| Issue |
J. Eur. Opt. Society-Rapid Publ.
Volume 22, Number 1, 2026
|
|
|---|---|---|
| Article Number | 25 | |
| Number of page(s) | 10 | |
| DOI | https://doi.org/10.1051/jeos/2026014 | |
| Published online | 17 April 2026 | |
Research Article
Laplace–Beltrami shape analysis of ocular or wavefront surfaces
Instituto de Óptica (CSIC), Serrano 121, Madrid, Spain
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
2
December
2025
Accepted:
8
February
2026
Abstract
Shape analysis techniques are widely used across biomedical fields for processing surface shape properties. The Laplace–Beltrami operator, as an extension of the Laplacian to surfaces, reveals geometrical properties related to surface curvature through its spectral decomposition, making it a promising tool in visual optics. I introduce Laplace–Beltrami shape analysis for ocular, or wavefront, surfaces of the human eye, described as meshes. I present a set of techniques and their numerical implementation for this purpose. Two particular tools, spectral decomposition and shape-DNA analysis, are explained in detail and illustrated with an example of application: a keratoconus cornea model.
Key words: Laplace–Beltrami operator / Shape analysis / Ocular surfaces / Surface curvature
© The Author(s), published by EDP Sciences, 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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