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

Date Published: May 24, 2019

Publisher: Public Library of Science

Author(s): Piers Allen, Antonio Calcagni, Anthony G. Robson, Ela Claridge, Knut Stieger.


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.

Partial Text

Age-related Macular Degeneration (AMD) accounts for over 50% of all cases of registered blindness in people over 65 years in the UK [1]. It is a progressive disease affecting the macula, a small region in the centre of the retina responsible for detailed vision. The macula is a circular area of approximately 6mm in diameter, which may also be defined as the portion of the posterior retina that contains two or more layers of ganglion cells. It comprises a cone-dominated fovea, which measures approximately 1.5mm, with the cone-only foveola (approximately 0.35mm) at its centre and surrounded by the parafovea and the perifovea [2, 3].

This study investigated the potential of Zernike polynomials to characterise the level and distribution of MP by a set of abstract indices and the ability of this representation to examine associations of MP patterns with age and AMD.

The results of this study suggest that Zernike polynomials (ZP) are capable of representing macular pigment (MP) distribution computed using the multispectral retinal image analysis (MRIA) technique, and potentially other imaging techniques such as 2W-AF and FLIO. Appropriately chosen subsets of Zernike basis functions were shown to characterise three aspects of MP distribution: magnitude, radial asymmetry and pattern irregularity. Using the ZP representation, MRIA MP maps could be classified according to both age and disease status with mean accuracy exceeding 80%.




Leave a Reply

Your email address will not be published.