  Acquisition of training data for the standard semantic segmentation is
expensive if requiring that each pixel is labeled. Yet, current methods
significantly deteriorate in weakly supervised settings, e.g. where a fraction
of pixels is labeled or when only image-level tags are available. It has been
shown that regularized losses - originally developed for unsupervised low-level
segmentation and representing geometric priors on pixel labels - can
considerably improve the quality of weakly supervised training. However, many
common priors require optimization stronger than gradient descent. Thus, such
regularizers have limited applicability in deep learning. We propose a new
robust trust region approach for regularized losses improving the
state-of-the-art results. Our approach can be seen as a higher-order
generalization of the classic chain rule. It allows neural network optimization
to use strong low-level solvers for the corresponding regularizers, including
discrete ones.
