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Mach bands explained by response normalization.

Kingdom FA - Front Hum Neurosci (2014)

Bottom Line: More recently, the dominant idea has been that Mach bands are a consequence of a visual process that generates a sparse, binary description of the image in terms of "edges" and "bars".Another recent explanation is that Mach bands result from learned expectations about the pattern of light typically found on sharply curved surfaces.I show that a simple one-dimensional model of response normalization explains the range of conditions under which Mach bands occur, and as importantly, the conditions under which they do not occur.

View Article: PubMed Central - PubMed

Affiliation: McGill Vision Research, Department of Ophthalmology, McGill University Montreal, Quebec, Canada.

ABSTRACT
Mach bands are the illusory dark and bright bars seen at the foot and knee of a luminance trapezoid. First demonstrated by Ernst Mach in the latter part of the 19th century, Mach bands are a test bed not only for models of brightness illusions but of spatial vision in general. Up until 50 years ago the dominant explanation of Mach Bands was that they were caused by lateral inhibition among retinal neurons. More recently, the dominant idea has been that Mach bands are a consequence of a visual process that generates a sparse, binary description of the image in terms of "edges" and "bars". Another recent explanation is that Mach bands result from learned expectations about the pattern of light typically found on sharply curved surfaces. In keeping with recent multi-scale filtering accounts of brightness illusions as well as current physiology, I show however that Mach bands are most simply explained by response normalization, whereby the gains of early visual channels are adjusted on a local basis to make their responses more equal. I show that a simple one-dimensional model of response normalization explains the range of conditions under which Mach bands occur, and as importantly, the conditions under which they do not occur.

No MeSH data available.


Related in: MedlinePlus

Schematic of the principle behind Feature models of Mach bands that employ even- and odd-symmetric filters. (A) even-symmetric (B) odd-symmetric filter. (C) trapezoidal edge profile. (D) response of even (green) and odd (purple) filters. The even-symmetric filter gives a strong response at the foot and knee of the trapezoid whereas the odd –symmetric filter gives zero response. (E) bars are signaled at the trapezoid’s foot and knee.
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Figure 2: Schematic of the principle behind Feature models of Mach bands that employ even- and odd-symmetric filters. (A) even-symmetric (B) odd-symmetric filter. (C) trapezoidal edge profile. (D) response of even (green) and odd (purple) filters. The even-symmetric filter gives a strong response at the foot and knee of the trapezoid whereas the odd –symmetric filter gives zero response. (E) bars are signaled at the trapezoid’s foot and knee.

Mentions: Ernst Mach was the first to report the illusory dark and bright bars on a luminance trapezoid that now bear his name (Mach, 1865; translated by Ratliff, 1965)—see Figure 1. As with other illusory brightness phenomena, numerous explanations for this intriguing phenomenon have since been proposed (the earlier explanations are reviewed by Ratliff (1965) and more recent ones by Pessoa (1996) and, briefly, by Kingdom (2011)). Mach proposed that the bands were seen at the peaks and troughs in the second derivative of the luminance profile, and conjectured that this was due to reciprocal interactions between neighboring retinal cells, in other words “lateral inhibition”. As noted by Wallis and Georgeson (2012), a similar conclusion was reached by investigators who began the re-examination of the phenomenon some 60 years ago (Burnham and Jackson, 1955; O’Brien, 1958; Charman and Watrasiewicz, 1964; Thomas, 1965). Indeed, if one convolves a trapezoidal function with an even-symmetric bandpass filter, such as a model of a retinal ganglion or lateral-geniculate-nucleus (LGN) cell, one observes a dip at the foot and a bump at the knee of the trapezoid. However, any single bandpass filter account of Mach bands is problematic for two reasons. First, if the filter is dc-balanced, it incorrectly predicts the same brightness either side of the ramp (Figures 2, 3). Unbalancing the filter gets round this problem but a second problem remains: the single-filter response shows the largest Mach bands at step edges, where none occur (Fiorentini, 1972; Tolhurst, 1972; Ross et al., 1981; Ratliff, 1984). That Mach bands are not seen at a step edge is arguably a defining constraint of any model of the phenomenon. However the observation itself is not always appreciated, so given that the appearance of a step edge is a matter of some importance it will be considered in detail here.


