Non-isometric colour similarity

This paper presents the findings obtained in an experimental study of metric underlying the perceptual colour space. Previous studies evidenced that, in tasks of evaluation of colour similarity, the subjects don't refer to the most general category of “colour”, but rather rely on the introduction of subordinate categories containing all variations of a colour. Besides, categories related to different colours can sometimes overlap. This forces to conclude that perception of colour variations is not isometric, but is rather weighed in different ways for different colours. In order to detect the metric of colour space we performed an experiment with multiple conditions within the subjects, designed to determine the form of the function that ties the independent variable (tonality of colour) with the dependent variable (similarity judgement). To each subject we presented simultaneously a pair of images, the target one and another differing from the target only for its colour (a suitable perturbation of the tonality). The subject task was to rate the similarity of the second image with the target. The frequency distribution of similarity judgments for each colour gave a qualitative description of how the different colours are represented at the cognitive level. We applied to the observed frequencies a unidimensional scaling procedure to obtain a precise measure of the distance between the variation steps for each colour. We were allowed to choose a single dimension because we limited the study only to the variation of tonality. The scaling was applied separately to each colour scale. The results showed that different colours were associated to different measure scales. Besides, once chosen a particular colour, its measure scale itself was depending on the direction of variation chosen for its tonality during the experimental presentation. We can conclude that the geometry of colour space looks very complicated and not reducible to familiar mathematical concepts.