Fig. 2: Online hierarchical inference replicates human perception of classical motion displays.

a In object-indexed experiment designs, every observable velocity is bound to an object irrespective of its location. Many psychophysics studies fall into this class of experiment design. b Johansson’s 3-dot motion display. Humans perceive the stimulus as shared horizontal motion with the central dot oscillating vertically between the outer dots. c The online model’s estimate of the motion strengths, λ_t (a single motion strength is shared across both spatial dimensions). The component matrix, C, is shown in the top-left as a legend for the line colors. Circles next to the matrix show the assignment of the rows in C to the dots in panel b. d The model’s posterior distribution over the motion sources, s_t, during the gray-shaded period in panel c. Shown are the mean values, μ_t, as lines along with the model’s estimated standard deviation (shaded, only for two components for visual clarity). e The Duncker wheel resembles a rolling wheel of which only the hub and one dot on the rim are visible. f Despite its minimalist trajectory pattern, humans perceive a rolling wheel. g Inferred motion strengths, λ_t. The model identifies shared motion plus an individual component for the revolving dot. h Inferred motion sources, μ_t, for the duration in panel g. Color gradients along the lines indicate time (from low to high contrast). For visual clarity, μ_t has been smoothed with a 50 ms box filter for plotting. Source data are provided as a Source Data file.