  Recent 4D shape representations model continuous temporal evolution of
implicit shapes by (1) learning query flows without leveraging shape and
articulation priors or (2) decoding shape occupancies separately for each time
value. Thus, they do not effectively capture implicit correspondences between
articulated shapes or regularize jittery temporal deformations. In this work,
we present FourierHandFlow, which is a spatio-temporally continuous
representation for human hands that combines a 3D occupancy field with
articulation-aware query flows represented as Fourier series. Given an input
RGB sequence, we aim to learn a fixed number of Fourier coefficients for each
query flow to guarantee smooth and continuous temporal shape dynamics. To
effectively model spatio-temporal deformations of articulated hands, we compose
our 4D representation based on two types of Fourier query flow: (1) pose flow
that models query dynamics influenced by hand articulation changes via implicit
linear blend skinning and (2) shape flow that models query-wise displacement
flow. In the experiments, our method achieves state-of-the-art results on
video-based 4D reconstruction while being computationally more efficient than
the existing 3D/4D implicit shape representations. We additionally show our
results on motion inter- and extrapolation and texture transfer using the
learned correspondences of implicit shapes. To the best of our knowledge,
FourierHandFlow is the first neural 4D continuous hand representation learned
from RGB videos. The code will be publicly accessible.
