Abstract
It is well known from psychophysical studies that stochastic resonance, in its simplest threshold paradigm, can be used as a tool to measure the detection sensitivity to fine details in noise contaminated stimuli. In the present manuscript, we report simulation studies conducted in the similar threshold paradigm of stochastic resonance. We have estimated the contrast sensitivity in detecting noisy sine-wave stimuli, with varying area and spatial frequency, as a function of noise strength. In all the cases, the measured sensitivity attained a peak at intermediate noise strength, which indicate the occurrence of stochastic resonance. The peak sensitivity exhibited a strong dependence on area and spatial frequency of the stimulus. We show that the peak contrast sensitivity varies with spatial frequency in a nonmonotonic fashion and the qualitative nature of the sensitivity variation is in good agreement with human contrast sensitivity function. We also demonstrate that the peak sensitivity first increases and then saturates with increasing area, and this result is in line with the results of psychophysical experiments. Additionally, we also show that critical area, denoting the saturation of contrast sensitivity, decreases with spatial frequency and the associated maximum contrast sensitivity varies with spatial frequency in a manner that is consistent with the results of psychophysical experiments. In all the studies, the sensitivities were elevated via a nonlinear filtering operation called stochastic resonance. Because of this nonlinear effect, it was not guaranteed that the sensitivities, estimated at each frequency, would be in agreement with the corresponding results of psychophysical experiments; on the contrary, close agreements were observed between our results and the findings of psychophysical investigations. These observations indicate the utility of stochastic resonance in human vision and suggest that this paradigm can be useful in psychophysical studies.
Similar content being viewed by others
References
Adams R, Courage M (2002) Using a single test to measure human contrast sensitivity from early childhood to maturity. Vis Res 42:1205–1210
Arden G (1978) The importance of measuring contrast sensitivity in cases of visual disturbance. Br J Ophthalmol 62:198–209
Arundale K (1978) An investigation into the variation of human contrast sensitivity with age and ocular pathology. Br J Ophthalmol 62:213–215
Betts LR, Sekuler AB, Bennett PJ (2007) The effects of aging on orientation discrimination. Vis Res 47:1769–1780. doi:10.1016/j.visres.2007.02.016
Blackwell KT (1998) The effect of white and filtered noise on contrast detection thresholds. Vis Res 38:267–280
Blakemore C, Campbell F (1969) On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images. J Physiol 203:237–260
Campbell F, Green D (1965) Optical and retinal factors affecting visual resolution. J Physiol 181:576–593
Campbell F, Robson J (1968) Application of Fourier analysis to the visibility of gratings. J Physiol 197:551–566
Chiou-Tan FY, Magee KN, Robinson LR, Nelson MR, Tuel SS, Krouskop TA, Moss F (1996) Enhancement of subthreshold sensory nerve action potentials during muscle tension mediated noise. Int J Bifurc Chaos 7:1389
Collins JJ, Imhoff TT, Grigg P (1996) Noise-enhanced tactile sensation. Nature 383:770
Collins JJ, Imhoff TT, Grigg P (1997) Noise-mediated enhancements and decrements in human tactile sensation. Phys Rev E 56(1):923
De Valois RL, De Valois KK (1980) Spatial vision. Ann Rev Psychol 31:309–341
Douglass JK, Wilkens L, Pantazelou E, Moss F (1993) Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance. Nature 365:337–340
Field D, Tolhurst D (1986) The structure and symmetry of simple-cell receptive-field profiles in the cat’s visual cortex. Proc R Soc Lond Ser B 228:379–400
