Bayesian Inference of Two-Dimensional Contrast Sensitivity Function from Data Obtained with Classical One-Dimensional Algorithms Is Efficient

Abstract

The contrast sensitivity function that spans the two dimensions of contrast and spatial frequency is crucial in predicting functional vision both in research and clinical applications. In this study, the use of Bayesian inference was proposed to determine the parameters of the two-dimensional contrast sensitivity function. Two-dimensional Bayesian inference was extensively simulated in comparison to classical one-dimensional measures. Its performance on two-dimensional data gathered with different sampling algorithms was also investigated. The results showed that the two-dimensional Bayesian inference method significantly improved the accuracy and precision of the contrast sensitivity function, as compared to the more common one-dimensional estimates. In addition, applying two-dimensional Bayesian estimation to the final data set showed similar levels of reliability and efficiency across widely disparate and established sampling methods (from classical one-dimensional sampling, such as Ψ or staircase, to more novel multi-dimensional sampling methods, such as quick contrast sensitivity function and Fisher information gain). Furthermore, the improvements observed following the application of Bayesian inference were maintained even when the prior poorly matched the subject's contrast sensitivity function. Simulation results were confirmed in a psychophysical experiment. The results indicated that two-dimensional Bayesian inference of contrast sensitivity function data provides similar estimates across a wide range of sampling methods. The present study likely has implications for the measurement of contrast sensitivity function in various settings (including research and clinical settings) and would facilitate the comparison of existing data from previous studies.

Differential impact of exogenous and endogenous attention on the contrast sensitivity function across eccentricity

“…In particular, we modeled the monotonic increase in discrimination performance with increasing stimulus contrast using Naka-Rushton functions (e.g., Herrmann et al, 2010;Huang & Dobkins, 2005;Ling & Carrasco, 2006b;Pestilli et al, 2009). Furthermore, for each eccentricity, we constrained the variation in contrast thresholds across SF by a functional form of the CSF that adheres to its conventional bandpass shape (Movshon & Kiorpes, 1988;Wang et al, 2017). In doing so, we greatly improved the parsimony of our modeling approach while conforming to known variations of contrast sensitivity across SF (Campbell & Robson, 1968;De Valois et al, 1974;Hilz & Cavonius, 1974;Kelly, 1977;Owsley, 2003;Robson, 1966;Robson & Graham, 1981;Rovamo et al, 1978;Virsu & Rovamo, 1979).…”

“…Neutral CSF . Contrast thresholds for all SFs in the Neutral condition were governed by a double-exponential function (adapted from Movshon & Kiorpes, 1988 ; Wang et al, 2017 ) of the form: where f csf defines the peak SF of the CSF (i.e., the SF where contrast sensitivity is highest) and s controls the slope of the function about its peak. The peak amplitude of the CSF ( γ csf ) is defined by the following: …”

“…First, the monotonic increase in discrimination performance with stimulus contrast was modeled by a Naka-Rushton function (e.g., Herrmann et al, 2010;Huang & Dobkins, 2005;Ling & Carrasco, 2006b;Pestilli et al, 2009). Second, the conventional bandpass shape of the CSF was modeled by a double-exponential function (Movshon & Kiorpes, 1988;Wang, Wang, Huang, Zhou, & Tzvetanov, 2017) and generated the values of contrast threshold used by the Naka-Rushton function. By constraining contrast thresholds to a functional form of the CSF, we greatly reduced the number of parameters required to explain each observers' dataset while adhering to known characteristics of the human visual system.…”

“…Neutral CSF. Contrast thresholds for all SFs in the Neutral condition were governed by a doubleexponential function (adapted from Movshon & Kiorpes, 1988;Wang et al, 2017) of the form:…”

Contrast Response Function Estimation with Nonparametric Bayesian Active Learning

“…Methods have been proposed for accelerating CSF testing while preserving sufficient accuracy for clinical decision making (Gu et al, 2016; Lesmes et al, 2010; Wang et al, 2016). Because of intrinsic noisiness, speeding up the estimates typically requires making assumptions—incompletely justified in most cases—about some model parameters in order to reduce the degrees of freedom of the model to be learned (Treutwein & Strasburger, 1999).…”