  We present Canonical Consolidation Fields (CanFields): a method for
reconstructing a time series of independently-sampled point clouds into a
single deforming coherent shape. Such input often comes from motion capture.
Existing methods either couple the geometry and the deformation, where by doing
so they smooth fine details and lose the ability to track moving points, or
they track the deformation explicitly, but introduce topological and geometric
artifacts. Our novelty lies in the consolidation of the point clouds into a
single canonical shape in a way that reduces the effect of noise and outliers,
and enables us to overcome missing regions. We simultaneously reconstruct the
velocity fields that guide the deformation. This consolidation allows us to
retain the high-frequency details of the geometry, while faithfully reproducing
the low-frequency deformation. Our architecture comprises simple components,
and fits any single input shape without using datasets. We demonstrate the
robustness and accuracy of our methods on a diverse benchmark of dynamic point
clouds, including missing regions, sparse frames, and noise.
