YirongMengman

Introduction

Human pattern sensitivity has been studied for a long time.[1][2] Theories of human pattern sensitivity changed from single-resolution theories to modern multiresolution theories. Contrast sensitivity functions(CSF) are used as one of experimental measures to compare the properties of human neural mechanisms and theories. Contrast sensitivity is the inverse of contrast threhold, which is the minimum amount of contrast that a target on a uniform background must have so that human can see.

The first measurement of contrast sensitivity as a function of spatial frequency was in 1956 from Schade. Observers needed to decide what contrast was necessary to just detect the patterns. Figure 1 was his experimental result. The horizontal axis was spatial frequency measured in terms of the display. The vertical axis was contrast sensitivity, that is $log(1/c)$ where c was the contrast of the pattern of detection threshold[1][3].

Fig. 1 : CFS Experiment result from Schade

He found that contrast sensitivity decreased as the spatial frequency increased and there was no improvement of contrast sensitivity at low spatial frequencies. It was also found that the contrast sensitivity function (CSF) was a product of optical and neural factors[2]. The decrease in the high spatial frequency was due to the optical blurring of the lens and the feature of retinal ganglion cells with center-surround receptive fields[3]. As for the low frequency fall off, center surround receptive field was one possible reason. Later, some researchers in neuroscience found the existence of multiple channels in vision, each of them selective to a band of spatial frequencies[4]. This finding made more and more scientists interested in measuring the CSF.

Human vision adapts quickly to new viewing conditions. Therefore, a single CFS is not enough to describe human pattern sensitivity. By using small sinusoidal grating presented in front of observers within the middle few degrees of the visual field, factors like temporal properties, the mean background illuminance background level and the wavelength composition of the stimulus all had great influence on pattern sensitivity. Also, if the sinusoidal grating was put on peripheral locations in the visual field, sensitivity decreased. Figure 2 showed the CSF measured at retina eccentricities of 0, 1.5, 4, 7.5, 14 and 30 degrees[5]. The observers’ peak contrast sensitivity was nearly 100 for gratings near 5-8 cpd and could still resolve gratings in about 50 cpd while the limit of observers was 2 cpd when measured in the visual periphery.

Fig. 2: CSFs with different retina eccentricity

Several neural factors could explain the deduction of absolute sensitivity and spatial resolution[3]. The density of retinal ganglion cells drops and therefore there is less cortical area used to represent the periphery. Also, there are fewer sensors in periphery because the density of cone mosaic falls off quickly as a function of retina eccentricity. Besides, the photoreceptors in the fovea are much smaller than those in the periphery. This change of size may have something to do with the visual sensitivity as well.

Background

In some objective contrast sensitivity experiments, observers need to make yes or no judgement about the detection of the stimulus. According to Green and Swets, people say “yes” if the internal magnitude of the stimulus exceeds an internal criterion. For one thing, many things, like instructions, can cause the observers to change their criterions. For another thing, observers have various critierions and criterions differ over time. Some computational methods model the stages of human visual encoding, which make computations accessible and benefit the communication across various fields. For example, ISETBio allows researchers to create spectral radiance scenes as input to estimate the effects of human optics, eye movements, cone absorptions etc.

For the modelling of contrast sensitivity function, various algorithms can be used to analyze the computed visual system responses and further associate them with psychophysical performance. In contrast sensitivity experiments, a computer-controlled two alternative forced choice method is often used. Contrast threshold in this case is the contrast at which the observer's response is correct on a given percentage(eg. 75%). For example, in the experiments of Jyrki et.al, the subject heard two sound signals with an interval of 0.5s and he had to decide during which signal the blank stimulus field was replaced by a vertical, stationsay grating. Similar to this, Cottaris, Wandell et.al modelled a two-alternative forced choice version of the contrast sensitivity experiment with ISETBio. They first demonstrated that the CSF derived from ISETBio agreed with ones derived with traditional ideal-observer approaches when all conditions were matched. An SVM classifier was used as an inference engine to link visual representations to psychological performance. The efficiency of the classifier’s calculation played an important role in the final performance.

Methods

We first use ISETBio[6] to generate experiment stimulus and corresponding cone mosaic response to it. The process and corresponding functions in ISETBio toolbox is described in the following figure.

Fig. 3 : Using ISETBio to generate harmonic stimulus and corresponding cone mosaic response

In our experiment, we generate a simple individual specific contrast sensitivity function, which has no eye movement during the test, and the cone mosaic distribution is fixed during the test.

Our goal is to use computational method to compute the threshold contrast, with which, the harmonic pattern is just barely visible. We use signal detection algorithm to automatically compute the threshold contrast from the cone mosaic response to the stimulus of different frequencies. The process is described in following figure.

Fig. 4 : Using signal detection algorithm to compute threshold contrast. 1: compute likelihood parameters; 2: compute likelihood value; 3: compare likelihood ratio and update threshold

First, we generate $N$ trials of realizations of cone mosaic response to a spatially uniform pattern (null stimulus). We view the response of each single cone as independent Poisson variables. By fitting the realizations with Poisson distribution (using poissfit function in MATLAB 2020b), we can get the Poisson parameter $\Lambda$ of each cone. We can write the distribution of the response of $M$ cones to null stimulus as $Poiss({\Lambda }_1^0)$

Reference

[1] Otto H. Schade, Optical and Photoelectric Analog of the Eye, J. Opt. Soc. Am. 46, 721-739 (1956)

[2] Campbell, F W, and D G Green. Optical and retinal factors affecting visual resolution. The Journal of physiology vol. 181,3 (1965): 576-93. doi:10.1113/jphysiol.1965.sp007784

[3] Wandell, Brian A. Foundations of Vision Link

[4] Campbell FW, Robson JG. Application of Fourier analysis to the visibility of gratings. J Physiol. 1968 Aug;197(3):551-66. doi: 10.1113/jphysiol.1968.sp008574. PMID: 5666169; PMCID: PMC1351748.

[5] ROVAMO, J., VIRSU, V. & NÄSÄNEN, R. Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision. Nature 271, 54–56 (1978). https://doi.org/10.1038/271054a0.

[6] Nicolas P. Cottaris, Haomiao Jiang, Xiaomao Ding, Brian A. Wandell, David H. Brainard; A computational-observer model of spatial contrast sensitivity: Effects of wave-front-based optics, cone-mosaic structure, and inference engine. Journal of Vision 2019;19(4):8. doi: 10.1167/19.4.8.

[7] Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. John Wiley.

[8] Pelli DG, Bex P. Measuring contrast sensitivity. Vision Res. 2013 Sep 20;90:10-4. doi: 10.1016/j.visres.2013.04.015. Epub 2013 May 3. PMID: 23643905; PMCID: PMC3744596.

[9] Rovamo J, Leinonen L, Laurinen P, Virsu V. Temporal Integration and Contrast Sensitivity in Foveal and Peripheral Vision. Perception. 1984;13(6):665-674. doi:10.1068/p130665