Predicting the responses in colour matching experiments from the symmetries of colour space

In conceptual spaces, the distance between concepts is represented by a metric that cannot usually be expressed as a function of a few, salient physical properties of the represented items. For example, the space of colours can be endowed with a metric capturing the degree to which two chromatic stimuli are perceived as different. As many optical illusions have shown, the colour with which a stimulus is perceived depends, among other contextual factors, on the chromaticity of its surround, an effect called "chromatic induction". Heuristically, the surround pushes the colour of the stimulus away from its own chromaticity, increasing the salience of the boundary. Previous studies have described how the magnitude of the push depends on the chromaticity of both the stimulus and the surround, concluding that the space of colours contains anisotropies and inhomogeneities. The importance of contextuality has cast doubt on the practical or predictive utility of perceptual metrics, beyond a mathematical curiosity. Here we provide evidence that the metric structure of the space of colours is indeed useful and has predictive power. By using a notion of distance between colours emerging from a subjective metric, we show that the anisotropies and inhomogeneities reported in previous studies can be eliminated. The resulting symmetry allows us to derive a universal curve for the average chromatic induction that contains no fitting parameters and is confirmed by experimental data. The theory also predicts the magnitude of chromatic induction for every possible combination of stimulus and surround demonstrating that, at least in the case of colours, the metric captures the symmetries of perception, and augments the predictive power of theories.