cs.LGAug 16, 2026

Population Structure Analysis of an Inbred Population using Quantitative Shape Phenotyping from Stereo Retinal Photographs

Authors: Li Tang, Michael D Abramoff

Organizations: Department of Ophthalmology and Visual Sciences, University of Iowa, Iowa City, IA, USA · Department of Ophthalmology and Visual Sciences, Stephen A Wynn Institute for Vision Research, Department of Biomedical Engineering, and Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USA; Iowa City Veterans Administration Medical Center, Iowa City, IA, USA

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Abstract

The population structure of an inbred population of 781 people on Norfolk Island in the Pacific, 318 of which are descendants of the original Mutineers of the Bounty, is analyzed phenotypically using shape from stereo retinal fundus photographs. Three-dimensional optic nerve head (ONH) shape is reconstructed from stereo pairs by a multi-scale stereo matching algorithm. Using deep neural network, the shape of ONH, which is under genetic control, is decomposed into a set of hierarchical features through self-taught learning. Features captured at different levels are selected according to their discriminant power in identifying the two populations. The prediction accuracy is evaluated with stratified cross validation. Given the selected feature set, individuals are grouped into k hierarchical clusters and cluster membership fractions are determined for k=2,3,4,5,6,7. Population structure analysis on the basis of phenotypes through image analysis allows heritability and linkage analysis, including founder effects from English and Polynesian ancestors, potentially leading to new genetic risk factors for glaucoma and other ONH-related eye diseases.

Figures & tables

Figure 1: Network structure of a sparse autoencoder and its simplified representation.
Figure 2: Pretraining is performed by training each of the sparse autoencoder sequentially in the stack.
Figure 3: Network structure to fine tune the stacked autoencoder.
Figure 4: Disparity map and its tilt correction: (a) Cropped stereo fundus photographs centered at ONH; (b) Shape estimate of the optic nerve represented as a grayscale map, where darker pixels indicate points further away from the camera; (c) Reference plane by fitting an orthogonal regression to the optic disc margin; (d) Disparity map after tilt correction by aligning the reference plane horizontally.
Figure 5: Original and reconstructed ONH shape from a two-layer SAE with 300 hidden units for the first layer and 100 units for the second layer: (a) Stereo pair centered at ONH; (b) Original disparity map from stereo matching and reconstructed disparity map from SAE; (c) 3D shape visualization by wrapping the reference (left) fundus image onto the topography described by the original disparity map and the reconstructed one. The orientation of the view angle is indicated by colored dots at four corners.
Figure 6: 300 features learned by the first autoencoder captured localized variability of the cupping of ONH.
Figure 7: 100 features learned by the second autoencoder abstract more global and higher level structure of ONH.
Figure 8: The optimal stimulus for the 30 neurons at the third layer confirm that the deep network indeed learned the ONH shape of a right eye.
Figure 9: First 18 eigen disparity maps from PCA.
Figure 10: The mean area under the receiver operating characteristic curve in predicting the two population with 15 selected features using ten-fold cross-validation: (a) SAE: 0.59 (95% CI: [0.545, 0.630]); (b) PCA: 0.53 (95% CI: [0.498, 0.565]).
Figure 11: Fifteen features selected from: (a) two-layer SAE: feature 4, 6, 8, 9, 11, 12, 14 are from the first layer and feature 1, 2, 3, 5, 7, 10, 13, 15 are from the second layer; (b) PCA components.
Figure 12: Two different clusters grouped in terms of ONH shape proximity.
Figure 13: Estimated population structure at cluster number k=2,3,4,5,6,7. The first 636 optic disc are from inhabitants of Pitcairn and the last 808 from inhabitants of Norfolk (separated by a vertical black line). Cluster membership fractions are indicated by the length of color segments.

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