Global processing of random-phase radial frequency patterns but not modulated lines

Abstract

Previously, researchers have used circular contours with sinusoidal deformations of the radius (radial frequency [RF] patterns) to investigate the underlying processing involved in simple shape perception. On finding that the rapid improvement in sensitivity to deformation as more cycles of modulation were added was greater than expected from probability summation across sets of local independent detectors, they concluded that global integration of contour information was occurring. More recently, this conclusion has been questioned by researchers using a method of calculating probability summation derived from signal detection theory (Baldwin, Schmidtmann, Kingdom, & Hess, 2016). They could not distinguish between global integration and probability summation. Furthermore, it has been argued that RF patterns and lines are processed in a similar manner (Mullen, Beaudot, & Ivanov, 2011; Schmidtmann & Kingdom, 2017). The current study investigates these claims using fixed-phase (in which the local elements have spatial certainty) and random-phase (in which the local elements have spatial uncertainty) RF patterns and modulated lines. Thresholds were collected from eight naïve observers and compared to probability summation estimates calculated using methods derived from both high threshold theory and signal detection theory. The results indicate global processing of random-phase RF patterns and evidence for an interaction between local and global cues for fixed-phase RF patterns. They also show no evidence of global integration with modulated line stimuli. The results provide further evidence for the global processing of random-phase RF patterns and indicate that RF patterns and modulated lines are processed differently.

The effect of spatiotemporal displacement on the integration of shape information

“…Or et al (2011) did compare thresholds for a constant retinal speed and constant angular velocity presentation of their stimulus; however, they only examined these effects on complete motion RFs (i.e., patterns with all cycles of modulation present) and correctly concluded that there was no significant difference in thresholds for these patterns. Our investigation of these effects extended to incompletely modulated motion RF patterns and suggests a result similar to that of Green et al (2017), an interaction between a salient local cue and the global cue of the pattern. The salient local cue is detected first when the global signal is low, but as more cycles of modulation are added, the global signal increases and detection becomes a result of this global cue.…”

“…Both the pattern of results and the comparison to probability summation estimates suggest that motion RF patterns are processed differently to motion line patterns. These findings support that of Green et al (2017), but are contrary to those of (Schmidtmann & Kingdom, 2017) and are discussed as follows.…”

“…There were three line conditions: motion line; motion line fixation; and contour line. The purpose of the motion line conditions is to determine if, similar to the contour-defined results found by Green et al (2017), open motion patterns are processed in a different way to the closed contour motion RF patterns. The motion line and motion line fixation conditions consist of a DOG dot (as defined in Equation 7) tracing out the path of a modulated line which was either by itself (motion line) or 18 of visual angle to the side of a solid black line (motion line fixation; the same distance as between the fixation point and the dot used for the motion RF patterns).…”

“…For the contour line condition and similar to conventional RF patterns (Loffler et al, 2003) and previous contour-defined modulated lines (Green et al, 2017), the cross section of the luminance profile of the path conformed to a fourth derivative of a Gaussian (D4) with a frequency spectrum peaking at 8 c/deg where f peak ¼ ffiffi ffi 2 p =pr (Loffler et al, 2003;Wilkinson et al, 1998) and obtained using a r of 3.376 0 of visual angle.…”

Radial frequency patterns describe a small and perceptually distinct subset of all possible planar shapes

“…More importantly, the method used here generates a combination of many RF patterns, whereas most previous studies used either single component RF patterns (e.g. Bell & Badcock, 2008Bell et al, 2007;Green, Dickinson, & Badcock, 2017, 2018a, Green, Dickinson, & Badcock, 2018bHess, Achtman, & Wang, 2001;Jeffrey et al, 2002;Schmidtmann et al, 2012;Loffler et al, 2003), combinations of two Bell et al, 2007;Lawrence et al, 2016) or three RF components (Schmidtmann, Jennings, & Kingdom, 2015). Given that the aim of this study was to explore the limits of what can be represented by compound RF patterns, the stimuli used here are combinations of an arbitrary number of RF patterns (see Methods).…”