  We propose CaSPR, a method to learn object-centric Canonical Spatiotemporal
Point Cloud Representations of dynamically moving or evolving objects. Our goal
is to enable information aggregation over time and the interrogation of object
state at any spatiotemporal neighborhood in the past, observed or not.
Different from previous work, CaSPR learns representations that support
spacetime continuity, are robust to variable and irregularly spacetime-sampled
point clouds, and generalize to unseen object instances. Our approach divides
the problem into two subtasks. First, we explicitly encode time by mapping an
input point cloud sequence to a spatiotemporally-canonicalized object space. We
then leverage this canonicalization to learn a spatiotemporal latent
representation using neural ordinary differential equations and a generative
model of dynamically evolving shapes using continuous normalizing flows. We
demonstrate the effectiveness of our method on several applications including
shape reconstruction, camera pose estimation, continuous spatiotemporal
sequence reconstruction, and correspondence estimation from irregularly or
intermittently sampled observations.
