Deep Convolutional Neural Networks with Spatial Regularization, Volume and Star-shape Priori for Image Segmentation

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.