Vertebra partitioning with thin-plate spline surfaces steered by a convolutional neural network

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.