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.

翻译：我们提出因子场（Factor Fields），一种用于建模和表示信号的新框架。因子场将信号分解为多个因子的乘积，每个因子由运行在坐标变换后的输入信号上的神经或常规场表示来表征。我们证明这种分解产生了一个统一框架，能够泛化包括NeRF、PlenOxels、EG3D、Instant-NGP和TensoRF在内的多种近期信号表示。此外，该框架允许创建强大的新信号表示，例如本文提出的系数-基因子分解（CoBaFa）。实验表明，CoBaFa在神经信号表示的三个关键目标（逼近质量、紧凑性和效率）上较之前快速重建方法均有改进。实验证明，我们的表示在二维图像回归任务中实现了更好的图像逼近质量，在三维符号距离场重建中达到更高的几何质量，在辐射场重建任务中相比以往快速重建方法具有更高的紧凑性。此外，CoBaFa表示通过训练期间跨信号共享基函数实现泛化能力，从而支持稀疏观测的图像回归和少样本辐射场重建等泛化任务。