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Alexander Logvinenko; Achromatic colours of 3D objects under different orientations. Journal of Vision 2004;4(8):343. https://doi.org/10.1167/4.8.343.
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A multidimensional scaling (MDS) technique was used to study the effect of the orientation of a surface on its achromatic colour. Observers were presented with two identical 3D hexagonal pyramids, the sides of which were covered with Munsell chips. Their reflectance varied from 7.7% to 78.7%. While the illumination of the pyramids was fairly homogeneous, the pyramids' sides reflected different amount of light even when covered by the same chip. For the white chip, luminance variations due to its slant were from 1090 to 321 cd/m2. Three observers were employed. The task was to evaluate the dissimilarity between sides of the pyramids using a 30-point scale. Each pair of sides was evaluated three times. A matrix of dissimilarities, averaged across all observers and presentations, was used as an input into a non-metric MDS algorithm. The output was a two-dimensional array (6×7 grid). Sides with the same reflectance lie along the same column of the grid. Sides of the same orientation have a tendency to lie along the same row. The columns are ordered with respect to reflectance. After a rotation of approximately 45 deg the axes may be interpreted as perceptual dimensions correlated with (i) lightness, and (ii) surface brightness (which is different from brightness of light reflected from the surface). These results corroborate our previous study (ECVP'03) showing that achromatic colours constitute an essentially two-dimensional manifold.
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