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.
Highlights
Ernst Mach was the first to report the illusory dark and bright bars on a luminance trapezoid that bear his name (Mach, 1865; translated by Ratliff, 1965)—see Figure 1
We have shown that a bare-bones and simplified 1D model of response normalization provides a good account of the conditions in which Mach bands occur as well as when they do not occur
As such this modeling exercise represents a “proof-of-concept” alternative explanation of Mach bands to that of Feature models, as well as to the more recent models of Mach bands based on learnt image statistics
Summary
Ernst Mach was the first to report the illusory dark and bright bars on a luminance trapezoid that bear his name (Mach, 1865; translated by Ratliff, 1965)—see Figure 1. Www.frontiersin.org bands are seen in trapezoids, but crucially why they are not seen at step edges In this communication the case will be put that in spite of the superiority of Feature models over earlier lateral inhibition models, there is a simpler and more parsimonious explanation of Mach bands: response normalization. The inspiration for considering response normalization as a possible cause for Mach bands comes from a recent class of model aimed at providing low-level accounts of a variety of brightness illusions This class of model combines multi-scale filtering with response (often termed contrast) normalization (Blakeslee and McCourt, 1999; Dakin and Bex, 2003; Blakeslee et al, 2005; Robinson et al, 2007; Otazu et al, 2008). The slight but broad brightening and darkening either side of the edge is captured by the model; it is caused by the fact that the filter set employed is not fully complete due to the absence of filters tuned to very low spatial frequencies
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