  Accurately and efficiently modeling dynamic scenes and motions is considered
so challenging a task due to temporal dynamics and motion complexity. To
address these challenges, we propose DynMF, a compact and efficient
representation that decomposes a dynamic scene into a few neural trajectories.
We argue that the per-point motions of a dynamic scene can be decomposed into a
small set of explicit or learned trajectories. Our carefully designed neural
framework consisting of a tiny set of learned basis queried only in time allows
for rendering speed similar to 3D Gaussian Splatting, surpassing 120 FPS, while
at the same time, requiring only double the storage compared to static scenes.
Our neural representation adequately constrains the inherently underconstrained
motion field of a dynamic scene leading to effective and fast optimization.
This is done by biding each point to motion coefficients that enforce the
per-point sharing of basis trajectories. By carefully applying a sparsity loss
to the motion coefficients, we are able to disentangle the motions that
comprise the scene, independently control them, and generate novel motion
combinations that have never been seen before. We can reach state-of-the-art
render quality within just 5 minutes of training and in less than half an hour,
we can synthesize novel views of dynamic scenes with superior photorealistic
quality. Our representation is interpretable, efficient, and expressive enough
to offer real-time view synthesis of complex dynamic scene motions, in
monocular and multi-view scenarios.
