Mach edges: a critical test of the nonlinear 3rd derivative model for edge-detection

Stuart A. Wallis, Mark A. Georgeson

Research output: Unpublished contribution to conferencePosterpeer-review


Feature detection is a crucial stage of visual processing. In previous feature-marking experiments we found that peaks in the 3rd derivative of the luminance profile can signify edges where there are no 1st derivative peaks nor 2nd derivative zero-crossings (Wallis and George 'Mach edges' (the edges of Mach bands) were nicely predicted by a new nonlinear model based on 3rd derivative filtering. As a critical test of the model, we now use a new class of stimuli, formed by adding a linear luminance ramp to the blurred triangle waves used previously. The ramp has no effect on the second or higher derivatives, but the nonlinear model predicts a shift from seeing two edges to seeing only one edge as the added ramp gradient increases. In experiment 1, subjects judged whether one or two edges were visible on each trial. In experiment 2, subjects used a cursor to mark perceived edges and bars. The position and polarity of the marked edges were close to model predictions. Both experiments produced the predicted shift from two to one Mach edge, but the shift was less complete than predicted. We conclude that the model is a useful predictor of edge perception, but needs some modification.
Original languageEnglish
Publication statusUnpublished - 2007
EventApplied Vision Association Annual 2007 Meeting - Bradford , United Kingdom
Duration: 20 Apr 2007 → …


OtherApplied Vision Association Annual 2007 Meeting
Country/TerritoryUnited Kingdom
Period20/04/07 → …

Bibliographical note

Abstract published in Applied Vision Association Annual 2007 Meeting "Active and Passive Vision", Perception, 36(9), pp.1409-1410, ISSN 0001-4966. If you have discovered material in AURA which is unlawful e.g. breaches copyright, (either yours or that of a third party) or any other law, including but not limited to those relating to patent, trademark, confidentiality, data protection, obscenity, defamation, libel, then please read our Takedown Policy and contact the service immediately.


  • feature detection
  • visual processing
  • 3rd derivative
  • luminance profile
  • edges
  • zero-crossings
  • 3rd derivative filtering
  • edge perception


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