Radial frequency (RF) patterns are a class of visual stimuli characterized by a sinusoidal modulation of the radius in polar coordinates. They are commonly used to study shape perception in humans.

Human vision has been shown to be highly sensitive (hyper-acuity) to such radial deformations. Though controversial, it is believed that this cannot be simply explained by a local analysis of orientation or curvature, but would rather require a global pooling of contour information.

Functional magnetic resonance imaging (fMRI) suggests that the radial frequency of a closed contour is one of the cortical shape analysis dimensions, represented in the early and mid-level visual areas.

References:

  Wilkinson et al (1998) Detection and recognition of radial frequency patterns. Vision Research 38(22):3555–3568

  Jeffrey et al (2002) Circular contour frequency in shape discrimination. Vision Research 42(25):2773–2779

  Mullen et al (2011) Evidence that global processing does not limit thresholds for RF shape discrimination. Journal Of Vision 11(3):6

  Wilson & Wilkinson (2015) From orientations to objects: Configural processing in the ventral stream. Journal Of Vision 15(7):4

  Salmela et al (2016) Radial Frequency Analysis of Contour Shapes in the Visual Cortex. PLoS Comput Biol 12(2):e1004719

  Schmidtmann & Kingdom (2017) Nothing more than a pair of curvatures: A common mechanism for the detection of both radial and non-radial frequency patterns. Vision Research 134:18–25

Here is the math behind this stimulus:

 radmod = radius*(1+0.01*ram*sin(rf*theta+phi)) # Radial amplitude modulation
 ar = (r-radmod)/sigma               # Annulus modulation
 ar2 = ar*ar                     # Useful precomputation
 z = (1-4*(ar2)+4*(ar2*ar2)/3)*(exp(-(ar2)))      # Radial profile

The whole stimulus is generated in real-time using a GLSL shader that runs right inside your WebGL-compatible browser. The plain Math behind the stimulus was converted to this optimized GLSL shader using the new Psykinematix Pro Edition. Translation to Matlab and Python code is also possible !

This whole widget was also fully generated using Psykinematix Pro Edition. The parameters that control the stimulus properties through the sliders are the same as the ones you would define as dependent or independent variables when using the stimulus in an actual psychophysical experiment run in Psykinematix. The widget creation is otherwise fully customizable with your own logo, copyright, links, etc.

To learn more about the widget creation, click on the above "Made With" button !