  We propose a novel approach to image segmentation based on combining implicit
spline representations with deep convolutional neural networks. This is done by
predicting the control points of a bivariate spline function whose zero-set
represents the segmentation boundary. We adapt several existing neural network
architectures and design novel loss functions that are tailored towards
providing implicit spline curve approximations. The method is evaluated on a
congenital heart disease computed tomography medical imaging dataset.
Experiments are carried out by measuring performance in various standard
metrics for different networks and loss functions. We determine that splines of
bidegree $(1,1)$ with $128\times128$ coefficient resolution performed optimally
for $512\times 512$ resolution CT images. For our best network, we achieve an
average volumetric test Dice score of almost 92%, which reaches the state of
the art for this congenital heart disease dataset.
