An exploratory analysis grouped the front-surface maps of normal adult corneas into three recurring shape clusters, a pattern the authors say could eventually support a limited number of biosynthetic implants adapted to individual anatomy. The analysis used 8,609 anterior-surface topographies from 4,941 consenting adults.
The study used a database of normal adult anterior-surface topographies. Experienced ophthalmologists and trained technicians screened the records for ocular disease, ocular surgery and recent contact-lens wear. The sample included 4,245 female and 4,364 male topographies, along with 4,438 right-eye and 4,171 left-eye topographies. Those sex and eye-side figures are counts of topographies.
How the clusters were chosen
To represent the surfaces mathematically, the researchers reduced each elevation map to a 91 × 91 matrix and removed 0.5 mm from the radius to reduce peripheral artifacts. They then fitted 16 non-piston Zernike coefficients, a compact set of numbers used to describe the map’s shape. The fit’s root mean square error, a measure of the remaining mismatch, was 2.98 µm, compared with a reported topographer repeatability error of 6.18 µm for a 91 × 91 matrix.
The researchers compared several hard and soft, linear and nonlinear clustering methods, then judged k-means sufficient for the task. They ran k-means 10 times with different starting centroids, selected the run with the best within-cluster sum of squares, and reported no significant differences between the runs.
To decide how many groups to keep, they used SPR2 and R² scores. Those plots made three or four clusters plausible, but instability sometimes appeared at five or more. The final choice was a three-cluster linear k-means solution, selected with stability and overfitting control in mind.
What the groups captured
The clearest dividing feature was C4, the coefficient corresponding to the Zernike polynomial Z20, or defocus. C4 was the main shape feature separating the three groups in the analysis.
The clusters also showed progressive differences in several measured features. Mean BFS radius rose from 7.60 ±0.12 mm in cluster 1 to 7.89 ±0.09 mm in cluster 2 and 8.21 ±0.15 mm in cluster 3. WTW rose from 11.63 ±0.36 mm to 11.80 ±0.35 mm to 11.94 ±0.37 mm, while the reported sex score fell from 0.66 ±0.47 to 0.50 ±0.50 to 0.36 ±0.48. C4 rose from -0.541 ±0.011 to -0.516 ±0.007 to -0.491 ±0.010. Each table-marked effect had p < 0.0001.
These figures describe associations between the clusters and the measured variables. Confidence intervals, detailed ANOVA results and the handling of multiple comparisons were not reported in the analysis.
A separate check using left-eye corneas found that the average maps from a three-cluster analysis resembled the right-eye maps, apart from the expected mirror symmetry. The comparison was a map-level robustness check, not validation of clinical outcomes.
A design idea, not a clinical result
The authors frame the three groups as candidate normal corneal-shape categories for biosynthetic implant design. Their proposal is to use a limited set of categories when adapting implants to individual anatomy, but the categories remain a proposed application of the clustering analysis.
The result may not transfer unchanged beyond this dataset. It predominantly represented White participants, included more myopic corneas than expected in the general normal population, and relied on Orbscan II measurements. Other topographers could yield somewhat different results.
The study’s main contribution is therefore a way to organize normal anterior corneal shapes into a small set of candidate patterns. Implant selection, visual outcomes and patient benefit were not tested.
The work was supported by the Quebec Vision Health Research Network, FRQNT and MUTAN.
Paper data and sources
Original title: Clustering of anterior corneal surface shapes in normal adults
Authors: Hala Bouazizi, Isabelle Brunette, Jean Meunier
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
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