  We demonstrate an object tracking method for 3D images with fixed
computational cost and state-of-the-art performance. Previous methods predicted
transformation parameters from convolutional layers. We instead propose an
architecture that does not include either flattening of convolutional features
or fully connected layers, but instead relies on equivariant filters to
preserve transformations between inputs and outputs (e.g. rot./trans. of inputs
rotate/translate outputs). The transformation is then derived in closed form
from the outputs of the filters. This method is useful for applications
requiring low latency, such as real-time tracking. We demonstrate our model on
synthetically augmented adult brain MRI, as well as fetal brain MRI, which is
the intended use-case.
