Fig. 1: Visual motion perception as an online hierarchical inference task.

a Scene with nested motion relations. Observed velocities reaching the observer’s retina are perceived as a combination of self-motion, flock motion and every bird’s individual motion relative to the flock. b Formal decomposition of the scene’s motion into latent motion sources. c Tree-structured graph representation of the underlying motion structure with nodes corresponding to latent motion sources. Self-motion contributes in the opposite direction to retinal velocity (−1). Vertical distances between nodes, termed motion strengths, λ, describe the long-term average speed of the source. Vanishing motion strength indicates that the corresponding motion source is not present the scene. d–g Generative model of structured motion. d Graph for a simpler motion scene with three flocking birds and a stationary observer. e Latent motion sources follow independent Ornstein–Uhlenbeck processes. f The component matrix, C, composes noise-free velocities from the motion sources, such that each velocity is the sum of all its ancestral sources. g Observed velocities are noisy versions of the noise-free velocities. h Inverting the generative model according to Bayes’ rule poses an online hierarchical inference task characterized by interdependent updates of motion sources and structure. i Using an adiabatic approximation, the motion sources’ posterior variances reduce to a function of the motion strengths. Panels a–h are derived from artwork by Vladimír Čerešňák ("Migrating geese in the spring and autumn” licensed from Depositphotos Inc.) and Gordon Dylan Johnson ("Vintage Brother And Sister Bicycle Silhouette” from Openclipart.org, public domain).