  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.
