Ultra-widefield (UWF) fundus images are replacing traditional fundus images in screening, detection, prediction, and treatment of complications related to myopia because their much broader visual range is advantageous for highly myopic eyes. Spherical equivalent (SE) is extensively used as the main myopia outcome measure, and axial length (AL) has drawn increasing interest as an important ocular component for assessing myopia. Cutting-edge studies show that SE and AL are strongly correlated. Using the joint information from SE and AL is potentially better than using either separately. In the deep learning community, though there is research on multiple-response tasks with a 3D image biomarker, dependence among responses is only sporadically taken into consideration. Inspired by the spirit that information extracted from the data by statistical methods can improve the prediction accuracy of deep learning models, we formulate a class of multivariate response regression models with a higher-order tensor biomarker, for the bivariate tasks of regression-classification and regression-regression. Specifically, we propose a copula-enhanced convolutional neural network (CeCNN) framework that incorporates the dependence between responses through a Gaussian copula (with parameters estimated from a warm-up CNN) and uses the induced copula-likelihood loss with the backbone CNNs. We establish the statistical framework and algorithms for the aforementioned two bivariate tasks. We show that the CeCNN has better prediction accuracy after adding the dependency information to the backbone models. The modeling and the proposed CeCNN algorithm are applicable beyond the UWF scenario and can be effective with other backbones beyond ResNet and LeNet.

翻译：超广角眼底图像因其更宽广的视野范围在高度近视眼的筛查、检测、预测及相关并发症治疗中正逐步取代传统眼底图像。等效球镜作为主要近视结局指标被广泛使用，而眼轴长度作为评估近视的重要眼部组成部分日益受到关注。前沿研究表明，等效球镜与眼轴长度之间存在强相关性。联合使用等效球镜与眼轴长度的信息可能优于单独使用任一指标。在深度学习领域，尽管已有研究针对三维图像生物标志物开展多响应任务，但响应变量间的依赖性仅被零星考虑。受统计学方法从数据中提取的信息可提升深度学习模型预测准确率这一理念启发，我们针对回归-分类与回归-回归二元任务，构建了一类以高阶张量生物标志物为特征的多变量响应回归模型。具体而言，我们提出Copula增强卷积神经网络框架，通过高斯Copula（其参数由预热训练的CNN估计）纳入响应变量间的依赖性，并利用该Copula似然损失函数与骨干CNN协同训练。我们为上述两类二元任务建立了统计框架与算法。实验证明，将依赖性信息纳入骨干模型后，CeCNN具有更优的预测准确率。所提出的建模方法与CeCNN算法不仅适用于超广角眼底图像场景，还可有效迁移至ResNet及LeNet之外的其它骨干网络。