Blue-noise sampling for human retinal cone spatial distribution modeling

Matteo Paolo Lanaro,David Coeurjolly,Victor Ostromoukhov,Hélène Perrier,Alessandro Rizzi

doi:10.1088/2399-6528/ab8064

Abstract

This paper proposes a novel method for modeling retinal cone distribution in humans. It is based on Blue-noise sampling algorithms being strongly related with the mosaic sampling performed by cone photoreceptors in the human retina. Here we present the method together with a series of examples of various real retinal patches. The same samples have also been created with alternative algorithms and compared with plots of the center of the inner segments of cone photoreceptors from imaged retinas. Results are evaluated with different distance measure used in the field, like nearest-neighbor analysis and pair correlation function. The proposed method can effectively describe features of a human retinal cone distribution by allowing to create samples similar to the available data. For this reason, we believe that the proposed algorithm may be a promising solution when modeling local patches of retina.

Highlights

Sampling is the reduction of a continuous signal into a discrete one, or the selection of a subset from a discrete set of signals
He performed spectral analysis to an array of cones treated as sampling points and observed that the spectral properties of cones mosaic are representative of a Poisson disk array, with the additional restriction of a minimum distance between the center of the cells and their nearest neighbors, because of the size of the cells
This was confirmed by Galli-Resta et al, which investigated the spatial features of the ground squirrel retinal mosaics, suggesting that a minimal-spacing rule dmin in conjunction with an adequate density of receptors can adequately describe the array of rods and S cones [27]

Summary

Introduction

Sampling is the reduction of a continuous signal into a discrete one, or the selection of a subset from a discrete set of signals. Yellott [67] discovered that the photoreceptors in the human retina, especially the cones, are distributed conforming to a Poisson disk distribution He performed spectral analysis to an array of cones treated as sampling points and observed that the spectral properties of cones mosaic are representative of a Poisson disk array, with the additional restriction of a minimum distance between the center of the cells and their nearest neighbors, because of the size of the cells. This was confirmed by Galli-Resta et al, which investigated the spatial features of the ground squirrel retinal mosaics, suggesting that a minimal-spacing rule dmin in conjunction with an adequate density of receptors can adequately describe the array of rods and S cones [27]. Poisson disk distribution is regarded as one of the best sampling patterns, by virtue of its blue-noise power spectrum [38]

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