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 $128\times 128$ coefficient resolution performed optimally for $512\times 512$ resolution CT images. For our best network, we achieve an average volumetric test Dice score of close to 92%, which reaches the state of the art for this congenital heart disease dataset.

我们提出了一种基于隐式样条表示与深度卷积神经网络相结合的图像分割新方法。这是通过预测一个双变量样条函数的控制点来完成的，该变量的零集表示分割边界。我们采用了几种现有的神经网络架构，并设计了新颖的损失函数，这些函数专门用于提供隐式样条曲线近似值。该方法在先天性心脏病计算机断层扫描医学成像数据集上进行评估。通过测量针对不同网络和损失功能的各种标准指标的性能来进行实验。我们确定双学位样条$（\mathrm{1个}，\mathrm{1个}）$ 和 $128\times 128$ 最佳执行的系数解析 $512\times 512$分辨率的CT图像。对于我们最好的网络，我们获得的平均Dice体积测试Dice分数接近92％，达到了该先天性心脏病数据集的最新水平。