多分辨率神经场建模,兼顾空间与频率细节。
MDNF: Multi-Diffusion-Nets for Neural Fields on Meshes
- 分层扩散网络实现几何感知的空间分解
- 高频信号在细粒度网格上学习,精度更高
- 适合处理纹理、法向等复杂几何属性
我们提出一种在三角网格上表示神经场的新框架,该框架在空间和频率域均支持多分辨率。受神经傅里叶滤波器组(NFFB)启发,架构将更细的空间分辨率与更高频带关联,粗分辨率则对应低频。通过多个与不同空间层级对应的DiffusionNet组件实现几何感知的空间分解,并对各层级应用傅里叶特征映射,促进细粒度部分学习高频内容。最终信号以类似小波的方式组合,使用正弦激活的MLP,将高频信号叠加于低频之上。该方法在学习复杂神经场时表现高精度,对不连续性、目标场的指数尺度变化及网格修改具有鲁棒性。我们在合成RGB函数、UV纹理坐标和顶点法向等多样化任务中验证了其有效性,对比两种替代方法,凸显多分辨率结构的优势。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。