MDNF：面向网格上神经场的多扩散网络
MDNF: Multi-Diffusion-Nets for Neural Fields on Meshes
AI总结：
本文提出 MDNF 框架，通过多个 DiffusionNet 组件实现空间多分辨率分解，并结合傅里叶特征映射与正弦激活 MLP 在频率域进行多分辨率合成，从而在三角网格上高精度且鲁棒地表示复杂神经场。
摘要：
我们提出了一种新的框架，用于在三角网格上表示神经场，该框架在空间域和频率域上都具有多分辨率特性。受神经傅里叶滤波器组（NFFB）的启发，我们的架构通过将更精细的空间分辨率层级与更高的频带相关联，同时将更粗糙的分辨率映射到更低频率，来分解空间域和频率域。为了实现几何感知的空间分解，我们利用多个 DiffusionNet 组件，每个组件与不同的空间分辨率层级相关联。随后，我们应用傅里叶特征映射，以促使更精细的分辨率层级与更高频率相关联。最终信号以受小波启发的方式使用正弦激活的 MLP 进行合成，在较低频率信号之上聚合较高频率信号。我们的架构在学习复杂神经场方面达到了高精度，并且对不连续性、目标场的指数尺度变化以及网格修改具有鲁棒性。我们通过将其应用于多种神经场（如合成 RGB 函数、UV 纹理坐标和顶点法线）来展示我们方法的有效性，这些应用体现了不同的挑战。为了验证我们的方法，我们将其性能与两种替代方案进行比较，展示了我们多分辨率架构的优势。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
