Fig. 5: Noise-dependent perceptual changes for motion integration of spatially distributed stimuli.

a In the motion illusion from Lorenceau⁴², a vertically and a horizontally oscillating group of dots maintain a 90°-phase shift consistent with global clockwise rotation (indicated as gray arrow). b The noise-free stimulus (left branch) evokes transparent motion with an additional counter-clockwise rotating percept in human observers. Adding motion noise by disturbing dot trajectories orthogonally to their group’s oscillation axis (right branch; modeled by increased observation noise \({\sigma }_{{{{{{{{\rm{obs}}}}}}}}}^{2}\)) flips the percept to a single coherent rotation of all dots in clockwise direction. c The model’s perceived velocities in both stimulus conditions (time = color gradient from low to high contrast; t ≤ 2 s in noise-free condition; t ≤ 5 s in noisy condition). For visual clarity, perceived velocities have been smoothed with a 200 ms box filter for plotting. d Illustration of the model’s inferred motion decomposition. For noise-free stimuli, clockwise rotating self-motion is compensated by counter-clockwise rotating group motion (sketched here for the horizontal group). With motion noise, only a single, clockwise rotating shared motion component is inferred for all dots. Source data are provided as a Source Data file.