  Convolutional neural networks (CNNs) are the current state-of-the-art
meta-algorithm for volumetric segmentation of medical data, for example, to
localize COVID-19 infected tissue on computer tomography scans or the detection
of tumour volumes in magnetic resonance imaging. A key limitation of 3D CNNs on
voxelised data is that the memory consumption grows cubically with the training
data resolution. Occupancy networks (O-Nets) are an alternative for which the
data is represented continuously in a function space and 3D shapes are learned
as a continuous decision boundary. While O-Nets are significantly more memory
efficient than 3D CNNs, they are limited to simple shapes, are relatively slow
at inference, and have not yet been adapted for 3D semantic segmentation of
medical data. Here, we propose Occupancy Networks for Semantic Segmentation
(OSS-Nets) to accurately and memory-efficiently segment 3D medical data. We
build upon the original O-Net with modifications for increased expressiveness
leading to improved segmentation performance comparable to 3D CNNs, as well as
modifications for faster inference. We leverage local observations to represent
complex shapes and prior encoder predictions to expedite inference. We showcase
OSS-Net's performance on 3D brain tumour and liver segmentation against a
function space baseline (O-Net), a performance baseline (3D residual U-Net),
and an efficiency baseline (2D residual U-Net). OSS-Net yields segmentation
results similar to the performance baseline and superior to the function space
and efficiency baselines. In terms of memory efficiency, OSS-Net consumes
comparable amounts of memory as the function space baseline, somewhat more
memory than the efficiency baseline and significantly less than the performance
baseline. As such, OSS-Net enables memory-efficient and accurate 3D semantic
segmentation that can scale to high resolutions.
