Axial Length Matters: Scaling Effects in Retinal Fundus Image Analysis

This study demonstrates that axial length significantly biases retinal vascular metrics derived from fundus images, but these systematic errors can be effectively corrected using the Bennett-Littmann formula to ensure accurate biomarker development for systemic diseases.

The Gist

The "Zoom Lens" Problem: Why Eye Size Matters in Retinal Scans

Imagine you are trying to measure the size of a tree using a photograph. If you take a picture of a small sapling from 10 feet away, and a picture of a giant oak from 100 feet away, the oak will look tiny in the photo, even though it's actually huge. If you tried to measure the tree's height just by looking at the photo without knowing how far away the camera was, you'd get the wrong answer.

This is exactly the problem scientists faced when analyzing retinal fundus images (photos of the back of the eye) to detect diseases like diabetes or heart problems.

The Hidden Variable: Axial Length

The back of the eye isn't the same size for everyone.

• Short eyes (Hyperopia): The eye is shorter, so the retina is "cramped." The image looks zoomed in (magnified).
• Long eyes (Myopia/Nearsightedness): The eye is longer, so the retina is stretched out. The image looks zoomed out (minified).

In the past, computer algorithms (AI) looked at these eye photos and assumed every eye was the same "standard size." They measured things like blood vessel width and length directly from the pixels in the image.

The Analogy:
Think of the AI as a robot trying to measure the width of a river.

• If the robot looks at a photo of a river taken from a helicopter (zoomed out), it thinks the river is narrow.
• If it looks at a photo taken from a boat (zoomed in), it thinks the river is wide.
• The Mistake: The robot didn't know the camera height (the eye's length), so it kept making the same mistake for every photo.

What This Study Found

The researchers analyzed over 2,300 eye scans from children and young adults. They compared the "naive" measurements (ignoring eye size) against "corrected" measurements (using a mathematical formula called Bennett-Littmann to account for the actual eye length).

Here is what they discovered:

1. The "1mm Rule": For every 1 millimeter difference in eye length from the average, the measurements were off by about 4.5%.

   • Example: If a person has a long eye (nearsighted), the AI thought their blood vessels were 10% thinner than they actually were.
   • Example: If a person has a short eye (farsighted), the AI thought their vessels were 10% wider.

2. Area is Even Worse: Because area is a 2D measurement (width × height), the error doubles. A 1mm difference in eye length caused a 9–10% error in the calculated area of the blood vessels.

3. The "Branch Count" Exception: Interestingly, counting how many times a blood vessel splits (like a tree branching) was not affected by eye size. Whether the image is zoomed in or out, the number of branches stays the same. This is like counting the number of leaves on a tree; it doesn't matter how far away you are, the count is the same.

Why Should You Care?

These retinal measurements are becoming "biomarkers"—clues that doctors use to predict serious health issues like heart attacks, kidney disease, and even Alzheimer's.

• The Danger: If a nearsighted person (long eye) has their blood vessels measured without correction, the AI might think their vessels are dangerously thin. This could lead to a false alarm, telling a healthy person they are at high risk for a heart attack.
• The Reverse: A farsighted person might have their vessels measured as "too wide," potentially hiding a real health risk.

The Solution

The paper argues that we need to stop treating all eye photos as if they were taken with the same zoom level.

• The Fix: Before an AI analyzes an eye photo, it should ask: "How long is this person's eye?"
• The Result: Using a simple math formula (Bennett-Littmann), we can "un-zoom" or "re-zoom" the image to a standard size. This ensures that a 5mm blood vessel in a nearsighted eye is measured the same way as a 5mm vessel in a farsighted eye.

The Bottom Line

Just as you wouldn't measure a map without knowing its scale, we shouldn't measure the tiny blood vessels in our eyes without knowing the size of the eye itself. By fixing this "zoom lens" error, we can make AI diagnostics much more accurate and prevent people from getting the wrong diagnosis based on how long their eyeball happens to be.

Technical Summary

1. Problem Statement

Retinal fundus photography is increasingly used as a non-invasive "window" into systemic health, with Artificial Intelligence (AI) models extracting quantitative biomarkers (e.g., vessel caliber, tortuosity, area, and density) to predict cardiovascular, metabolic, and neurological diseases.

However, a critical systematic error exists in current analytical pipelines: ocular magnification.

• The Issue: The size of retinal structures in a fundus image is inversely proportional to the eye's axial length (AL). Longer eyes (myopia) project smaller images of retinal structures, while shorter eyes (hyperopia) project larger images.
• The Consequence: Most AI algorithms and quantitative studies assume a uniform scale across all patients, implicitly treating fundus images as if they share a common magnification. This leads to systematic biases where vascular metrics are underestimated in myopic eyes and overestimated in hyperopic eyes.
• The Gap: While magnification correction is standard in Optical Coherence Tomography (OCT) for optic disc analysis, it is largely overlooked in fundus-based vascular biomarker studies. No quantitative model previously existed describing how this error scales specifically for vascular segmentation metrics across a broad population.

