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 reg-ularizations 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.
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