  Deep learning models dealing with image understanding in real-world settings
must be able to adapt to a wide variety of tasks across different domains.
Domain adaptation and class incremental learning deal with domain and task
variability separately, whereas their unified solution is still an open
problem. We tackle both facets of the problem together, taking into account the
semantic shift within both input and label spaces. We start by formally
introducing continual learning under task and domain shift. Then, we address
the proposed setup by using style transfer techniques to extend knowledge
across domains when learning incremental tasks and a robust distillation
framework to effectively recollect task knowledge under incremental domain
shift. The devised framework (LwS, Learning with Style) is able to generalize
incrementally acquired task knowledge across all the domains encountered,
proving to be robust against catastrophic forgetting. Extensive experimental
evaluation on multiple autonomous driving datasets shows how the proposed
method outperforms existing approaches, which prove to be ill-equipped to deal
with continual semantic segmentation under both task and domain shift.
