  The scarcity of labeled data often impedes the application of deep learning
to the segmentation of medical images. Semi-supervised learning seeks to
overcome this limitation by leveraging unlabeled examples in the learning
process. In this paper, we present a novel semi-supervised segmentation method
that leverages mutual information (MI) on categorical distributions to achieve
both global representation invariance and local smoothness. In this method, we
maximize the MI for intermediate feature embeddings that are taken from both
the encoder and decoder of a segmentation network. We first propose a global MI
loss constraining the encoder to learn an image representation that is
invariant to geometric transformations. Instead of resorting to
computationally-expensive techniques for estimating the MI on continuous
feature embeddings, we use projection heads to map them to a discrete cluster
assignment where MI can be computed efficiently. Our method also includes a
local MI loss to promote spatial consistency in the feature maps of the decoder
and provide a smoother segmentation. Since mutual information does not require
a strict ordering of clusters in two different assignments, we incorporate a
final consistency regularization loss on the output which helps align the
cluster labels throughout the network. We evaluate the method on three
challenging publicly-available datasets for medical image segmentation.
Experimental results show our method to outperform recently-proposed approaches
for semi-supervised segmentation and provide an accuracy near to full
supervision while training with very few annotated images
