NeuRBF：具有自适应径向基函数的神经场表示

摘要

我们提出了一种新型的神经场，使用通用径向基来表示信号。当前最先进的神经场通常依赖于基于网格的表示来存储本地神经特征和N维线性核以在连续查询点上插值特征。它们的神经特征的空间位置固定在网格节点上，不能很好地适应目标信号。相比之下，我们的方法建立在具有灵活核位置和形状的通用径向基之上，具有更高的空间适应性，可以更紧密地拟合目标信号。为了进一步提高径向基函数的通道容量，我们建议将它们与多频正弦函数组合。这种技术将径向基扩展到不同频段的多个傅立叶径向基，而无需额外参数，有助于表示细节。此外，通过将自适应径向基与基于网格的基结合，我们的混合组合继承了适应性和插值平滑性。我们精心设计了加权方案，使径向基能够有效地适应不同类型的信号。我们在2D图像和3D有符号距离场表示上的实验表明，我们的方法比先前的方法具有更高的准确性和紧凑性。当应用于神经辐射场重建时，我们的方法实现了最先进的渲染质量，模型尺寸小，训练速度可比。

English

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.

NeuRBF：具有自适应径向基函数的神经场表示

NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions

摘要

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