  Active Surface Models have a long history of being useful to model complex 3D
surfaces but only Active Contours have been used in conjunction with deep
networks, and then only to produce the data term as well as meta-parameter maps
controlling them. In this paper, we advocate a much tighter integration. We
introduce layers that implement them that can be integrated seamlessly into
Graph Convolutional Networks to enforce sophisticated smoothness priors at an
acceptable computational cost. We will show that the resulting Deep Active
Surface Models outperform equivalent architectures that use traditional
regularization loss terms to impose smoothness priors for 3D surface
reconstruction from 2D images and for 3D volume segmentation.
