Hierarchical motion perception as causal inference.

Motion can only be defined relative to a reference frame; yet it remains unclear which reference frame guides perception. A century of psychophysical studies has produced conflicting evidence: retinotopic, egocentric, world-centric, or even object-centric. We introduce a hierarchical Bayesian model mapping retinal velocities to perceived velocities. Our model mirrors the structure in the world, in which visual elements move within causally connected reference frames. Friction renders velocities in these reference frames mostly stationary, formalized by an additional delta component (at zero) in the prior. Inverting this model automatically segments visual inputs into groups, groups into supergroups, progressively inferring structured reference frames and "perceives" motion in the appropriate reference frame. Critical model predictions are supported by two experiments, and fitting our model to the data allows us to infer the subjective set of reference frames used by individual observers. Our model provides a quantitative normative justification for key Gestalt principles providing inspiration for building better models of visual processing in general.