Global processing of random-phase radial frequency patterns but not modulated lines Robert J. Green School of Psychological Science, The University of Western Australia, Perth, Australia $ J. Edwin Dickinson School of Psychological Science, The University of Western Australia, Perth, Australia School of Psychological Science, The University of Western Australia, Perth, Australia $ David R. Badcock School of Psychological Science, The University of Western Australia, Perth, Australia $ 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 na¨ ıve 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. Introduction The perception of shapes is a critical task for the human visual system as it helps us navigate and interact with the world around us. However, the processes underlying the recognition of simple shapes are still not fully understood. A stimulus that has been extensively used in the study of simple shape perception is the radial frequency (RF) pattern. These patterns are made by sinusoidally modulating a circle’s radius such that it approximates simple shapes (e.g., triangle, square, etc.). Adjusting the amplitude of the sine wave adjusts the size of the deformation, which adjusts the salience of the stimulus, while changing the wavelength, and therefore, the number of complete sine waves that can fit around the circle’s circumference (the RF number) changes the shape it deforms into. Previous studies interested in the visual system’s ability to globally integrate shape information using RF patterns have examined the effect of varying the number of complete cycles of modulation on the RF pattern while the wavelength remains the same (see Figure 1; Dickinson, Bell, & Badcock, 2013; Dickinson, Cribb, Riddell, & Badcock, 2015; Dickinson, McGinty, Webster, & Badcock, 2012; Loffler, Wilson, & Wil- kinson, 2003; Schmidtmann, Kennedy, Orbach, & Loffler, 2012; Tan, Dickinson, & Badcock, 2013). They found that observer thresholds for detecting the presence of modulation decreased faster than was predicted by probability summation (PS; the increased chance of detection of local features due to an increase in the number of local elements available to detect) when modeled under high threshold theory (HTT; Citation: Green, R. J., Dickinson, J. E., & Badcock, D. R. (2017). Global processing of random-phase radial frequency patterns but not modulated lines. Journal of Vision, 17(9):18, 1–11, doi:10.1167/17.9.18. Journal of Vision (2017) 17(9):18, 1–11 1 doi: 10.1167/17.9.18 ISSN 1534-7362 Copyright 2017 The Authors Received January 13, 2017; published August 24, 2017 This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Downloaded from jov.arvojournals.org on 05/28/2020