Rectified Point Flow unifies pairwise point cloud registration and multi-part shape assembly through a continuous point-wise velocity field, achieving state-of-the-art performance on various benchmarks.
We introduce Rectified Point Flow, a unified parameterization that formulates
pairwise point cloud registration and multi-part shape assembly as a single
conditional generative problem. Given unposed point clouds, our method learns a
continuous point-wise velocity field that transports noisy points toward their
target positions, from which part poses are recovered. In contrast to prior
work that regresses part-wise poses with ad-hoc symmetry handling, our method
intrinsically learns assembly symmetries without symmetry labels. Together with
a self-supervised encoder focused on overlapping points, our method achieves a
new state-of-the-art performance on six benchmarks spanning pairwise
registration and shape assembly. Notably, our unified formulation enables
effective joint training on diverse datasets, facilitating the learning of
shared geometric priors and consequently boosting accuracy. Project page:
https://rectified-pointflow.github.io/.
