K-Planes: Explicit Radiance Fields in Space, Time, and Appearance

We introduce k-planes, a white-box model for radiance fields in arbitrary dimensions. Our model uses ((d)(2)) ("d-choose-2") planes to represent a d-dimensional scene, providing a seamless way to go from static (d = 3) to dynamic (d = 4) scenes. This planar factorization makes adding dimension-specific priors easy, e.g. temporal smoothness and multi-resolution spatial structure, and induces a natural decomposition of static and dynamic components of a scene. We use a linear feature decoder with a learned color basis that yields similar performance as a nonlinear black-box MLP decoder. Across a range of synthetic and real, static and dynamic, fixed and varying appearance scenes, k-planes yields competitive and often state-of-the-art reconstruction fidelity with low memory usage, achieving 1000x compression over a full 4D grid, and fast optimization with a pure PyTorch implementation. For video results and code, please see sarafridov.github.io/K-Planes.