Gaussian scale spaces are a cornerstone of signal representation and processing, with applications in filtering, multiscale analysis, anti-aliasing, and many more. However, obtaining such a scale space is costly and cumbersome, in particular for continuous representations such as neural fields. We present an efficient and lightweight method to learn the fully continuous, anisotropic Gaussian scale space of an arbitrary signal. Based on Fourier feature modulation and Lipschitz bounding, our approach is trained self-supervised, i.e., training does not require any manual filtering. Our neural Gaussian scale-space fields faithfully capture multiscale representations across a broad range of modalities, and support a diverse set of applications. These include images, geometry, light-stage data, texture anti-aliasing, and multiscale optimization.

翻译：高斯尺度空间是信号表示与处理的基础，在滤波、多尺度分析、抗锯齿等诸多领域具有重要应用。然而，获取此类尺度空间的计算成本高昂且过程繁琐，尤其对于神经场等连续表示形式。本文提出一种高效轻量的方法，用于学习任意信号的完全连续、各向异性的高斯尺度空间。基于傅里叶特征调制与Lipschitz边界约束，我们的方法采用自监督训练，即训练过程无需任何人工滤波操作。所提出的神经高斯尺度空间场能够准确捕捉多种模态下的多尺度表示，并支持图像处理、几何建模、光场数据、纹理抗锯齿及多尺度优化等多样化应用场景。