Laplace–Beltrami shape analysis of ocular or wavefront surfaces

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.