Gammaitoni L (1995) Stochastic resonance and the dithering effect in threshold physical systems. Phys Rev E 52:4691
Gammaitoni L (1995) Stochastic resonance in multi-threshold systems. Phys Lett A 208:315–322
Gammaitoni L, Hanggi P, Jung P, Marchesoni F (1998) Stochastic resonance. Rev Mod Phys 70(1):223–287
Ghosh K, Sarkar S, Bhaumik K (2005) A possible mechanism of zero-crossing detection using the concept of the extended classical receptive field of retinal ganglion cells. BiolCybern 93:1–5
Ghosh K, Sarkar S, Bhaumik K (2009) A possible mechanism of stochastic resonance in the light of an extra-classical receptive field model of retinal ganglion cells. BiolCybern 100(5):351–359
Gingl Z, Kiss L, Moss F (1995) Stochastic resonance, signal processing and related phenomena. Nuovo Cimento D 17:795
Gingl Z, Kiss LB, Moss F (1995a) Non-dynamical stochastic resonance: theory and experiments with white and arbitrarily coloured noise. Europhys Lett 29(3):191–196
Goris RL, Zaenen P, Wagemans J (2008) Some observations on contrast detection in noise. J Vis 8(4):1–15. doi:10.1167/8.9.4
Hertle R, Reese M (2007) Clinical contrast sensitivity testing in patients with infantile nystagmus syndrome compared with age-matched controls. Am J Ophthalmol 143:1063–1065
Howell ER, Hess RF (1978) The functional area for summation to threshold for sinusoidal gratings. Vis Res 18:369–374
Huang C, Tao L, Zhou Y, Lu Z-L (2007) Treated amblyopes remain deficient in spatial vision: a contrast sensitivity and external noise study. Vis Res 47:2234. doi:10.1016/j.visres.2006.09.015
Jaramillo F, Wiesenfeld K (1998) Mechanoelectrical transduction assisted by Brownian motion: a role for noise in the auditory system. Nat Neurosci 1:384–388
Jones DG, Anderson ND, Murphy KM (2003) Orientation discrimination in visual noise using global and local stimuli. Vis Res 43:1223–1233
Karmakar S, Sarkar S (2013) Orientation enhancement in early visual processing can explain time course of brightness contrast and White’s illusion. Biol Cybern. doi:10.1007/s00422-013-0553-7
Kitajo K, Nozaki D, Ward LM, Yamamoto Y (2003) Behavioral stochastic resonance within the human brain. Phys Rev Lett 90:218103
Koenderink JJ (1984) The structure of images. Biol Cybern 50:363–370
Landahl H, McCulloch W, Pitts W (1943) A statistical consequence of the logical calculus of nervous nets. Bull Math Biophys 5(4):135–137. doi:10.1007/BF02478260
Levin JE, Miller JP (1996) Broadband neural encoding in the cricket cercal sensory system enhanced by stochastic resonance. Nature 380:165–168
Lindeberg T (1994) Scale-space theory: a basic tool for analysing structures at different scales. J Appl Stat 21(2):224–270
Longtin A, Bulsara A, Moss F (1991) Time-interval sequences in bistable systems and the noise-induced transmission of information by sensory neurons. PRL 67(5):656
Luntinen O, Rovamo J, Näsänen R (1995) Modeling the increase of contrast sensitivity with grating area and exposure time. Vis Res 35(16):2339–2346
Mach E (1868) On the physiological effects of spatially distributed light stimuli. Translated in F Ratliff, “Mach Bands: Quantitative Studies on Neural Networks in the Retina”, Holden-Day, Sanfrancisco, pp 299–306 (1965). Here Ernst Mach proposed that if \(u=f(x, y)\) is the intensity of illumination then, the brightness sensation at the corresponding retinal point will be given by \(v=u-m(d^{2}u/dx^{2}+d^{2}u/dy^{2})\). The brightness sensation v is thus the combined effect of the original illumination and its second differential quotient
Manahilov V, Calvert J, Simpson WA (2003) Temporal properties of the visual responses to luminance and contrast modulated noise. Vis Res 43:1855–1867. doi:10.1016/S0042-6989(03)00275-X
Mannos J, Sakrison D (1974) The effects of a visual fidelity criterion on the encoding of images. IEEE Trans Inf Theory 20(4):525–535
