Towards human retinal cones spatial distribution modeling

International audienceSampling is the reduction of a continuous signal into a discrete one, or the selection of a subset from a discrete set of signals. In the human retina, the mosaic of the cone photoreceptor cells samples the retinal optical projection of the scene, achieving the first neural coding of the spectral information from the light that enters the eye. To solve the sampling problem, the human retina has adopted an arrangement of photoreceptors that is neither perfectly regular nor perfectly random. Local analysis of foveal mosaics shows that cones are arranged in hexagonal or triangular clusters but extending this analysis to larger areas shows characteristics such as parallel curving and circular rows of cones associated with rotated local clusters. This aim of this study is to identify an algorithm capable of generating sampling arrays with the same range of densities in the retina and use specific metrics to compare the spatial and spectral properties of the cones' distribution. We examined the human cone sampling by calculating the Nearest Neighbor (NN) regularity index of the population of cones in images of human retina. For testing, we used pure uniform sampling, Green noise and Pink noise samplers, a jittered sampler, a Poisson-Disk sampler and a Blue noise sampler. As reference we adopted the approach called Blue Noise Through Optimal Transport (BNOT), developed by de Goes et al. [1], because it allows to achieve the best Blue Noise distribution known today. The cone mosaics used for this work are from previously published images of patches of real human retinas. The x and y coordinates of the cells inner segments were manually plotted, a k-d tree structure has been used to find the nearest neighbor for each point, the Euclidean distance was calculated for each pair found this way and all the results are classified in histograms. Each distribution of nearest neighbors can be described by a normal Gaussian distribution: the regularity index is a quantitative method used for assessing spatial regularity of photoreceptor distributions and is expressed by the ratio of the mean µ by the standard deviation σ. This index is reported to be 1.9 for a full random sampling and the more regular the arrangement, the higher the value, usually in the range of 3-8 for retinal mosaics. In contrast with previous claims, our calculated indexes range from 8 to 12. The indexes for data generated with Green noise and Pink noise are assimilable to those of a full random sampling, in fact they are even lower, averaging 1.3 and 1.4 respectively; meanwhile, for the BNOT data, the indexes values are much higher, more than the double of the highest values for retinal RIs. Given the fact that fully regular hexagonal or square patterns are proven to have poor sampling properties and therefore not suitable for simulating cones distribution, while having infinite RI, in the scope of this work a higher RI indicates that BNOT is better at generating point processes than the other analyzed point processes. Our results show that blue noise sampling can describe features of a human retinal cone distribution with a certain degree of similarity to the available data and can be efficiently used for modeling local patches of retina. Given the nature of blue noise algorithms, it should be possible to develop an adaptive sampling model that spans the whole retina. We hope this work can be useful to understand how spatial distribution affects the sampling of a retinal image, or the mechanisms underlying the development of this singular distribution of neuron cells and the implications it has on human vision

TOWARDS A COMPUTATIONAL MODEL OF RETINAL STRUCTURE AND BEHAVIOR

Human vision is our most important sensory system, allowing us to perceive our surroundings. It is an extremely complex process that starts with light entering the eye and ends inside of the brain, with most of its mechanisms still to be explained. When we observe a scene, the optics of the eye focus an image on the retina, where light signals are processed and sent all the way to the visual cortex of the brain, enabling our visual sensation. The progress of retinal research, especially on the topography of photoreceptors, is often tied to the progress of retinal imaging systems. The latest adaptive optics techniques have been essential for the study of the photoreceptors and their spatial characteristics, leading to discoveries that challenge the existing theories on color sensation. The organization of the retina is associated with various perceptive phenomena, some of them are straightforward and strictly related to visual performance like visual acuity or contrast sensitivity, but some of them are more difficult to analyze and test and can be related to the submosaics of the three classes of cone photoreceptors, like how the huge interpersonal differences between the ratio of different cone classes result in negligible differences in color sensation, suggesting the presence of compensation mechanisms in some stage of the visual system. In this dissertation will be discussed and addressed issues regarding the spatial organization of the photoreceptors in the human retina. A computational model has been developed, organized into a modular pipeline of extensible methods each simulating a different stage of visual processing. It does so by creating a model of spatial distribution of cones inside of a retina, then applying descriptive statistics for each photoreceptor to contribute to the creation of a graphical representation, based on a behavioral model that determines the absorption of photoreceptors. These apparent color stimuli are reconstructed in a representation of the observed scene. The model allows the testing of different parameters regulating the photoreceptor's topography, in order to formulate hypothesis on the perceptual differences arising from variations in spatial organization

