Nothing more than a curve: a common mechanism for the detection of radial and non-radial frequency patterns!
Gunnar Schmidtmann & Frederick Kingdom
Radial frequency (RF) patterns, which are sinusoidal modulations of a radius in polar coordinates, have been frequently used to study shape perception. Discriminating RF patterns from circles could be accomplished either by mechanisms sensitive to local parts of the pattern, or by a global mechanism operating at the scale of the entire shape. Previous studies have argued that the detection of RF patterns could not be achieved by local curvature analysis, but instead by a specialized global mechanism for RF shapes.Here we challenge this hypothesis and suggest a model based on the detection of local curvature to account for the pattern of thresholds observed for both radial and non-radial (e.g. modulated around a straight line) frequency patterns. We introduce the Curve Frequency Sensitivity Function, or CSFF, which is characterized by a flat followed by declining response to curvature as a function of modulation frequency. The decline in response to curvature at high modulation frequencies embodies the idea of a perceptual limitation for high curve frequencies. The CSFF explains the initial decrease in detection thresholds for low RFs followed by the asymptotic thresholds for higher RFs (Wilkinson, Wilson, & Habak, 1998) and similarly accounts for results with non-radial frequency patterns (Prins, Kingdom, & Hayes, 2007).
In summary, our analysis suggests that the detection of shape modulations is processed by a common curvature-sensitive mechanism that is independent of whether the modulation is applied to a circle or a straight line and that therefore radial frequency patterns are not special.