We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

翻译：我们提出了一种新型神经场，利用通用径向基进行信号表示。现有的先进神经场通常依赖基于网格的表示来存储局部神经特征，并使用N维线性核在连续查询点处插值特征。其神经特征的空间位置固定于网格节点，难以充分适配目标信号。而我们的方法基于具有灵活核位置与形状的通用径向基，具备更高的空间自适应性，能更紧密地拟合目标信号。为进一步提升径向基函数的通道容量，我们提出将其与多频正弦函数进行组合。该技术无需额外参数即可将单个径向基扩展为多个不同频段的傅里叶径向基，从而促进细节的表示。此外，通过将自适应径向基与基于网格的径向基相结合，我们的混合方式继承了自适应性及插值平滑性。我们精心设计了权重方案，使径向基能有效适应不同类型的信号。在二维图像与三维符号距离场表示上的实验表明，相比现有方法，我们的方法具有更高的精度与紧凑性。当应用于神经辐射场重建时，我们的方法以较小的模型规模和相当的训练速度实现了最优的渲染质量。