Factor Fields: A Unified Framework for Neural Fields and Beyond

We present Factor Fields, a novel framework for modeling and representing signals. Factor Fields decomposes a signal into a product of factors, each of which is represented by a neural or regular field representation operating on a coordinate transformed input signal. We show that this decomposition yields a unified framework that generalizes several recent signal representations including NeRF, PlenOxels, EG3D, Instant-NGP, and TensoRF. Moreover, the framework allows for the creation of powerful new signal representations, such as the Coefficient-Basis Factorization (CoBaFa) which we propose in this paper. As evidenced by our experiments, CoBaFa leads to improvements over previous fast reconstruction methods in terms of the three critical goals in neural signal representation: approximation quality, compactness and efficiency. Experimentally, we demonstrate that 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 compared to previous fast reconstruction methods. Besides, our CoBaFa representation enables generalization by sharing the basis across signals during training, enabling generalization tasks such as image regression with sparse observations and few-shot radiance field reconstruction.