Abstract
The present work proposes a unified model to explain two previously reported properties of the Mach band illusion. The first is the frequently referenced fact that Mach bands are prominently visible at ramps, but practically vanish at intensity steps. The second property, less studied, on the other hand may also be related to the first. It concerns the fact that the width of the illusory Mach bands appears to be a function of the slope of the ramp itself. The model proposed here combines the difference of Gaussians (DOG) model of lateral inhibition in receptive fields with the models of feature detection, based on a holistic approach. The sharpness of discontinuity (SOD) concept for Mach band stimulus has been defined and is related to the slope of the ramp. It is suggested that calculation of SOD leads to an adaptive change in inhibitory surround, a notion that has the support of physiological experiments too.
References
Albrecht DG, Hamilton DB (1982) Striate cortex of monkey and cat: contrast response function. J Neurophysiol 48:217–237
Bakshi A, Ghosh K (2012) Some insights into why the perception of Mach bands is strong for luminance ramps and weak or vanishing for luminance steps. Perception 41:1403–1408
Barlow H, Fitzhugh R, Kuffler S (1957) Change in organization in the receptive fields of the cat’s retina during dark adaptation. J Physiol 137(3):338–354
Békésy GV (1968a) Brightness distribution across the Mach bands measured with flicker photometry, and the linearity of sensory nervous interaction. J Opt Soc Am 58(1):1–8
Békésy GV (1968b) Mach- and Hering-type lateral inhibition in vision. Vis Res 8(12):1483–1499
Blakeslee B, McCourt ME (1999) A multiscale spatial filtering account of the White effect, simultaneous brightness contrast and grating induction. Vis Res 39:4361–4377
Bowers JS (2009) On the biological plausibility of grandmother cells: implications for neural network theories in psychology and neuroscience. Psychol Rev 116:220–251
Campbell FW, Robson JG (1968) Application of Fourier analysis to the visibility of gratings. J Physiol 197(3):551–566
De MS, Li B (1998) Derivative computation by multiscale filters. Image Vis Comput 16:43–53
Enroth-Cugell C, Lennie P (1975) The control of retinal ganglion cell discharge by receptive field surrounds. J Physiol 247(3):551–578
Fiorentini A (1972) Mach band phenomena. In: Jameson D, Hurvich LM (eds) Handbook of sensory physiology, vol. VII/4. Visual psychophysics. Springer, New York, pp 188–201
Ghosh K, Sarkar S, Bhaumik K, (2005a) Image enhancement by high-order gaussian derivative filters simulating non-classical receptive fields in the human visual system. In: Pattern recognition and machine intelligence: lecture notes in computer science, vol 3776. Springer, Berlin, pp 453–458
Ghosh K, Sarkar S, Bhaumik K (2005b) A possible mechanism of zero-crossing detection using the concept of extended classical receptive field model of retinal ganglion cells. Biol Cybern 93(1):1–5
Ghosh K, Sarkar S, Bhaumik K (2006) A possible explanation of the low-level brightness-contrast illusions in the light of an extended classical receptive field model of retinal ganglion cells. Biol Cybern 94(2):89–96
Ghosh K, Sarkar S, Bhaumik K (2007a) Understanding image structure from a new multi-scale representation of higher order derivative filters. Image Vis Comput 25(8):1228–1238
Ghosh K, Bhaumik K, Sarkar S (2007b) Retinomorphic image processing. Prog Brain Res 168:175–191
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. Biol Cybern 100:351–359
Gross CG (2002) Genealogy of grandmother cell. Neuroscientist 8(5):512–518
Hartline HK (1940) The receptive fields of optic nerve fibres. Am J Physiol 130(4):690–699
Hubel DH, Wiesel TN (1962) Receptive fields binocular interaction and functional architecture in the cat’s visual cortex. J Physiol 60:106–154
Kuffler SW (1952) Neurons in the retina: organization, inhibition and excitation problems. Cold Spring Harb Symp Quant Biol 17:281–292
Marr D, Hildreth E (1980) Theory of edge detection. Proc R Soc Lond B 207:187–217
Marr D (1982) Vision: a computational investigation into the human representation and processing of visual information. WH Freeman, New York
Matthews ML (1966) Appearance of Mach bands for short durations and at sharply focused contours. J Opt Soc Am 56(10):1401–1402
Morrone MC, Ross J, Burr DC, Owens R (1986) Mach bands are phase dependent. Nature 324:250–253
Pessoa L (1996) Mach bands: How many models are possible? Recent experimental findings and modelling attempts. Vis Res 36(19):3205–3227
Poggio T, Voorhees H, Yuille A (1988) A regularized solution of edge detection. J Complex 4(2):106–123
Ratliff F (ed) (1965) Mach bands: quantitative studies on neural networks in the retina. Holden-Day, San Francisco
Ratliff F, Milkman N, Rennert N (1983) Attenuation of Mach bands by adjacent stimuli. Proc Nat Acad Sci 80(14):4554–4558
Ratliff F (1984) Why Mach bands are not seen at the edges of a step. Vis Res 24(2):163–165
Robinson A, Hammon P, de Sa V (2007) Explaining brightness illusions using spatial filtering and local response normalization. Vis Res 47:1631–1644
Rodieck RW, Stone J (1965) Analysis of receptive fields of cat retinal ganglion cells. J Neurophysiol 28(5):833–849
Ross J, Holt JJ, Johnstone J (1981) High frequency limitation on Mach bands. Vis Res 21(7):1165–1167
Ross J, Morrone MC, Burr DC (1989) The conditions under which Mach bands are visible. Vis Res 29(6):699–715
Sceniak MP, Ringach DL, Hawken MJ, Shapley R (1999) Contrast’s effect on spatial summation by macaque V1 neurons. Nat Neurosci 2:733–739
Sherman SM, Guillery RW (2006) Exploring the thalamus and its role in cortical function, 2nd edn. MIT Press, Cambridge
Syrkin G, Yinon U, Gur M (1994) Simple cells may lie at the basis of Mach bands: evidence from physiological studies in the cat’s visual cortex. Exp Brain Res 102(2):319–326
Tsui JM, Pack CC (2011) Contrast sensitivity of MT receptive field centers and surrounds. J Neurophysiol 106(4):1888–1900
Tolhurst DJ (1972) On the possible existence of edge detector neuron in the human visual system. Vis Res 12:797–804
Wielaard J, Sajda P (2005) Neural mechanisms of contrast dependent receptive field size in V1. In: Proceedings of the neural information processing systems conference (NIPS 2005), pp 1505–1512
Young RA (1987) The Gaussian derivative model for vision: I. Retinal mechanisms. Spat Vis 2:273–293
Young RA, Lesperance RM, Meyer WW (2001) The Gaussian derivative model for spatial–temporal vision: I. Cortical model. Spat Vis 14:261–319
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mazumdar, D., Mitra, S., Ghosh, K. et al. A DOG filter model of the occurrence of Mach bands on spatial contrast discontinuities. Biol Cybern 110, 229–236 (2016). https://doi.org/10.1007/s00422-016-0683-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00422-016-0683-9