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（UWF）眼底图像因其更广阔的视野范围对高度近视眼具有显著优势，正在逐步取代传统眼底图像，应用于近视相关并发症的筛查、检测、预测和治疗。等效球镜度（SE）被广泛用作近视的主要结果指标，而眼轴长度（AL）作为评估近视的重要眼部组成部分，正受到越来越多的关注。前沿研究表明，SE与AL之间存在强相关性。联合利用SE与AL的信息可能比单独使用任一指标更具优势。在深度学习领域，尽管已有研究涉及基于三维图像生物标志物的多响应任务，但对响应间依赖关系的考虑仍较为零散。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精度这一理念的启发，我们针对回归-分类与回归-回归两类双变量任务，构建了一类具有高阶张量生物标志物的多元响应回归模型。具体而言，我们提出了一种Copula增强的卷积神经网络（CeCNN）框架，该框架通过高斯Copula（其参数由预热CNN估计）纳入响应间的依赖关系，并在主干CNN中使用由此导出的Copula似然损失。我们为上述两种双变量任务建立了统计框架与算法。实验表明，在主干模型中添加依赖信息后，CeCNN具有更优的预测精度。该建模方法与所提出的CeCNN算法可推广至UWF场景之外，且能有效适配ResNet与LeNet之外的其他主干网络。