  Our work expands the use of capsule networks to the task of object
segmentation for the first time in the literature. This is made possible via
the introduction of locally-constrained routing and transformation matrix
sharing, which reduces the parameter/memory burden and allows for the
segmentation of objects at large resolutions. To compensate for the loss of
global information in constraining the routing, we propose the concept of
"deconvolutional" capsules to create a deep encoder-decoder style network,
called SegCaps. We extend the masked reconstruction regularization to the task
of segmentation and perform thorough ablation experiments on each component of
our method. The proposed convolutional-deconvolutional capsule network,
SegCaps, shows state-of-the-art results while using a fraction of the
parameters of popular segmentation networks. To validate our proposed method,
we perform experiments segmenting pathological lungs from clinical and
pre-clinical thoracic computed tomography (CT) scans and segmenting muscle and
adipose (fat) tissue from magnetic resonance imaging (MRI) scans of human
subjects' thighs. Notably, our experiments in lung segmentation represent the
largest-scale study in pathological lung segmentation in the literature, where
we conduct experiments across five extremely challenging datasets, containing
both clinical and pre-clinical subjects, and nearly 2000 computed-tomography
scans. Our newly developed segmentation platform outperforms other methods
across all datasets while utilizing less than 5% of the parameters in the
popular U-Net for biomedical image segmentation. Further, we demonstrate
capsules' ability to generalize to unseen rotations/reflections on natural
images.
