Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges


Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding.

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Divisions: College of Health & Life Sciences > School of Optometry > Optometry
Additional Information: Creative Commons Attribution Non-Commercial No Derivatives License
Uncontrolled Keywords: bars,edges,even and odd filters,feature detection,gaussian derivatives,human vision,mach bands,psychophysics,scale-space,Ophthalmology,Sensory Systems
Publication ISSN: 1534-7362
Last Modified: 04 Jan 2024 08:09
Date Deposited: 03 Jan 2013 13:51
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://jov.arvo ... ticleid=2121187 (Publisher URL)
PURE Output Type: Article
Published Date: 2012-12-21
Authors: Wallis, Stuart (ORCID Profile 0000-0002-3588-055X)
Georgeson, Mark (ORCID Profile 0000-0002-8173-9522)

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