Performance Analysis of Cone Detection Algorithms

Many algorithms have been proposed to help clinicians evaluate cone density and spacing, as these may be related to the onset of retinal diseases. However, there has been no rigorous comparison of the performance of these algorithms. In addition, the performance of such algorithms is typically determined by comparison with human observers. Here we propose a technique to simulate realistic images of the cone mosaic. We use the simulated images to test the performance of two popular cone detection algorithms and we introduce an algorithm which is used by astronomers to detect stars in astronomical images. We use Free Response Operating Characteristic (FROC) curves to evaluate and compare the performance of the three algorithms. This allows us to optimize the performance of each algorithm. We observe that performance is significantly enhanced by up-sampling the images. We investigate the effect of noise and image quality on cone mosaic parameters estimated using the different algorithms, finding that the estimated regularity is the most sensitive parameter. This paper was published in JOSA A and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/abstract.cfm?msid=224577. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.Comment: 13 pages, 7 figures, 2 table

The Properties of Outer Retinal Band Three Investigated With Adaptive-Optics Optical Coherence Tomography.

PurposeOptical coherence tomography's (OCT) third outer retinal band has been attributed to the zone of interdigitation between RPE cells and cone outer segments. The purpose of this paper is to investigate the structure of this band with adaptive optics (AO)-OCT.MethodsUsing AO-OCT, images were obtained from two subjects. Axial structure was characterized by measuring band 3 thickness and separation between bands 2 and 3 in segmented cones. Lateral structure was characterized by correlation of band 3 with band 2 and comparison of their power spectra. Band thickness and separation were also measured in a clinical OCT image of one subject.ResultsBand 3 thickness ranged from 4.3 to 6.4 μm. Band 2 correlations ranged between 0.35 and 0.41 and power spectra of both bands confirmed peak frequencies that agree with histologic density measurements. In clinical images, band 3 thickness was between 14 and 19 μm. Measurements of AO-OCT of interband distance were lower than our corresponding clinical OCT measurements.ConclusionsBand 3 originates from a structure with axial extent similar to a single surface. Correlation with band 2 suggests an origin within the cone photoreceptor. These two observations indicate that band 3 corresponds predominantly to cone outer segment tips (COST). Conventional OCT may overestimate both the thickness of band 3 and outer segment length

Investigation of adaptive optics imaging biomarkers for detecting pathological changes of the cone mosaic in patients with type 1 diabetes mellitus