2. Methodology

The study employed a retrospective analysis of clinical data to quantify and model these scaling errors.

• Study Population:
  • Cohort: 2,309 clinic visits from patients aged ≤21 years (children and young adults) to minimize age-related confounding.
  • Data Sources: Fundus photographs and axial length measurements from The Hong Kong Polytechnic University Optometry Clinic (2022–2025).
  • Exclusion: Patients with missing data or extreme axial lengths (<18mm or >32mm).
• Imaging & Segmentation:
  • Hardware: Three Topcon fundus cameras with varying resolutions (3216, 3696, and 4176 pixels width) but a nominal 45° field of view.
  • Segmentation: Automated extraction of vascular metrics using AutoMorph, a deep learning-based pipeline that generates binary vessel masks and skeletonized centerlines.
• Metrics Calculated (in Pixel Space):
  • Vessel Area ($A_{px}$)
  • Vessel Skeleton Length ($L_{px}$)
  • Mean Trunk-Vessel Diameter ($D_{px}$)
  • Branch Count (Topological metric)
• Magnification Correction (The Core Method):
  • Reference Condition: Metrics were calculated assuming a fixed reference axial length ($AL_{ref} = 24.0$ mm), representing the "uncorrected" state.
  • Corrected Condition: Metrics were converted to physical units (mm) using the Bennett–Littmann formula based on the patient's true measured axial length ($AL_{true}$).
  • Scaling Factor ($r$): A ratio was derived to convert pixel measurements to physical dimensions, accounting for the specific camera resolution and the individual's AL.
• Statistical Analysis:
  • Percentage errors ($\Delta$) were calculated by comparing uncorrected values against the AL-corrected "ground truth."
  • Regression models (linear and polynomial) were fitted to determine the functional relationship between axial length and measurement error.

3. Key Results

The study quantified the magnitude of systematic bias introduced by ignoring axial length:

• Linear Metrics (Diameter & Length):

  • There is a linear relationship between axial length deviation and measurement error.
  • Error Rate: Approximately 4.5% error per 1 mm deviation from the reference 24 mm AL.
  • Direction:
    • $AL < 24$ mm (Hyperopia): Vessel diameter/length is overestimated by ~4.5% per mm.
    • $AL > 24$ mm (Myopia): Vessel diameter/length is underestimated by ~4.5% per mm.
  • Example: An eye with $AL = 26$ mm (2mm longer than reference) would have its vessel diameter underestimated by ~9%.

• Area Metrics (Vessel Area):

  • Area errors follow a quadratic relationship (scaling with the square of linear dimensions).
  • Error Rate: Approximately 9–10% error per 1 mm deviation.
  • Example: An eye with $AL = 26$ mm would have its vessel area underestimated by ~20–25%.

• Topological Metrics (Branch Count):

  • Branch count showed no significant correlation with axial length ($R^2 \approx 0.003$).
  • This confirms that topological features are scale-invariant and do not require magnification correction.

• Stratified Findings:

  • For $AL < 22$ mm: Diameter/length overestimated by 8–10%; Area overestimated by 17–20%.
  • For $AL \ge 26$ mm: Diameter/length underestimated by 10–12%; Area underestimated by 22–25%.

4. Key Contributions

1. Quantitative Error Modeling: The study provides the first explicit functional models (linear for length/diameter, quadratic for area) describing how axial length deviation translates to percentage error in retinal vascular biomarkers.
2. Validation of Bennett–Littmann for Vascular AI: It demonstrates that applying the Bennett–Littmann correction is not just for structural imaging (OCT) but is critical for quantitative fundus analysis to prevent systematic bias in AI-derived biomarkers.
3. Topological vs. Geometric Distinction: It clarifies that while geometric metrics (area, length) are highly sensitive to AL, topological metrics (branching) are robust, offering guidance on which features require correction in AI pipelines.
4. Practical Correction Framework: The authors propose that future AI pipelines should either:
   • Embed a Bennett–Littmann correction module if individual AL data is available.
   • Use "error look-up tables" or stratified calibration if AL data is missing but population distributions are known.

5. Significance and Implications

• Clinical Accuracy: Ignoring axial length leads to misclassification of disease risk. For instance, myopic patients (longer AL) may appear to have "narrower" vessels or "reduced" vascular density due to optical scaling rather than true pathology. This could lead to false positives for cardiovascular risk in myopic populations.
• AI Development: Current deep learning models trained on uncorrected data may learn spurious correlations between axial length and disease. Incorporating AL scaling is essential for developing robust, generalizable biomarkers for systemic diseases (e.g., hypertension, diabetes, Alzheimer's).
• Standardization: The paper argues for a new standard in retinal imaging analysis where physical dimensions are normalized to true retinal size, ensuring that biomarkers reflect biological reality rather than optical artifacts.

Conclusion: The study concludes that axial-length-related magnification introduces significant, systematic bias into retinal vascular metrics. Adopting the Bennett–Littmann correction is mandatory for accurate quantitative fundus imaging and the development of reliable AI-based biomarkers for systemic health.