Human lightness perception is guided by simple assumptions about reflectance and lighting

Lightness constancy is the remarkable ability of human observers to perceive surface reflectance accurately despite variations in illumination and context. Two successful approaches to understanding lightness perception that have developed along independent paths are anchoring theory and Bayesian theories. Anchoring theory is a set of rules that predict lightness percepts under a wide range of conditions. Some of these rules are counterintuitive and difficult to motivate, e.g., a rule that large surfaces tend to look lighter than small surfaces. Bayesian theories are formulated as probabilistic assumptions about lights and objects, and they model percepts as rational inferences from sensory data. Here I reconcile these two seemingly divergent approaches by showing that many rules of anchoring theory follow from simple probabilistic assumptions about lighting and reflectance. I describe a simple Bayesian model that makes maximum a posteriori interpretations of luminance images, and I show that this model predicts many of the phenomena described by anchoring theory, including anchoring to white, scale normalization, and rules governing glow. Thus anchoring theory can be formulated naturally in a Bayesian framework, and this approach shows that many seemingly idiosyncratic properties of human lightness perception are actually rational consequences of simple assumptions about lighting and reflectance.