  We present Factor Fields, a novel framework for modeling and representing
signals. Factor Fields decomposes a signal into a product of factors, each
represented by a classical or neural field representation which operates on
transformed input coordinates. This decomposition results in a unified
framework that accommodates several recent signal representations including
NeRF, Plenoxels, EG3D, Instant-NGP, and TensoRF. Additionally, our framework
allows for the creation of powerful new signal representations, such as the
"Dictionary Field" (DiF) which is a second contribution of this paper. Our
experiments show that DiF leads to improvements in approximation quality,
compactness, and training time when compared to previous fast reconstruction
methods. Experimentally, our representation achieves better image approximation
quality on 2D image regression tasks, higher geometric quality when
reconstructing 3D signed distance fields, and higher compactness for radiance
field reconstruction tasks. Furthermore, DiF enables generalization to unseen
images/3D scenes by sharing bases across signals during training which greatly
benefits use cases such as image regression from sparse observations and
few-shot radiance field reconstruction.
