  In this paper, we introduce SpaER, a pioneering method for fetal motion
tracking that leverages equivariant filters and self-attention mechanisms to
effectively learn spatio-temporal representations. Different from conventional
approaches that statically estimate fetal brain motions from pairs of images,
our method dynamically tracks the rigid movement patterns of the fetal head
across temporal and spatial dimensions. Specifically, we first develop an
equivariant neural network that efficiently learns rigid motion sequences
through low-dimensional spatial representations of images. Subsequently, we
learn spatio-temporal representations by incorporating time encoding and
self-attention neural network layers. This approach allows for the capture of
long-term dependencies of fetal brain motion and addresses alignment errors due
to contrast changes and severe motion artifacts. Our model also provides a
geometric deformation estimation that properly addresses image distortions
among all time frames. To the best of our knowledge, our approach is the first
to learn spatial-temporal representations via deep neural networks for fetal
motion tracking without data augmentation. We validated our model using real
fetal echo-planar images with simulated and real motions. Our method carries
significant potential value in accurately measuring, tracking, and correcting
fetal motion in fetal MRI sequences.
