Abstract
The perception of brightness depends on spatial context: the same stimulus can appear light or dark depending on what surrounds it. A less well-known but equally important contextual phenomenon is that the colour of a stimulus can also alter its brightness. Specifically, stimuli that are more saturated (i.e. purer in colour) appear brighter than stimuli that are less saturated at the same luminance. Similarly, stimuli that are red or blue appear brighter than equiluminant yellow and green stimuli. This non-linear relationship between stimulus intensity and brightness, called the Helmholtz-Kohlrausch (HK) effect, was first described in the nineteenth century but has never been explained. Here, we take advantage of the relative simplicity of this ‘illusion’ to explain it and contextual effects more generally, by using a simple Bayesian ideal observer model of the human visual ecology. We also use fMRI brain scans to identify the neural correlates of brightness without changing the spatial context of the stimulus, which has complicated the interpretation of related fMRI studies. Rather than modelling human vision directly, we use a Bayesian ideal observer to model human visual ecology. We show that the HK effect is a result of encoding the non-linear statistical relationship between retinal images and natural scenes that would have been experienced by the human visual system in the past. We further show that the complexity of this relationship is due to the response functions of the cone photoreceptors, which themselves are thought to represent an efficient solution to encoding the statistics of images. Finally, we show that the locus of the response to the relationship between images and scenes lies in the primary visual cortex (V1), if not earlier in the visual system, since the brightness of colours (as opposed to their luminance) accords with activity in V1 as measured with fMRI. The data suggest that perceptions of brightness represent a robust visual response to the likely sources of stimuli, as determined, in this instance, by the known statistical relationship between scenes and their retinal responses. While the responses of the early visual system (receptors in this case) may represent specifically the statistics of images, post receptor responses are more likely represent the statistical relationship between images and scenes. A corollary of this suggestion is that the visual cortex is adapted to relate the retinal image to behaviour given the statistics of its past interactions with the sources of retinal images: the visual cortex is adapted to the signals it receives from the eyes, and not directly to the world beyond.