  In image segmentation, there is often more than one plausible solution for a
given input. In medical imaging, for example, experts will often disagree about
the exact location of object boundaries. Estimating this inherent uncertainty
and predicting multiple plausible hypotheses is of great interest in many
applications, yet this ability is lacking in most current deep learning
methods. In this paper, we introduce stochastic segmentation networks (SSNs),
an efficient probabilistic method for modelling aleatoric uncertainty with any
image segmentation network architecture. In contrast to approaches that produce
pixel-wise estimates, SSNs model joint distributions over entire label maps and
thus can generate multiple spatially coherent hypotheses for a single image. By
using a low-rank multivariate normal distribution over the logit space to model
the probability of the label map given the image, we obtain a spatially
consistent probability distribution that can be efficiently computed by a
neural network without any changes to the underlying architecture. We tested
our method on the segmentation of real-world medical data, including lung
nodules in 2D CT and brain tumours in 3D multimodal MRI scans. SSNs outperform
state-of-the-art for modelling correlated uncertainty in ambiguous images while
being much simpler, more flexible, and more efficient.