Marr D (1982) Vision: a computational investigation into the human representation and processing of visual information. W H Freeman and Company, New York
Marr D, Hildreth E (1980) Theory of edge detection. Proc R Soc Lond Ser B Biol Sci 207:187–217
Marr D, Poggio T, Ullman S (1979) Bandpass channels, zero-crossings and early visual information processing. J Opt Soc Am 70:868–870
McAnany JJ, Alexander KR (2010) Spatial contrast sensitivity in dynamic and static additive luminance noise. Vis Res 50:1957–1965. doi:10.1016/j.visres.2010.07.006
McCann J, Savoy RL, Hall JA Jr (1978) Visibility of low-frequency targets: dependence on number of cycles and surround parameters. Vis Res 18:891–894
McDonnell M, Abbott D (2009) What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology. PLoS Comput Biol 5(5):e1000348
Mead C (1990) Neuromorphic electronic system. Proc IEEE 78(10):1629–1636
Piana M, Canfora M, Riani M (2000) Role of noise in image processing by the human perceptive system. Phys Rev E 62(1):1104
Ringach D, Hawken M, Shapley R (2002) Receptive field structure of neurons in monkey primary visual cortex revealed by stimulation with natural image sequences. J Vis 2:12–24
Rovamo J, Luntinen O, Nasanen R (1993) Modelling the dependence of contrast sensitivity on grating area and spatial frequency. Vis Res 33:2773–2788
Rovamo J, Mustonen J, Nasanen R (1994) Modelling contrast sensitivity as a function of retinal illuminance and grating area. Vis Res 33:1301–1314
Russell D, Wilkens L, Moss F (1999) Use of behavioural stochastic resonance by paddle fish for feeding. Nature 402:291–294
Santos NA, Alencar CCG, Dias YHN (2009) Contrast sensitivity function of sine-wave gratings in children with acute malnutrition. Psychol Neurosci 2(1):11–15
Simonotto E, Riani M, Seife C, Roberts M, Twitty J, Moss F (1997) Visual perception of stochastic resonance. Phys Rev Lett 78:1186–1189
Simonotto E, Spano F, Riani M, Ferrari A, Levrero F, Pilot A, Renzetti P, Parodi RC, Sardabelli F, Vitali P, Twitty J, Chiou-Tan F, Moss F (1999) fMRI studies of visual cortical activity during noise stimulation. Neurocomputing 26:511–516
Spagnolo B, Spezia S, Curcio L, Pizzolato N, Fiasconaro A, Valenti D, Bue PL, Peri E, Colazza S (2009) Noise effects in two different biological systems. Eur Phys J B 69:133–146
Virsu V, Rovamo J (1979) Visual resolution, contrast sensitivity, and the cortical magnification factor. Exp Brain Res 37:475–494
Ward LM, Neiman A, Moss F (2002) Stochastic resonance in psychophysics and in animal behavior. Biol Cybern 87:91–101
Wisenfeld K, Moss F (1995) Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs. Nature 373:33
Yates J, Leys M, Green M et al (1999) Parallel pathways, noise masking and glaucoma detection: behavioral and electrophysiological measures. Doc Ophthalmol Adv Ophthalmol 95:283–299
Young RA (1987) The Gaussian derivative model for spatial vision: I. Retinal mechanisms. Spat Vis 2(4):273–293
Young RA, Lesperance RM, Meyer WW (2001) The Gaussian Derivative model for spatial-temporal vision: I. Cortical model. Spat Vis 14(3–4):261–319
Yuille AL, Poggio TA (1986) Scaling theorems for zero crossings. IEEE Trans Pattern Anal Mach Intell PAMI 8(1):15–25
Zetzsche C, Barth E (1990) Fundamental limits of linear filters in the visual processing of two-dimensional signals. Vis Res 30:1111–1117
Acknowledgments
We are thankful to an anonymous reviewer for his valuable suggestions in the preparation of the final manuscript. We are also grateful to Subhajit Karmakar for stimulating discussions and important suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kundu, A., Sarkar, S. Stochastic resonance in visual sensitivity. Biol Cybern 109, 241–254 (2015). https://doi.org/10.1007/s00422-014-0638-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00422-014-0638-y