Mach bands explained by response normalization.

Kingdom FA - Front Hum Neurosci (2014)

Schematic of the principle behind Feature models of Mach bands that employ even- and odd-symmetric filters. (A) even-symmetric (B) odd-symmetric filter. (C) trapezoidal edge profile. (D) response of even (green) and odd (purple) filters. The even-symmetric filter gives a strong response at the foot and knee of the trapezoid whereas the odd –symmetric filter gives zero response. (E) bars are signaled at the trapezoid’s foot and knee.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4219435&req=5

Figure 2: Schematic of the principle behind Feature models of Mach bands that employ even- and odd-symmetric filters. (A) even-symmetric (B) odd-symmetric filter. (C) trapezoidal edge profile. (D) response of even (green) and odd (purple) filters. The even-symmetric filter gives a strong response at the foot and knee of the trapezoid whereas the odd –symmetric filter gives zero response. (E) bars are signaled at the trapezoid’s foot and knee.
Mentions: Ernst Mach was the first to report the illusory dark and bright bars on a luminance trapezoid that now bear his name (Mach, 1865; translated by Ratliff, 1965)—see Figure 1. As with other illusory brightness phenomena, numerous explanations for this intriguing phenomenon have since been proposed (the earlier explanations are reviewed by Ratliff (1965) and more recent ones by Pessoa (1996) and, briefly, by Kingdom (2011)). Mach proposed that the bands were seen at the peaks and troughs in the second derivative of the luminance profile, and conjectured that this was due to reciprocal interactions between neighboring retinal cells, in other words “lateral inhibition”. As noted by Wallis and Georgeson (2012), a similar conclusion was reached by investigators who began the re-examination of the phenomenon some 60 years ago (Burnham and Jackson, 1955; O’Brien, 1958; Charman and Watrasiewicz, 1964; Thomas, 1965). Indeed, if one convolves a trapezoidal function with an even-symmetric bandpass filter, such as a model of a retinal ganglion or lateral-geniculate-nucleus (LGN) cell, one observes a dip at the foot and a bump at the knee of the trapezoid. However, any single bandpass filter account of Mach bands is problematic for two reasons. First, if the filter is dc-balanced, it incorrectly predicts the same brightness either side of the ramp (Figures 2, 3). Unbalancing the filter gets round this problem but a second problem remains: the single-filter response shows the largest Mach bands at step edges, where none occur (Fiorentini, 1972; Tolhurst, 1972; Ross et al., 1981; Ratliff, 1984). That Mach bands are not seen at a step edge is arguably a defining constraint of any model of the phenomenon. However the observation itself is not always appreciated, so given that the appearance of a step edge is a matter of some importance it will be considered in detail here.

Bottom Line: More recently, the dominant idea has been that Mach bands are a consequence of a visual process that generates a sparse, binary description of the image in terms of "edges" and "bars".Another recent explanation is that Mach bands result from learned expectations about the pattern of light typically found on sharply curved surfaces.I show that a simple one-dimensional model of response normalization explains the range of conditions under which Mach bands occur, and as importantly, the conditions under which they do not occur.

View Article: PubMed Central - PubMed

Affiliation: McGill Vision Research, Department of Ophthalmology, McGill University Montreal, Quebec, Canada.

ABSTRACT
Mach bands are the illusory dark and bright bars seen at the foot and knee of a luminance trapezoid. First demonstrated by Ernst Mach in the latter part of the 19th century, Mach bands are a test bed not only for models of brightness illusions but of spatial vision in general. Up until 50 years ago the dominant explanation of Mach Bands was that they were caused by lateral inhibition among retinal neurons. More recently, the dominant idea has been that Mach bands are a consequence of a visual process that generates a sparse, binary description of the image in terms of "edges" and "bars". Another recent explanation is that Mach bands result from learned expectations about the pattern of light typically found on sharply curved surfaces. In keeping with recent multi-scale filtering accounts of brightness illusions as well as current physiology, I show however that Mach bands are most simply explained by response normalization, whereby the gains of early visual channels are adjusted on a local basis to make their responses more equal. I show that a simple one-dimensional model of response normalization explains the range of conditions under which Mach bands occur, and as importantly, the conditions under which they do not occur.

No MeSH data available.


Related in: MedlinePlus