Third-derivative filters predict edge locations in spatial vision

Stuart A. Wallis, Mark A. Georgeson

Research output: Unpublished contribution to conferencePosterpeer-review


Edge detection is crucial in visual processing. Previous computational and psychophysical models have often used peaks in the gradient or zero-crossings in the 2nd derivative to signal edges. We tested these approaches using a stimulus that has no such features. Its luminance profile was a triangle wave, blurred by a rectangular function. Subjects marked the position and polarity of perceived edges. For all blur widths tested, observers marked edges at or near 3rd derivative maxima, even though these were not 1st derivative maxima or 2nd derivative zero-crossings, at any scale. These results are predicted by a new nonlinear model based on 3rd derivative filtering. As a critical test, we added a ramp of variable slope to the blurred triangle-wave luminance profile. The ramp has no effect on the (linear) 2nd or higher derivatives, but the nonlinear model predicts a shift from seeing two edges to seeing one edge as the ramp gradient increases. Results of two experiments confirmed such a shift, thus supporting the new model. [Supported by the Engineering and Physical Sciences Research Council].
Original languageEnglish
Publication statusPublished - 2007
Event13th European Conference on Visual Perception - Arezzo (IT), Italy
Duration: 27 Aug 200731 Aug 2007


Conference13th European Conference on Visual Perception
CityArezzo (IT)

Bibliographical note

Abstract published in Applied Vision Association Annual 2007 Meeting "Active and Passive Vision", Perception, 36 (Suppl. S), pp. 1401-1402. 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.


  • edge detection
  • visual processing
  • 2nd derivative
  • signal edges
  • luminance profile
  • perceived edges
  • blur widths
  • 3rd derivative maxima
  • 1st derivative maxima
  • 2nd derivative zero-crossings


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