💻 computer science

UPolarSQ: Polar Representation Learning for Optic Disc and Peripapillary Atrophy Segmentation and Quantification in Fundus Photographs

The paper proposes UPolarSQ, a unified polar-domain framework that transforms myopic fundus images into radial profiles to improve the segmentation of the optic disc and peripapillary atrophy while enabling direct, reliable quantification of clinical biomarkers.

Original authors: Mengxian He, Yunyun sun, Ziyue Gao, Wengkei Lam, Shunyi Zhang, Wu Yuan

Published 2026-08-11

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Mengxian He, Yunyun sun, Ziyue Gao, Wengkei Lam, Shunyi Zhang, Wu Yuan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to measure the shape of a crumpled piece of paper by looking at it from the side. It's messy, right? The edges are jagged, the curves are confusing, and trying to draw a perfect line around a specific spot is a nightmare. This is exactly the kind of problem doctors face when looking at the back of the human eye, specifically in people with high myopia (severe nearsightedness). In these eyes, the optic disc (the spot where the optic nerve enters the eye) and the surrounding tissue often get stretched and deformed, looking less like a neat circle and more like a weird, broken crescent moon.

To understand what's happening, doctors need to segment (draw a perfect outline around) these areas and measure them. But doing this by hand is slow, boring, and different doctors often draw different lines. Computers can help, but they usually try to solve this problem using standard "square" math, like a grid of pixels. When you try to fit a square grid onto a curved, stretched-out shape, the computer gets confused, leading to jagged, broken outlines. This paper enters the scene with a clever idea: instead of forcing the eye to fit into a square grid, why not reshape the grid to fit the eye?

The Paper's Big Idea: Unrolling the Eye

The researchers behind this study, led by Mengxian He and colleagues, propose a new way to look at these tricky eye images called UPolarSQ. Think of the back of a myopic eye not as a flat, square picture, but as a map of a city that has been wrapped around a cylinder. If you try to draw a street on that cylinder using a flat map, the lines get distorted. But if you "unroll" the cylinder onto a flat sheet of paper, the streets become straight lines again.

That is exactly what UPolarSQ does. It takes the image of the eye and mathematically "unrolls" it into a polar coordinate system. Instead of thinking in terms of left-right and up-down (x and y coordinates), the computer thinks in terms of distance from the center and the angle around the circle (radius and angle). In this new "unrolled" view, the messy, curved boundaries of the optic disc and the surrounding atrophy (damaged tissue) transform into simple, straight vertical lines. Suddenly, a complex 2D puzzle becomes a much easier 1D problem: just measure how tall the lines are at different angles.

How They Built the "Unroller"

To make this work, the team didn't just change the math; they built a special computer brain called UPolarSeg. Standard AI models are great at recognizing patterns in square grids, but they struggle with the weird stretching that happens when you unroll a circle. The researchers realized that in this unrolled view, the "up-down" direction (radius) and the "side-to-side" direction (angle) behave very differently.

Imagine a pizza. If you cut a slice, the crust is a long curve, but the distance from the tip to the crust is a straight line. In the unrolled eye image, the "crust" (the edge of the tissue) stretches out as you get further from the center. The team added a special module to their AI that treats these two directions separately. It's like giving the AI two different pairs of glasses: one pair to look at how things change as you move away from the center, and another pair to look at how things change as you spin around. This helps the AI understand the shape without getting confused by the stretching.

They also added a "helper" during the training phase. While the AI learns, it gets extra hints about where the edges of the shapes are, acting like a teacher pointing at the board. Once the AI is trained, this helper is removed, so the final tool is fast and efficient.

What They Found

The team tested their new method on two groups of patients: one group from their own hospital (internal) and another group from a different location (external) to see if it would work on different types of data. The results were quite promising.

When it came to drawing the outlines, their method was very accurate. On the internal group, it correctly identified the optic disc 98.36% of the time and the surrounding atrophy 89.59% of the time. On the external group, it still performed very well, getting 97.63% for the disc and 77.46% for the atrophy. This is a big deal because the surrounding atrophy is usually the hardest part to find, often looking like a faint, broken crescent.

More importantly, because the shapes were so clean in the unrolled view, the computer could measure the "biomarkers" (the specific numbers doctors use to track disease) much more accurately. For example, they could measure the width of the damaged tissue (PPA) with an error of only 2.4 pixels on the internal group and 6.7 pixels on the external group. This is significantly better than other popular AI models they compared against, which had errors ranging from 8.0 to 13.4 pixels for the same measurements.

Why This Matters

The paper suggests that by changing how we represent the image—from a square grid to a "unrolled" polar map—we can make AI much better at understanding the specific geometry of the eye. It's not just about drawing a better picture; it's about getting the numbers right. Since the measurements come directly from the unrolled lines, there's no need for messy post-processing or guessing.

The researchers found that this approach works well even when looking at eyes with different levels of myopia, from mild to severe. While they admit their dataset is still relatively small and they need to test it on even more diverse groups of people, the results suggest that this "unrolling" trick is a powerful tool. It turns a confusing, curved medical mystery into a straight-forward measurement, potentially helping doctors spot and track eye diseases earlier and more reliably.

