Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Chong Zhong, Yang Li, Danjuan Yang, Meiyan Li, Xingyao Zhou, Bo Fu, Catherine C. Liu, A. H. Welsh

TL;DR

CeCNN introduces a copula-based multi-task CNN framework to jointly predict spherical equivalence, axial length, and high myopia status from ultra-widefield fundus images. By modeling mixed-type outputs with a Gaussian copula and a copula-likelihood loss, it captures conditional dependence among responses beyond what is explained by the image covariate, and it uses a three-module training pipeline (warm-up, copula estimation, and end-to-end optimization). Across a UWF dataset and synthetic simulations, CeCNN improves regression and classification metrics (e.g., RMSE, MAE, AUC) compared to empirical losses, with larger gains for richer backbones, and provides statistical interpretations of the efficiency gains. This work demonstrates that AL provides complementary predictive value for myopia screening and offers a principled approach to harness conditional dependence in multi-task ophthalmic AI.

Abstract

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.

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

TL;DR

CeCNN introduces a copula-based multi-task CNN framework to jointly predict spherical equivalence, axial length, and high myopia status from ultra-widefield fundus images. By modeling mixed-type outputs with a Gaussian copula and a copula-likelihood loss, it captures conditional dependence among responses beyond what is explained by the image covariate, and it uses a three-module training pipeline (warm-up, copula estimation, and end-to-end optimization). Across a UWF dataset and synthetic simulations, CeCNN improves regression and classification metrics (e.g., RMSE, MAE, AUC) compared to empirical losses, with larger gains for richer backbones, and provides statistical interpretations of the efficiency gains. This work demonstrates that AL provides complementary predictive value for myopia screening and offers a principled approach to harness conditional dependence in multi-task ophthalmic AI.

Abstract

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.
Paper Structure (19 sections, 2 theorems, 30 equations, 7 figures, 2 algorithms)

This paper contains 19 sections, 2 theorems, 30 equations, 7 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivations
  3. Related work
  4. CeCNN: Copula Enhanced CNN framework
  5. Our contributions
  6. Regression-classification task
  7. Copula-likelihood loss
  8. End-to-end CeCNN
  9. Regression-regression task
  10. Rethinking the copula-likelihood loss: relative efficiency
  11. Application to the UWF fundus image dataset
  12. Data preparation
  13. Structure of backbone CNNs
  14. Results on the UWF dataset
  15. Simulations on synthetic data
  16. ...and 4 more sections

Key Result

Theorem 2.1

Suppose the joint distribution of $\bm{Y} = (y_1, y_2)$ is given by Gaussian copula Gaussian Copula with correlation matrix $\Gamma$, where the marginal distributions of $y_1$ and $y_2$ are given by Marginal R-C. Let $\mu_1 = g_1(\mathcal{X})$ and $\mu_2 = \mathcal{S} \circ g_2(\mathcal{X})$ be the

Figures (7)

  • Figure 1: Advantages of UWF imaging in myopia-related pathology. The orange dashed circle represents the area covered by regular fundus images. The area within the yellow circle indicates lesions caused by peripheral laser spots, the region within the blue circle shows extreme peripheral chorioretinal atrophy, and the area within the green circle contains pigmentary degeneration lesions.
  • Figure 2: Left: scatter plot; right:contour plot; x axis: AL; y axis: SE.
  • Figure 3: The architectures of backbone CNNs used. Top: architecture of simplified LeNet; middle: architecture of simplified ResNet; Bottom: architecture of simplified DenseNet.
  • Figure 4: The whole architecture of the CeCNN framework.
  • Figure 5: Box plots of RMSE, classficiation accuracy and AUC in 10 rounds of 5-fold validation of the R-C tasks. Top: with LeNet backbone; middle: with ResNet backbone; bottom: with DenseNet backbone.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Theorem 2.1
  • Theorem 4.1: Relative efficiency