  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 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 a
benchmark cardiac segmentation dataset show our method to yield a performance
near to full supervision.
