Discretely-constrained deep network for weakly supervised segmentation

An efficient strategy for weakly-supervised segmentation is to impose constraints or regularization priors on target regions. Recent efforts have focused on incorporating such constraints in the training of convolutional neural networks (CNN), however this has so far been done within a continuous optimization framework. Yet, various segmentation constraints and regularization priors can be modeled and optimized more efficiently in a discrete formulation. This paper proposes a method, based on the alternating direction method of multipliers (ADMM) algorithm, to train a CNN with discrete constraints and regularization priors. This method is applied to the segmentation of medical images with weak annotations, where both size constraints and boundary length regularization are enforced. Experiments on two benchmark datasets for medical image segmentation show our method to provide significant improvements compared to existing approaches in terms of segmentation accuracy, constraint satisfaction and convergence speed.