Investigating the potential of Zernike polynomials to characterise spatial distribution of macular pigment

Piers Allen, Antonio Calcagni, Anthony G. Robson, Ela Claridge*, Knut Stieger (Editor)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


It has been postulated that particular patterns of macular pigment (MP) distribution may be associated with the risk for eye diseases such as age-related macular degeneration (AMD). This work investigates the potential of Zernike polynomials (ZP) to characterise the level and distribution of MP, and their suitability as a representation for analysis of the effects of age and AMD on MP patterns. As the case study, MP distribution maps computed using an experimental method based on fundus reflectance (MRIA) were obtained for ninety volunteers representing three groups: under-fifty without AMD, fifty and over without AMD, and fifty and over with AMD. ZP with 105 coefficients were fitted to the maps using least-squares optimisation and found to represent MP maps accurately (RMSE<10-1). One-way MANOVA analysis carried out on ZP representations showed that the three subject groups have significantly different means (Wilk's Lambda 0.125, p<0.0001). Linear discriminant analysis with leave-one-out scheme resulted in accuracy, sensitivity and specificity of classification according to, respectively, disease status regardless of age (81% all); disease status in the age-matched groups (87%, 88%, 86%); age irrespective of disease status (81%, 83%, 73%); and age for subjects without AMD (83%, 88%, 80%). Mean MP distributions computed from ZP coefficients for the three groups showed more elevated and more peaked MP for the healthy under-fifty group; more irregular and more elevated peripheral levels in over-fifty AMD group than in over-fifty non-AMD group; and moderate radial asymmetry in non-AMD over-50 group. The results suggest that ZP coefficients are capable of accurately representing MP in a way that captures certain spatial patterns of its distribution. Using the ZP representation MP maps could be classified according to both age and disease status with accuracy significantly greater than chance, with peak elevation, pattern irregularity and radial asymmetry identified as important features.

Original languageEnglish
Article numbere0217265
JournalPLoS ONE
Issue number5
Publication statusPublished - 24 May 2019

Bibliographical note

© 2019 Allen et al. This is an open access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: Dunhill Medical Trust, grant number R116/0509, Paul & Yuanbi
Ramsay Research Fund, University of Birmingham, NIHR Biomedical Research Centre at Moorfields Eye Hospital NHS Foundation Trust and UCL Institute of Ophthalmology.


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