# CeCNN: Copula-enhanced convolutional neural networks in joint prediction of refraction error and axial length based on ultra-widefield fundus images

arXiv: https://arxiv.org/abs/2311.03967 · HTML: https://mlsanity.com/paper/2311.03967/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 72 references that are in the map.
- First posted on arXiv 7 Nov 2023.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Multi-Label Image Recognition with Graph Convolutional Networks](https://mlsanity.com/paper/1904.03582/) (2019)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Image Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2204.08610/) (2022)
- [Non-Convex Projected Gradient Descent for Generalized Low-Rank Tensor Regression](https://mlsanity.com/paper/1611.10349/) (2016)
- [Deep Structured Learning for Facial Action Unit Intensity Estimation](https://mlsanity.com/paper/1704.04481/) (2017)
- [Significance tests of feature relevance for a black-box learner](https://mlsanity.com/paper/2103.04985/) (2021)
- [Learning Structure and Strength of CNN Filters for Small Sample Size Training](https://mlsanity.com/paper/1803.11405/) (2018)
- [Single-Stage Broad Multi-Instance Multi-Label Learning (BMIML) with Diverse Inter-Correlations and its application to medical image classification](https://mlsanity.com/paper/2209.02625/) (2022)
- [Robust Sensible Adversarial Learning of Deep Neural Networks for Image Classification](https://mlsanity.com/paper/2205.10457/) (2022)

## Built on by (most cited first, 3 of 3)

- [OUCopula: Bi-Channel Multi-Label Copula-Enhanced Adapter-Based CNN for Myopia Screening Based on OU-UWF Images](https://mlsanity.com/paper/2403.11974/) (2024)
- [OU-CoViT: Copula-Enhanced Bi-Channel Multi-Task Vision Transformers with Dual Adaptation for OU-UWF Images](https://mlsanity.com/paper/2408.09395/) (2024)
- [Copula-enhanced Vision Transformer for high myopia diagnosis through OU UWF fundus images](https://mlsanity.com/paper/2501.06540/) (2025)

## Abstract (arXiv)

The ultra-widefield (UWF) fundus image is an attractive 3D biomarker in AI-aided myopia screening because it provides much richer myopia-related information. Though axial length (AL) has been acknowledged to be highly related to the two key targets of myopia screening, Spherical Equivalence (SE) measurement and high myopia diagnosis, its prediction based on the UWF fundus image is rarely considered. To save the high expense and time costs of measuring SE and AL, we propose the Copula-enhanced Convolutional Neural Network (CeCNN), a one-stop UWF-based ophthalmic AI framework to jointly predict SE, AL, and myopia status. The CeCNN formulates a multiresponse regression that relates multiple dependent discrete-continuous responses and the image covariate, where the nonlinearity of the association is modeled by a backbone CNN. To thoroughly describe the dependence structure among the responses, we model and incorporate the conditional dependence among responses in a CNN through a new copula-likelihood loss. We provide statistical interpretations of the conditional dependence among responses, and reveal that such dependence is beyond the dependence explained by the image covariate. We heuristically justify that the proposed loss can enhance the estimation efficiency of the CNN weights. We apply the CeCNN to the UWF dataset collected by us and demonstrate that the CeCNN sharply enhances the predictive capability of various backbone CNNs. Our study evidences the ophthalmology view that besides SE, AL is also an important measure to myopia.