Purpose To investigate a set of adaptive optics (AO) imaging biomarkers for the assessment of changes of the cone mosaic spatial arrangement in patients with type 1 diabetes mellitus (DM1). Methods 16 patients with 20/20 visual acuity and a diagnosis of DM1 in the past 8 years to 37 years and 20 age-matched healthy volunteers were recruited in this study. Cone density, cone spacing and Voronoi diagrams were calculated on 160x160 μm images of the cone mosaic acquired with an AO flood illumination retinal camera at 1.5 degrees eccentricity from the fovea along all retinal meridians. From the cone spacing measures and Voronoi diagrams, the linear dispersion index (LDi) and the heterogeneity packing index (HPi) were computed respectively. Logistic regression analysis was conducted to discriminate DM1 patients without diabetic retinopathy from controls using the cone metrics as predictors. Results Of the 16 DM1 patients, eight had no signs of diabetic retinopathy (noDR) and eight had mild nonproliferative diabetic retinopathy (NPDR) on fundoscopy. On average, cone density, LDi and HPi values were significantly different (P<0.05) between noDR or NPDR eyes and controls, with these differences increasing with duration of diabetes. However, each cone metric alone was not sufficiently sensitive to discriminate entirely between membership of noDR cases and controls. The complementary use of all the three cone metrics in the logistic regression model gained 100% accuracy to identify noDR cases with respect to controls. PLOS ONE | DOI:10.1371/journal.pone.0151380 March 10, 2016 1 / 14 OPEN ACCESS Citation: Lombardo M, Parravano M, Serrao S, Ziccardi L, Giannini D, Lombardo G (2016) Investigation of Adaptive Optics Imaging Biomarkers for Detecting Pathological Changes of the Cone Mosaic in Patients with Type 1 Diabetes Mellitus. PLoS ONE 11(3): e0151380. doi:10.1371/journal. pone.0151380 Editor: Knut Stieger, Justus-Liebig-University Giessen, GERMANY Received: December 17, 2015 Accepted: February 27, 2016 Published: March 10, 2016 Copyright: © 2016 Lombardo 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. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Funding: Research for this work was supported by the Italian Ministry of Health (5x1000 funding), by the National Framework Program for Research and Innovation PON (grant n. 01_00110) and by Fondazione Roma. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Vision Engineering Italy srl funder provided support in the form of salaries for author GL, but did not have any Conclusion The present set of AO imaging biomarkers identified reliably abnormalities in the spatial arrangement of the parafoveal cones in DM1 patients, even when no signs of diabetic retinopathy were seen on fundoscopy

Digital Color Imaging

This paper surveys current technology and research in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented us-ing vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided

Doctor of Philosophy

dissertationMany retinal pathologies, including age-related macular degeneration (AMD), display characteristic spatial patterns. AMD predominately a ects the macula, the central conedominated region of the human retina responsible for high-acuity daytime vision. An understanding of why the macula is speci cally susceptible to age-related changes would likely prove invaluable to understanding the pathology of AMD and the development of preventative therapies. Unfortunately, such an understanding has thus far proven elusive. A large number of physiological and anatomical parameters vary signi cantly between the central and peripheral human retina, and many of these parameters are altered during retinal degenerative disorders. This produces a large number of spatial associations between various parameters, obscuring causal relationships and making identi cation of timing and initiating factors very challenging. To address this challenge we developed RetSpace, an analytic software package designed to generate and analyze quantitative maps of anatomic and pathologic parameters within individual human retinas. The RetSpace system was speci cally designed to analyze image sets generated with computational molecular phenotyping (CMP), a technique pioneered by our laboratory to characterize the immense cellular diversity of the neural and sensory retina. By combining the sensitivity and diversity of CMP with the analytic power of RetSpace, we have produced a novel mechanism to study the spatial distributions and regional variability of various measures of retinal anatomy and pathology, as well as the extent to which di erent pathologies show regional correlations potentially indicative of shared pathological origins. To demonstrate the utility of our approach we have analyzed the severity and spatial distributions of an extensive set of anatomic and pathologic parameters in a series of aging human donor retinas. In doing so we have identi ed novel metabolic changes in the RPE and photoreceptors that are spatially and quantitatively correlated with known pathological characteristics of AMD and may serve as sensitive markers of early stress in AMD and other retinal diseases. Mathematical models of the heterocellular diversity of these metabolic changes provide further insight into the mechanisms behind these changes and hint at the origins and spatial specificity of the disease

A graphical, scalable and intuitive method for the placement and the connection of biological cells

We introduce a graphical method originating from the computer graphics domain that is used for the arbitrary and intuitive placement of cells over a two-dimensional manifold. Using a bitmap image as input, where the color indicates the identity of the different structures and the alpha channel indicates the local cell density, this method guarantees a discrete distribution of cell position respecting the local density function. This method scales to any number of cells, allows to specify several different structures at once with arbitrary shapes and provides a scalable and versatile alternative to the more classical assumption of a uniform non-spatial distribution. Furthermore, several connection schemes can be derived from the paired distances between cells using either an automatic mapping or a user-defined local reference frame, providing new computational properties for the underlying model. The method is illustrated on a discrete homogeneous neural field, on the distribution of cones and rods in the retina and on a coronal view of the basal ganglia.Comment: Corresponding code at https://github.com/rougier/spatial-computatio