  Segmentation of anatomical shapes from medical images has taken an important
role in the automation of clinical measurements. While typical deep-learning
segmentation approaches are performed on discrete voxels, the underlying
objects being analysed exist in a real-valued continuous space. Approaches that
rely on convolutional neural networks (CNNs) are limited to grid-like inputs
and not easily applicable to sparse or partial measurements. We propose a novel
family of image segmentation models that tackle many of CNNs' shortcomings:
Neural Implicit Segmentation Functions (NISF). Our framework takes inspiration
from the field of neural implicit functions where a network learns a mapping
from a real-valued coordinate-space to a shape representation. NISFs have the
ability to segment anatomical shapes in high-dimensional continuous spaces.
Training is not limited to voxelized grids, and covers applications with sparse
and partial data. Interpolation between observations is learnt naturally in the
training procedure and requires no post-processing. Furthermore, NISFs allow
the leveraging of learnt shape priors to make predictions for regions outside
of the original image plane. We go on to show the framework achieves dice
scores of 0.87 $\pm$ 0.045 on a (3D+t) short-axis cardiac segmentation task
using the UK Biobank dataset. We also provide a qualitative analysis on our
frameworks ability to perform segmentation and image interpolation on unseen
regions of an image volume at arbitrary resolutions.
