Illusory speeding-up and slowing-down of objects moving at constant speed emerges from natural motion detection algorithms

The footsteps illusion is a perceptual illusion in which two bars moving at the same constant speed on a stripey background are seen as alternately accelerating and decelerating like footsteps. The cortical mechanisms that give rise to footsteps and similar illusions remain to be fully understood and may reveal important neural computations. Using an implementation of the biologically inspired correlational model of motion detection, the 2DMD, this study had three aims. First, reproducing perceptual speed oscillations in model simulations. Second, mapping empirical reports of multiple illusion configurations onto model outputs. Third, inferring from the successful model, the role of multi-scale spatiotemporal channels in perception. We developed a 2DMD implementation adding a global (single value) frame-by-frame dynamic readout to quantify the continuous and oscillating response components. We confirmed that an expected signature oscillatory motion response corresponded to the footsteps illusion, demonstrating that its amplitude varied according to empirically measured illusion strength. We showed that with a global readout, the inherent pattern and contrast dependence of correlation detectors is sufficient to reproduce the surprising perceptual illusion. This evidence suggests spacetime correlation may be a fundamental sensory computation. Across species, filtering and global pooling operations might be adapted to process various complex phenomena.

Methods
For the simulations of the experimental data from the work done by colleagues (Kitaoka & Anstis, 2021;)  and ( Sunaga et al., 2008), corresponding input stimuli were generated using bespoke functions written in Mathworks MATLAB 2022 on PCs running Windows 10. The generated FI image sequences recreated the three manipulations of spatial configuration, speed and background grating waveform with matrices of 256 x 256 pixels in dimensions (w x h), an 8-bit luminance depth played over 100 frames (f). Each stimulus consisted of two moving bars (black and white) and a grayscale luminance grating background with values running from -1 (black) to 1 (white). Each foreground bar was characterised by its size BW x BH (typically 16 x 32 for a vertically oriented bar) and bar speed BS in pixels per frame. The generated stimulus was approximately matched to the relative scales and proportions in the studies. The generated stimulus matrix I(x,y,t) was used as an input into the models with x, y and t denoting functions of horizontal space, vertical space and time in pixels and frames respectively.

The code included runs simulations to generate the plots in the published work in Figures 2-6.