  We use Deep Convolutional Neural Networks (DCNNs) for image segmentation
problems. DCNNs can well extract the features from natural images. However, the
classification functions in the existing network architecture of CNNs are
simple and lack capabilities to handle important spatial information in a way
that have been done for many well-known traditional variational models. Prior
such as spatial regularity, volume prior and object shapes cannot be well
handled by existing DCNNs. We propose a novel Soft Threshold Dynamics (STD)
framework which can easily integrate many spatial priors of the classical
variational models into the DCNNs for image segmentation. The novelty of our
method is to interpret the softmax activation function as a dual variable in a
variational problem, and thus many spatial priors can be imposed in the dual
space. From this viewpoint, we can build a STD based framework which can enable
the outputs of DCNNs to have many special priors such as spatial regularity,
volume constraints and star-shape priori. The proposed method is a general
mathematical framework and it can be applied to any semantic segmentation
DCNNs. To show the efficiency and accuracy of our method, we applied it to the
popular DeepLabV3+ image segmentation network, and the experiments results show
that our method can work efficiently on data-driven image segmentation DCNNs.
