  Many segmentation tasks for biomedical images can be modeled as the
minimization of an energy function and solved by a class of max-flow and
min-cut optimization algorithms. However, the segmentation accuracy is
sensitive to the contrasting of semantic features of different segmenting
objects, as the traditional energy function usually uses hand-crafted features
in their energy functions. To address these limitations, we propose to
incorporate end-to-end trainable neural network features into the energy
functions. Our deep neural network features are extracted from the
down-sampling and up-sampling layers with skip-connections of a U-net. In the
inference stage, the learned features are fed into the energy functions. And
the segmentations are solved in a primal-dual form by ADMM solvers. In the
training stage, we train our neural networks by optimizing the energy function
in the primal form with regularizations on the min-cut and flow-conservation
functions, which are derived from the optimal conditions in the dual form. We
evaluate our methods, both qualitatively and quantitatively, in a brain tumor
segmentation task. As the energy minimization model achieves a balance on
sensitivity and smooth boundaries, we would show how our segmentation contours
evolve actively through iterations as ensemble references for doctor diagnosis.
