Geometrical structure of perceptual color space: mental representations and adaptation invariance

Abstract

A central issue in neuroscience is to understand how the brain builds structured representations of percepts that facilitate useful inferences about the world. Similarity between percepts is used to accomplish many everyday tasks, e.g. object identification, so is widely used to construct geometrical spaces that represent stimulus qualities, but the intrinsic validity of the geometry is not tested critically. We introduce an experimental approach to equating relative similarities by setting perceived midpoints between pairs of stimuli. Midpoint settings are used with Varignons Theorem to test the intrinsic geometry of a representation space, and its mapping to a physical space of stimuli. For perceptual color space, we demonstrate that geometrical structure depends on the mental representation used in judging similarity: an affine geometry is valid only when observers use an opponent-color mental representation. An affine geometry implies that similarity can be judged within straight lines and across parallel lines, and its neural coding could involve ratios of responses. We show that this perceptual space is invariant to changes in illumination color, providing a formal justification to generalize to all of color space, color constancy results measured for color categories. Our midpoint measurements deviate significantly from midpoints in the \"uniform\" color spaces CIELAB and CIELUV, used extensively in industry and research, so these spaces do not provide adequate metric representation of perceived colors. Our paradigm can thus test for intrinsic geometrical assumptions underlying the representation space for many perceptual modalities, and for the extrinsic perceptual geometry of the space of physical stimuli.\n\nSignificanceMathematical spaces based on similarity judgments are widely used to represent stimulus qualities in perception, cognition and neuroscience. We introduce a perceptual approach to equate relative similarities, and use them to test the geometry of a perceptual space and its mapping to a physical space of stimuli. For color perception, our results show that perceptual geometry depends on the mental representation used in judging similarity, and it has an affine structure when observers use an opponent-color representation. An affine geometry implies that neural coding of similarity could involve simple ratios of responses. Our measurements also reveal that the uniform color spaces CIELAB and CIELUV, used extensively in industrial applications, do not provide adequate representation of similarity between moderately spaced colors.