Skip to main content
Log in

Stochastic resonance in visual sensitivity

  • Original Paper
  • Published:
Biological Cybernetics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

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

    Article  PubMed  Google Scholar 

  • Arden G (1978) The importance of measuring contrast sensitivity in cases of visual disturbance. Br J Ophthalmol 62:198–209

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Arundale K (1978) An investigation into the variation of human contrast sensitivity with age and ocular pathology. Br J Ophthalmol 62:213–215

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • Blackwell KT (1998) The effect of white and filtered noise on contrast detection thresholds. Vis Res 38:267–280

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Campbell F, Green D (1965) Optical and retinal factors affecting visual resolution. J Physiol 181:576–593

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Campbell F, Robson J (1968) Application of Fourier analysis to the visibility of gratings. J Physiol 197:551–566

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • 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

    Article  Google Scholar 

  • Collins JJ, Imhoff TT, Grigg P (1996) Noise-enhanced tactile sensation. Nature 383:770

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  Google Scholar 

  • Douglass JK, Wilkens L, Pantazelou E, Moss F (1993) Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance. Nature 365:337–340

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • Gammaitoni L (1995) Stochastic resonance and the dithering effect in threshold physical systems. Phys Rev E 52:4691

    Article  CAS  Google Scholar 

  • Gammaitoni L (1995) Stochastic resonance in multi-threshold systems. Phys Lett A 208:315–322

    Article  CAS  Google Scholar 

  • Gammaitoni L, Hanggi P, Jung P, Marchesoni F (1998) Stochastic resonance. Rev Mod Phys 70(1):223–287

    Article  CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • Howell ER, Hess RF (1978) The functional area for summation to threshold for sinusoidal gratings. Vis Res 18:369–374

    Article  CAS  PubMed  Google Scholar 

  • 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

    Google Scholar 

  • Jaramillo F, Wiesenfeld K (1998) Mechanoelectrical transduction assisted by Brownian motion: a role for noise in the auditory system. Nat Neurosci 1:384–388

    Article  CAS  PubMed  Google Scholar 

  • Jones DG, Anderson ND, Murphy KM (2003) Orientation discrimination in visual noise using global and local stimuli. Vis Res 43:1223–1233

    Article  PubMed  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

  • Lindeberg T (1994) Scale-space theory: a basic tool for analysing structures at different scales. J Appl Stat 21(2):224–270

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • 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

    Article  Google Scholar 

  • Marr D (1982) Vision: a computational investigation into the human representation and processing of visual information. W H Freeman and Company, New York

    Google Scholar 

  • Marr D, Hildreth E (1980) Theory of edge detection. Proc R Soc Lond Ser B Biol Sci 207:187–217

    Article  CAS  Google Scholar 

  • Marr D, Poggio T, Ullman S (1979) Bandpass channels, zero-crossings and early visual information processing. J Opt Soc Am 70:868–870

    Article  Google Scholar 

  • 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

    Article  PubMed Central  PubMed  Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • Rovamo J, Luntinen O, Nasanen R (1993) Modelling the dependence of contrast sensitivity on grating area and spatial frequency. Vis Res 33:2773–2788

    Article  CAS  PubMed  Google Scholar 

  • Rovamo J, Mustonen J, Nasanen R (1994) Modelling contrast sensitivity as a function of retinal illuminance and grating area. Vis Res 33:1301–1314

    Article  Google Scholar 

  • Russell D, Wilkens L, Moss F (1999) Use of behavioural stochastic resonance by paddle fish for feeding. Nature 402:291–294

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  Google Scholar 

  • Simonotto E, Riani M, Seife C, Roberts M, Twitty J, Moss F (1997) Visual perception of stochastic resonance. Phys Rev Lett 78:1186–1189

    Article  CAS  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • Virsu V, Rovamo J (1979) Visual resolution, contrast sensitivity, and the cortical magnification factor. Exp Brain Res 37:475–494

    Article  CAS  PubMed  Google Scholar 

  • Ward LM, Neiman A, Moss F (2002) Stochastic resonance in psychophysics and in animal behavior. Biol Cybern 87:91–101

    Article  PubMed  Google Scholar 

  • Wisenfeld K, Moss F (1995) Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs. Nature 373:33

    Article  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • Young RA (1987) The Gaussian derivative model for spatial vision: I. Retinal mechanisms. Spat Vis 2(4):273–293

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

  • Yuille AL, Poggio TA (1986) Scaling theorems for zero crossings. IEEE Trans Pattern Anal Mach Intell PAMI 8(1):15–25

    Article  CAS  Google Scholar 

  • Zetzsche C, Barth E (1990) Fundamental limits of linear filters in the visual processing of two-dimensional signals. Vis Res 30:1111–1117

    Article  CAS  PubMed  Google Scholar 

Download references

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

Authors

Corresponding author

Correspondence to Sandip Sarkar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00422-014-0638-y

Keywords

Navigation