The Achromatic Object-Colour Manifold is Three-Dimensional.

When in shadow, the achromatic object colours appear different from when they are in light. This immediate observation was quantitatively confirmed by Logvinenko and Maloney (2006, Perception & Psychophysics, 68, 76-83) who, using multidimensional scaling (MDS), showed the two-dimensionality of achromatic object colours. As their experiments included only cast shadows, a question arises: is this also the case for attached shadows? Recently, Madigan and Brainard (2014) argued in favour of the negative answer. However, they also failed to confirm the two-dimensionality for cast shadows. To resolve this issue, an experiment was conducted in which observers rated the dissimilarity between achromatic Munsell chips presented in light and in shadows of both types. Specifically, the chips were presented in four conditions: in front in light; at slant in light; in front in shadow; and at slant in shadow. MDS analysis of the obtained dissimilarities confirmed the two-dimensionality of achromatic colours for both types of shadow. Furthermore, the dimension induced by the cast shadow (shadowedness) was found to be different from that induced by the attached shadow (shading). In the three-dimensional MDS output configuration these were represented by clearly different dimensions. This quantitatively supports a fact, well-known to artists, that attached and cast shadows are experienced as different phenomenological entities. It is argued that a shading gradient is perceptually experienced as shape (ie spatial relief).