Scale invariance is driven by stimulus density

Scale invariance refers to aspects of visual perception that remain constant with changes in viewing distance. Previously, Dakin and Herbert [Proc. Roy. Soc. B. 265 (1397) (1998) 659] reported that the spatial integration region (IR) for mirror symmetry in bandpass noise is scale invariant because its dimensions scale with the inverse of peak spatial frequency. In bandpass noise, however, peak spatial frequency covaries with stimulus numerosity (i.e. the total number of information samples) and density (i.e. the total number of information samples per unit area). In this study, we report four experiments that decoupled properties of the retinal image affected by viewing distance--spatial frequency, numerosity, size, and density--and measured their effect on IR size. Stimuli consisted of bandpass microelements with vertically mirror-symmetric but otherwise random positions, and we measured observer resistance to random jitter imposed on microelement position. Results show that jitter resistance and IR size vary with the inverse of stimulus density but are unaffected by changes in stimulus spatial frequency, numerosity, or size. We found the IR has a 2:1 height-to-width aspect ratio and integrates information from approximately 18 microelements regardless of their spatial separation. Our results reveal that stimulus density plays a central role in the visual system's implementation of scale invariance. Using an ideal-observer, we demonstrate that scale invariance reflects genuine neural scale selection rather than a physical limitation on the stimulus' information content. Our findings that jitter resistance and IR size vary with the inverse of density challenge current models of spatial vision but can be reconciled with a model that compares the output of bandpass non-Fourier mechanisms to select spatial scales that match stimulus density.