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.

我们提出了一种高效、轻量级的方法，用于学习任意信号的全连续、各向异性的高斯尺度空间。基于傅立叶特征调制和利普希茨边界，我们的方法通过自我监督训练，能够忠实地捕捉多尺度表示，支持各种应用，包括图像、几何、光场数据、纹理抗锯齿和多尺度优化。