Comparison of polynomial and rational function cornea models for effective dimensionality reduction

This study aims to examine geometric models of the corneal surface that can be used to reduce in reasonable time the dimensionality of datasets of normal anterior corneas. Polynomial models (P) like Zernike polynomials (ZP) and spherical harmonic polynomials (SHP) were obvious candidates along with...

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Vydáno v:Computers in biology and medicine Ročník 167; s. 107635
Hlavní autoři: Bouazizi, Hala, Brunette, Isabelle, Meunier, Jean
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States Elsevier Ltd 01.12.2023
Elsevier Limited
Témata:
Accuracy
Algorithms
Cornea
Corneal topography
Corneal Topography - methods
Harmonic functions
Humans
Internal Medicine
Keratoconus
Models, Statistical
Other
Polynomials
Rational functions
Reduction
Spherical harmonics
Topography
Zernike polynomials
Zernike polynomials
LM
Cornea
Spherical harmonics
P
R
MFS α
ZP
Rational functions
ZR
SHP
Z
SHR
Corneal topography
Polynomial
Spherical Harmonics Rational functions
Zernike Rational functions
Levenberg-Marquardt
Spherical Harmonic Polynomials
Minimum Fully Successful α
Zernike
ISSN:0010-4825, 1879-0534, 1879-0534
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Popis
Shrnutí:This study aims to examine geometric models of the corneal surface that can be used to reduce in reasonable time the dimensionality of datasets of normal anterior corneas. Polynomial models (P) like Zernike polynomials (ZP) and spherical harmonic polynomials (SHP) were obvious candidates along with their rational function (R) counterparts, namely Zernike rational functions (ZR) and spherical harmonic rational functions (SHR, new model). Knowing that both SHP and ZR were more accurate than ZP for the modeling of normal and keratoconus corneas, it was expected that both spherical harmonic (SH) models (SHP and SHR) would be more accurate than their Zernike (Z) counterparts (ZP and ZR, respectively), and both rational (R) models (SHR and ZR) more accurate than their polynomial counterparts (SHP and ZP, respectively) for a low dimensional space (coefficient number J < 30). This was the case. The SH factor contributed more to accuracy than the R factor. Considering the corneal processing time as a function of J, P models were processed in quasi-linear time with a quasi-null slope and rational models in polynomial time. Z models were faster than SH models, and increasingly so in their R version. In sum, for corneal dimensionality reduction, SHR is the most accurate model, but its processing time is increasingly prohibitive unless the best coefficient combination is identified beforehand. ZP is the fastest model and is reasonably accurate with normal corneas for exploratory tasks. SHP is the best compromise between accuracy and speed. [Display omitted] •Geometric models of corneas can substantially reduce corneal data dimensionality.•Spherical harmonic (SH) vs. Zernike (Z), polynomials (P) vs. rational functions (R).•Results - Accuracy: SHR > SHP > ZR > ZP ⇒ SH > Z & R > P.•Results - Speed: ZP > SHP > ZR > SHR ⇒ P > R & Z > SH.•⇒ ZP fastest, SHR (new model) most accurate, SHP best compromise.
Bibliografie:ObjectType-Article-1
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ISSN:0010-4825
1879-0534
1879-0534
DOI:10.1016/j.compbiomed.2023.107635