Mach Bands: multi-scale spatial filtering and co-operative coding of edges and bars

Stuart A. Wallis, Mark A. Georgeson

Research output: Contribution to conferencePoster

Abstract

Perception of Mach bands may be explained by spatial filtering ('lateral inhibition') that can be approximated by 2nd derivative computation, and several alternative models have been proposed. To distinguish between them, we used a novel set of ‘generalised Gaussian’ images, in which the sharp ramp-plateau junction of the Mach ramp was replaced by smoother transitions. The images ranged from a slightly blurred Mach ramp to a Gaussian edge and beyond, and also included a sine-wave edge. The probability of seeing Mach Bands increased with the (relative) sharpness of the junction, but was largely independent of absolute spatial scale. These data did not fit the predictions of MIRAGE, nor 2nd derivative computation at a single fine scale. In experiment 2, observers used a cursor to mark features on the same set of images. Data on perceived position of Mach bands did not support the local energy model. Perceived width of Mach bands was poorly explained by a single-scale edge detection model, despite its previous success with Mach edges (Wallis & Georgeson, 2009, Vision Research, 49, 1886-1893). A more successful model used separate (odd and even) scale-space filtering for edges and bars, local peak detection to find candidate features, and the MAX operator to compare odd- and even-filter response maps (Georgeson, VSS 2006, Journal of Vision 6(6), 191a). Mach bands are seen when there is a local peak in the even-filter (bar) response map, AND that peak value exceeds corresponding responses in the odd-filter (edge) maps.
LanguageEnglish
Publication statusUnpublished - 18 Dec 2010
EventFourteenth Applied Vision Association Christmas Meeting - University of Bristol, Bristol (UK)
Duration: 18 Dec 2009 → …

Other

OtherFourteenth Applied Vision Association Christmas Meeting
CityUniversity of Bristol, Bristol (UK)
Period18/12/09 → …

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filter
edge wave
plateau
prediction
energy
experiment
detection

Bibliographical note

Abstract published in Fourteenth Applied Vision Association Christmas Meeting, University of Bristol, Bristol, UK, 18 December 2009, Abstracts, Perception, (2010) 39 (2), p.272, 0301-0066.

Keywords

  • Mach bands
  • perception
  • spatial filtering
  • lateral inhibition
  • 2nd derivative computation
  • generalised Gaussian images
  • sharp ramp-plateau junction
  • Gaussian edge
  • sine-wave edge

Cite this

Wallis, S. A., & Georgeson, M. A. (2010). Mach Bands: multi-scale spatial filtering and co-operative coding of edges and bars. Poster session presented at Fourteenth Applied Vision Association Christmas Meeting, University of Bristol, Bristol (UK), .
Wallis, Stuart A. ; Georgeson, Mark A. / Mach Bands: multi-scale spatial filtering and co-operative coding of edges and bars. Poster session presented at Fourteenth Applied Vision Association Christmas Meeting, University of Bristol, Bristol (UK), .
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note = "Abstract published in Fourteenth Applied Vision Association Christmas Meeting, University of Bristol, Bristol, UK, 18 December 2009, Abstracts, Perception, (2010) 39 (2), p.272, 0301-0066.; Fourteenth Applied Vision Association Christmas Meeting ; Conference date: 18-12-2009",
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}

Wallis, SA & Georgeson, MA 2010, 'Mach Bands: multi-scale spatial filtering and co-operative coding of edges and bars' Fourteenth Applied Vision Association Christmas Meeting, University of Bristol, Bristol (UK), 18/12/09, .

Mach Bands: multi-scale spatial filtering and co-operative coding of edges and bars. / Wallis, Stuart A.; Georgeson, Mark A.

2010. Poster session presented at Fourteenth Applied Vision Association Christmas Meeting, University of Bristol, Bristol (UK), .

Research output: Contribution to conferencePoster

TY - CONF

T1 - Mach Bands: multi-scale spatial filtering and co-operative coding of edges and bars

AU - Wallis, Stuart A.

AU - Georgeson, Mark A.

N1 - Abstract published in Fourteenth Applied Vision Association Christmas Meeting, University of Bristol, Bristol, UK, 18 December 2009, Abstracts, Perception, (2010) 39 (2), p.272, 0301-0066.

PY - 2010/12/18

Y1 - 2010/12/18

N2 - Perception of Mach bands may be explained by spatial filtering ('lateral inhibition') that can be approximated by 2nd derivative computation, and several alternative models have been proposed. To distinguish between them, we used a novel set of ‘generalised Gaussian’ images, in which the sharp ramp-plateau junction of the Mach ramp was replaced by smoother transitions. The images ranged from a slightly blurred Mach ramp to a Gaussian edge and beyond, and also included a sine-wave edge. The probability of seeing Mach Bands increased with the (relative) sharpness of the junction, but was largely independent of absolute spatial scale. These data did not fit the predictions of MIRAGE, nor 2nd derivative computation at a single fine scale. In experiment 2, observers used a cursor to mark features on the same set of images. Data on perceived position of Mach bands did not support the local energy model. Perceived width of Mach bands was poorly explained by a single-scale edge detection model, despite its previous success with Mach edges (Wallis & Georgeson, 2009, Vision Research, 49, 1886-1893). A more successful model used separate (odd and even) scale-space filtering for edges and bars, local peak detection to find candidate features, and the MAX operator to compare odd- and even-filter response maps (Georgeson, VSS 2006, Journal of Vision 6(6), 191a). Mach bands are seen when there is a local peak in the even-filter (bar) response map, AND that peak value exceeds corresponding responses in the odd-filter (edge) maps.

AB - Perception of Mach bands may be explained by spatial filtering ('lateral inhibition') that can be approximated by 2nd derivative computation, and several alternative models have been proposed. To distinguish between them, we used a novel set of ‘generalised Gaussian’ images, in which the sharp ramp-plateau junction of the Mach ramp was replaced by smoother transitions. The images ranged from a slightly blurred Mach ramp to a Gaussian edge and beyond, and also included a sine-wave edge. The probability of seeing Mach Bands increased with the (relative) sharpness of the junction, but was largely independent of absolute spatial scale. These data did not fit the predictions of MIRAGE, nor 2nd derivative computation at a single fine scale. In experiment 2, observers used a cursor to mark features on the same set of images. Data on perceived position of Mach bands did not support the local energy model. Perceived width of Mach bands was poorly explained by a single-scale edge detection model, despite its previous success with Mach edges (Wallis & Georgeson, 2009, Vision Research, 49, 1886-1893). A more successful model used separate (odd and even) scale-space filtering for edges and bars, local peak detection to find candidate features, and the MAX operator to compare odd- and even-filter response maps (Georgeson, VSS 2006, Journal of Vision 6(6), 191a). Mach bands are seen when there is a local peak in the even-filter (bar) response map, AND that peak value exceeds corresponding responses in the odd-filter (edge) maps.

KW - Mach bands

KW - perception

KW - spatial filtering

KW - lateral inhibition

KW - 2nd derivative computation

KW - generalised Gaussian images

KW - sharp ramp-plateau junction

KW - Gaussian edge

KW - sine-wave edge

M3 - Poster

ER -

Wallis SA, Georgeson MA. Mach Bands: multi-scale spatial filtering and co-operative coding of edges and bars. 2010. Poster session presented at Fourteenth Applied Vision Association Christmas Meeting, University of Bristol, Bristol (UK), .