NeuRBF: A Neural Fields Representation with Adaptive Radial Basis
  Functions
Zhang Chen Zhong Li Liangchen Song Lele Chen Jingyi Yu Junsong Yuan Yi Xu
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.