# A General B'ezier Tree Encoding Counterfactual Framework for Retinal-Vessel-Mediated Disease Analysis

arXiv: https://arxiv.org/abs/2605.13015 · HTML: https://mlsanity.com/paper/2605.13015/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 62 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 10 of 10)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [BiomedCLIP: a multimodal biomedical foundation model pretrained from fifteen million scientific image-text pairs](https://mlsanity.com/paper/2303.00915/) (2023)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Robust image representations with counterfactual contrastive learning](https://mlsanity.com/paper/2409.10365/) (2024)
- [Generation of Structurally Realistic Retinal Fundus Images with Diffusion Models](https://mlsanity.com/paper/2305.06813/) (2023)
- [CauDR: A Causality-inspired Domain Generalization Framework for Fundus-based Diabetic Retinopathy Grading](https://mlsanity.com/paper/2309.15493/) (2023)
- [An Explainable Transformer Model for Alzheimer's Disease Detection Using Retinal Imaging](https://mlsanity.com/paper/2507.04259/) (2025)

## Abstract (arXiv)

The geometry of the retinal vessel is a key biomarker of vascular diseases, yet clinical evidence remains primarily observational. Existing generative counterfactuals intervene only at the image-level disease label, failing to isolate explicit anatomical structure. To address this limitation, we propose the B'ezier Tree Encoding Counterfactual Framework (BTECF). By abstracting vascular networks into interconnected cubic-B'ezier segments, BTECF establishes a disease-agnostic representation in which structural topology is explicitly preserved and atomically perturbable. Coupling this encoding with a diffusion-based generator enables parameter-level do-interventions on explicit geometric axes (e.g., tortuosity, caliber) while preserving background fundus textures. We validate BTECF on diabetic retinopathy, together with independent cohorts for ischemic stroke and Alzheimer's disease. Isolated counterfactual interventions produce dose-responsive shifts in classifier predictions; a matched pixel-drop control attenuates this response by an order of magnitude or more, ruling out out-of-distribution generation artifacts. By enforcing causal isolation between vessel topology and pixel-level confounders, BTECF provides a unified generative paradigm for hypothesis verification across systemic diseases. To support reproducibility, the code will be publicly released upon acceptance.