Fig. 4: Hierarchical inference explains motion illusions in location-indexed experiments.

a In location-indexed experiments, motion flow is presented at stationary spatial locations. b Considered latent motion components. Self-motion, which affects all retinal velocities in the opposite direction (−1) integrates both visual input and a vestibular signal (here: zero + noise). c Perceived object velocities, relative to the environment, are the sum of all inferred motion components excluding self-motion. d In motion direction repulsion experiments, two groups of dots move at constant velocity with opening angle γ. e The direction in which human perception of the opening angle is biased depends on the true opening angle. Black dots: human data, reproduced from ref. 36, error bars denote S.E. of the mean across subjects; n = 3 subjects, 80 trials per angle and subject. Purple line: model percept. Insets: the model’s inferred motion decomposition. f Varying the contrast of one dot group modulates the biased percept of the angle of the other group. Purple: model percept for γ = 45°, qualitatively matching data from ref. 37. Blue: predicted inversion of the bias for smaller opening angles. g Same as panel f, but for varying the speed of the second group. Purple: model percept for γ = 60°, qualitatively matching data from ref. 38. Dashed blue: model percept for γ = 90°, qualitatively matching data from ref. 36. Solid blue: predicted biphasic function for smaller opening angles. h–l Extended experiment from ref. 39 which surrounds the two central RDKs with additional RDKs in an annulus. The hierarchical inference model replicates human perception in various conditions. h A surround with dots moving vertically both up- and downwards ("bi-directional surround” in ref. 39, indicated by orange arrows in the top-left sketch’s annulus) causes no repulsion in the perceived directions of horizontally moving RDKs in the center (darker orange arrows in the top-left sketch’s center). Our model replicates this perception as shown in the histogram of 200 trial repetitions. i Coherently moving annulus RDKs cause the perceived inner velocities to be biased away from the surround direction. j For diagonally moving inner RDKs, the same coherent downward surround has no noticeable effect. k Neither does a bi-directional surround bias the percept of diagonally moving inner RDKs. l An upward surround, in contrast, biases the percept of the inner RDKs to close-to-horizontal motion. Source data are provided as a Source Data file.