Technical Summary: UPolarSQ

Problem Statement
Myopia-induced posterior-pole remodeling frequently results in Optic Disc (OD) deformation and Peripapillary Atrophy (PPA), which serve as critical structural biomarkers for ocular disease screening and progression monitoring. However, in standard Cartesian fundus images, PPA often presents as an irregular, partially visible crescent adjacent to the OD. This geometry leads to fragmented segmentation boundaries in Cartesian coordinate systems, necessitating complex post-processing for quantification. Furthermore, manual delineation is time-consuming and prone to inter-observer variability, particularly in highly myopic eyes where vessel occlusion and blurred boundaries are common. Existing deep learning methods often fail to explicitly encode the intrinsic radial-sector geometry of OD/PPA anatomy, leading to suboptimal performance in modeling these anisotropic structures.

Methodology
The authors propose UPolarSQ, a unified polar-domain framework designed to integrate OD/PPA segmentation and clinical biomarker quantification within a shared geometric representation. The framework operates in three stages:

OD-Centered Polar Transformation:
The system first localizes the OD center using a zero-shot model (RetSAM). It then crops a Region of Interest (ROI) centered on the OD and maps it from Cartesian coordinates $(x, y)$ to polar coordinates $(\theta, r)$ . This transformation unrolls complex curvatures into regular grids, converting 2D boundary modeling into 1D radial profile estimation. Theoretically, this mapping converts Cartesian rotation into linear translation along the angular axis and Cartesian scaling into radial dilation, aligning with the inductive biases of Convolutional Neural Networks (CNNs).
UPolarSeg Segmentation Network:
To adapt standard CNN architectures to the non-uniform geometry of the polar domain, the authors introduce UPolarSeg, a U-Net-based network enhanced with two specific modules:
- Radial-Angular-Decoupled Module (RADM): Addressing the anisotropic sampling metric of polar grids (where arc length scales with radius), RADM performs axis-specific feature refinement. It uses parallel anisotropic depthwise convolutions to separately capture radial transitions and angular continuity, injecting geometric priors into the skip connections.
- Boundary-Aware Auxiliary Supervision: An auxiliary decoder, active only during training, predicts radial boundaries (OD and outer OD/PPA) using a combination of Binary Cross-Entropy and soft Dice loss. This guides the shared representations toward clinically vital contours without adding inference-time computational cost.
Polar-Native Biomarker Quantification:
Unlike traditional methods requiring contour fitting or iterative post-processing, UPolarSQ directly extracts biomarkers from the predicted polar masks. By identifying the maximum radial indices for specific angles, the system deterministically calculates:
- Horizontal-to-Vertical Disc Diameter Ratio (HVDR).
- Maximum PPA Width (PMW).
- PPA-to-Vertical Disc Diameter Ratio (PVDR).

Key Contributions

Polar Representation Analysis: The paper formalizes OD/PPA analysis in an OD-centered polar representation, demonstrating how it converts 2D boundary modeling into radial profile estimation and provides inductive biases for CNNs while exposing polar-grid anisotropy.
Tailored Segmentation Network: The design of UPolarSeg explicitly models polar geometry through radial-angular decoupled feature refinement and boundary-aware auxiliary supervision, adapting CNN segmentation to polar constraints.
Unified Quantification Framework: UPolarSQ bridges the gap between segmentation and clinical quantification, enabling "polar-native" biomarker readouts that directly estimate OD deformation and PPA-width indicators from predicted radial profiles.

Experimental Results
The framework was evaluated on internal (Beijing) and external (Tibet) cohorts of myopic fundus images.

Segmentation Performance: UPolarSeg achieved OD/PPA Dice scores of 98.36% / 89.59% on the internal cohort and 97.63% / 77.46% on the external cohort. It outperformed state-of-the-art baselines (including UNet, SwinUNETR, and TransUNet) particularly in PPA segmentation, which is more challenging due to its irregular shape.
Quantification Accuracy: The method significantly reduced errors in clinical biomarker estimation. On the external cohort, it achieved the lowest Mean Absolute Error (MAE) for Maximum PPA Width (6.7 pixels) and PVDR (0.036).
Robustness: Subgroup analysis across low, moderate, and high myopia severities showed that UPolarSQ maintained consistent PPA delineation and quantification accuracy across varying disease severities and domain shifts, outperforming other models in high-myopia cases where anatomical deformation is pronounced.
Efficiency: The model operates with approximately 24.9M parameters, comparable to a vanilla UNet and significantly smaller than Transformer-based models like TransUNet or foundation models like RetSAM.

Significance and Claims
The paper claims that UPolarSQ provides an effective anatomical prior for the integrated analysis of myopic structures. By reformulating the problem in a polar coordinate system, the framework aligns anatomical structure, segmentation learning, and biomarker readout within a single coordinate system. The authors assert that this approach not only improves segmentation accuracy for irregular peripapillary structures but also supports reliable, direct estimation of clinical biomarkers without the need for complex post-processing. The study suggests that polar representation learning is a viable strategy for reducing estimation errors in myopic analysis, particularly under external domain shifts and varying disease severities.

Limitations
The authors acknowledge several limitations: the external cohort size is modest, requiring larger multi-center datasets for broader generalizability; the framework relies on accurate OD localization, which could be affected by severe artifacts or extreme disc deformation; and current biomarker readouts are derived solely from segmentation masks, suggesting a need for future integration with longitudinal outcomes to fully clarify clinical value.

Technical Summary: UPolarSQ

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