  Thin-plate splines can be used for interpolation of image values, but can
also be used to represent a smooth surface, such as the boundary between two
structures. We present a method for partitioning vertebra segmentation masks
into two substructures, the vertebral body and the posterior elements, using a
convolutional neural network that predicts the boundary between the two
structures. This boundary is modeled as a thin-plate spline surface defined by
a set of control points predicted by the network. The neural network is trained
using the reconstruction error of a convolutional autoencoder to enable the use
of unpaired data.
