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.
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