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.

我们提出了一种新型的神经场，使用了一般径向基函数进行信号表示。该方法相比于现有的神经场方法，能够更好地适应目标信号，提高径向基函数的通道能力，并且通过混合自适应的径向基函数和基于网格的径向基函数，继承了自适应性和插值平滑性，取得了比现有方法更高的精确度和紧凑性。在 2D 图像和 3D 有向距离场表示中的实验证明了我们方法的优越性，并且在神经辐射场重建方面，我们的方法实现了与现有方法相媲美的渲染质量，具有较小的模型大小和可比较的训练速度。