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.

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，每个因子由作用于变换后输入坐标的经典场或神经场表示。这种分解形成了一个统一框架，能够容纳多种近期信号表示方法，包括NeRF、Plenoxels、EG3D、Instant-NGP和TensoRF。此外，该框架允许创建强大的新信号表示，如本文的第二项贡献——"字典场"（DiF）。实验表明，与先前的快速重建方法相比，DiF在近似质量、紧凑性和训练时间方面均有提升。在二维图像回归任务中，我们的表示实现了更优的图像近似质量；在三维符号距离场重建中，获得了更高的几何质量；在辐射场重建任务中，达到了更强的紧凑性。此外，DiF通过在训练过程中跨信号共享基元实现对未见图像/三维场景的泛化，这极大促进了稀疏观测下的图像回归和少样本辐射场重建等应用场景。