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Learning Temporally Equivariance for Degenerative Disease Progression in OCT by Predicting Future Representations

Taha Emre, Arunava Chakravarty, Dmitrii Lachinov, Antoine Rivail, Ursula Schmidt-Erfurth, Hrvoje Bogunović

TL;DR

This work introduces Time-Equivariant Contrastive Learning (TC) to learn temporally sensitive representations from longitudinal OCT scans of AMD patients. By embedding time differences into a learnable displacement map within the representation space and applying a VICReg-based invariant projection, TC simultaneously models disease progression and preserves robustness to non-time-related perturbations. A novel regularization term prevents trivial collapse of the temporal predictor, enabling efficient training without extra contrastive tasks. On the HARBOR OCT dataset, TC outperforms existing equivariant methods in predicting conversion to wet-AMD within 6–12 months, demonstrating the value of explicit time-equivariant representations for early risk assessment in degenerative retinal diseases.

Abstract

Contrastive pretraining provides robust representations by ensuring their invariance to different image transformations while simultaneously preventing representational collapse. Equivariant contrastive learning, on the other hand, provides representations sensitive to specific image transformations while remaining invariant to others. By introducing equivariance to time-induced transformations, such as disease-related anatomical changes in longitudinal imaging, the model can effectively capture such changes in the representation space. In this work, we propose a Time-equivariant Contrastive Learning (TC) method. First, an encoder embeds two unlabeled scans from different time points of the same patient into the representation space. Next, a temporal equivariance module is trained to predict the representation of a later visit based on the representation from one of the previous visits and the corresponding time interval with a novel regularization loss term while preserving the invariance property to irrelevant image transformations. On a large longitudinal dataset, our model clearly outperforms existing equivariant contrastive methods in predicting progression from intermediate age-related macular degeneration (AMD) to advanced wet-AMD within a specified time-window.

Learning Temporally Equivariance for Degenerative Disease Progression in OCT by Predicting Future Representations

TL;DR

This work introduces Time-Equivariant Contrastive Learning (TC) to learn temporally sensitive representations from longitudinal OCT scans of AMD patients. By embedding time differences into a learnable displacement map within the representation space and applying a VICReg-based invariant projection, TC simultaneously models disease progression and preserves robustness to non-time-related perturbations. A novel regularization term prevents trivial collapse of the temporal predictor, enabling efficient training without extra contrastive tasks. On the HARBOR OCT dataset, TC outperforms existing equivariant methods in predicting conversion to wet-AMD within 6–12 months, demonstrating the value of explicit time-equivariant representations for early risk assessment in degenerative retinal diseases.

Abstract

Contrastive pretraining provides robust representations by ensuring their invariance to different image transformations while simultaneously preventing representational collapse. Equivariant contrastive learning, on the other hand, provides representations sensitive to specific image transformations while remaining invariant to others. By introducing equivariance to time-induced transformations, such as disease-related anatomical changes in longitudinal imaging, the model can effectively capture such changes in the representation space. In this work, we propose a Time-equivariant Contrastive Learning (TC) method. First, an encoder embeds two unlabeled scans from different time points of the same patient into the representation space. Next, a temporal equivariance module is trained to predict the representation of a later visit based on the representation from one of the previous visits and the corresponding time interval with a novel regularization loss term while preserving the invariance property to irrelevant image transformations. On a large longitudinal dataset, our model clearly outperforms existing equivariant contrastive methods in predicting progression from intermediate age-related macular degeneration (AMD) to advanced wet-AMD within a specified time-window.
Paper Structure (18 sections, 9 equations, 3 figures, 3 tables)

This paper contains 18 sections, 9 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Time-Equivariant Representations
  4. Time-Equivariant Contrastive Learning (TC)
  5. Experiments and Results
  6. Experimental Setup
  7. Dataset
  8. Implementation details
  9. Results
  10. Downstream prediction performance
  11. Evaluation of the equivariance module
  12. Ablation study
  13. Conclusion
  14. Acknowledgments.
  15. Disclosure of Interests.
  16. ...and 3 more sections

Figures (3)

  • Figure 1: An overview of TC architecture. (A) Representations of two scans acquired at two time points and the time difference are fed into $h_\psi$ for equivariance, then projected for the invariance loss. (B) Equivariance module with an additive displacement map.
  • Figure 2: Left: OCT scans with conversion to wet-AMD over time. Right: Contrastive augmentations examples.
  • Figure 3: Distance rankings between the original reprensentation $r_0$ and its propoageted prediction $r'_{t+ \Delta t}$ for 9 consecutive months for 40 patients.