We present MovingParts, a NeRF-based method for dynamic scene reconstruction and part discovery. We consider motion as an important cue for identifying parts, that all particles on the same part share the common motion pattern. From the perspective of fluid simulation, existing deformation-based methods for dynamic NeRF can be seen as parameterizing the scene motion under the Eulerian view, i.e., focusing on specific locations in space through which the fluid flows as time passes. However, it is intractable to extract the motion of constituting objects or parts using the Eulerian view representation. In this work, we introduce the dual Lagrangian view and enforce representations under the Eulerian/Lagrangian views to be cycle-consistent. Under the Lagrangian view, we parameterize the scene motion by tracking the trajectory of particles on objects. The Lagrangian view makes it convenient to discover parts by factorizing the scene motion as a composition of part-level rigid motions. Experimentally, our method can achieve fast and high-quality dynamic scene reconstruction from even a single moving camera, and the induced part-based representation allows direct applications of part tracking, animation, 3D scene editing, etc.

翻译：我们提出 MovingParts，一种基于 NeRF 的动态场景重建与部件发现方法。我们将运动视为识别部件的重要线索，即同一部件上的所有粒子共享相同的运动模式。从流体模拟的角度看，现有基于形变的动态 NeRF 方法可视为在欧拉视角下对场景运动进行参数化，即关注空间中特定位置，观察流体随时间流动的过程。然而，利用欧拉视角表示难以提取构成物体或其部件的运动。本文引入拉格朗日对偶视角，并强制欧拉/拉格朗日视角下的表示满足循环一致性。在拉格朗日视角下，我们通过追踪物体上粒子的轨迹来参数化场景运动。拉格朗日视角通过将场景运动分解为部件级刚性运动的组合，便于发现部件。实验表明，我们的方法仅需单个运动相机即可实现快速高质量的动态场景重建，且基于部件的表示可直接应用于部件追踪、动画、三维场景编辑等任务。