  In semantic segmentation tasks, input images can often have more than one
plausible interpretation, thus allowing for multiple valid labels. To capture
such ambiguities, recent work has explored the use of probabilistic networks
that can learn a distribution over predictions. However, these do not
necessarily represent the empirical distribution accurately. In this work, we
present a strategy for learning a calibrated predictive distribution over
semantic maps, where the probability associated with each prediction reflects
its ground truth correctness likelihood. To this end, we propose a novel
two-stage, cascaded approach for calibrated adversarial refinement: (i) a
standard segmentation network is trained with categorical cross entropy to
predict a pixelwise probability distribution over semantic classes and (ii) an
adversarially trained stochastic network is used to model the inter-pixel
correlations to refine the output of the first network into coherent samples.
Importantly, to calibrate the refinement network and prevent mode collapse, the
expectation of the samples in the second stage is matched to the probabilities
predicted in the first. We demonstrate the versatility and robustness of the
approach by achieving state-of-the-art results on the multigrader LIDC dataset
and on a modified Cityscapes dataset with injected ambiguities. In addition, we
show that the core design can be adapted to other tasks requiring learning a
calibrated predictive distribution by experimenting on a toy regression
dataset. We provide an open source implementation of our method at
https://github.com/EliasKassapis/CARSSS.
