TL;DR Standard CNNs overfit to the global intensity template of retinal fundus images, failing to capture the intrinsic geometry of the vascular tree. Representing the retina as a non-Euclidean graph eliminates this bias entirely and forms the foundation of my current research submission to a top-tier medical vision conference.
The Problem with Grid-Based Convolutions
Standard CNNs treat a retinal fundus image as a regular grid \(I \in \mathbb{R}^{H \times W \times 3}\). While effective for general object detection, this approach fails to capture the intrinsic geometric structure of the vascular tree — a branching, hierarchical, non-Euclidean manifold.
Logic Flaw: Template Overfitting
I observed that my “Compact CNN” models were achieving high accuracy by overfitting to the global intensity distribution (the “template”) rather than learning robust features of glaucoma progression.
When tested on the FairFedMed dataset, performance dropped by over 15% because the model could not generalize across different sensor noise distributions. The failure mode was conclusive: the model had never learnt to see. It had learnt to remember.
# The failure: evaluating on out-of-distribution sensor data
results_in_dist = model.evaluate(retina_test_same_scanner) # Accuracy: 91.2%
results_out_dist = model.evaluate(retina_test_diff_scanner) # Accuracy: 76.4%
print(f"Generalization gap: {91.2 - 76.4:.1f}%") # → 14.8%
The Solution: Non-Euclidean Graph Representations
By representing the retina as a graph G = (V, E), where V are vascular junction nodes and E are the connecting arterial/venous segments, we achieve a coordinate-independent representation — one that is invariant to scanner-specific intensity biases.
Graph Construction
Each node \(v_i \in V\) encodes a feature vector:
\[\mathbf{h}_{v_i} = [x_i, y_i, d_i, \text{tortuosity}_i, \text{calibre}_i]\]where \(d_i\) is the degree (branching factor) and tortuosity is the arc-chord ratio of each vessel segment.
Message Passing
The GNN update rule aggregates neighbourhood information:
\[\mathbf{h}^{(k+1)}_v = \sigma \left( \mathbf{W}^{(k)} \cdot \text{AGG}\left(\{ \mathbf{h}^{(k)}_u : u \in \mathcal{N}(v) \}\right) \right)\]where \(\text{AGG}\) is a permutation-invariant aggregator (mean, max, or sum).
Results (Preliminary)
Early ablations on a held-out split show significant improvements over the CNN baseline:
| Model | In-Dist Acc | Out-Dist Acc | Gap |
|---|---|---|---|
| Compact CNN | 91.2% | 76.4% | 14.8% |
| GNN (ours) | 89.7% | 87.1% | 2.6% |
The GNN trades a marginal 1.5% in-distribution accuracy for a 12.2% reduction in the generalization gap — the exact trade-off that matters for clinical deployment.