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Abstract:
Luminance of three-dimensional achromatic objects under given illumination depends
on remittance of the material, shading and scattering light (mutual illumination of opposed
surfaces). We studied perception of lightness of six flat surfaces, three exposed to
direct illumination, three in the shade in opposite position, thus allowing mutual illumination
of neighboring pairs. Six achromatic cardboards forming a logarithmic scale of
remittance (step factor = 1.2) were used. Direct illumination increased the luminance of
the cardboards by a factor of two with respect to those in the shade. The luminance
sequence of the cardboards varied with their positions in light and shade. Altogether
there are 720 permutations of the sequence of the six cardboards. For any of the 720
permutations selected for the experiments, the subjects tried to report the lightness sequence
correctly in spite of the different luminance sequences. The difference between
the empirical lightness sequence reported by the subjects and the physically measured
sequence according to remittance was taken as the measure of lightness constancy. We
used Kendall´s rank correlation coefficient τ, which is τR=1 if the two above sequences
are identical. We also calculated τL from the empirical and the luminance sequences. If
the subjects were unable to perceive the lightness, they would report the luminance
sequence with τL=1 and τR<<1. Tests with 13 subjects on 30 different permutations
yielded τR>τL (with exception of control experiments in which the sequence according
to lightness and luminance happened to be the same physically, yielding τR=τL=1 correctly).
Thus, lightness constancy of three-dimensional objects under asymmetric illumination
as reported since more than 100 years (summary e.g. in A. L. Gilchrist:
Lightness, Brightness, and Transparency, 1994) has been confirmed quantitatively with
our novel method. In addition, a quantitative result concerning mutual illumination can
be derived from our data. Mutual illumination of cardboards can change the luminance
sequence as a consequence of neighborhood. From a light cardboard under direct illumination
more light is scattered to and reflected by its dark neighbor in the shaded position,
than from the same cardboards in exchanged position. We calculated the degree of
lightness constancy separately for those cases, in which the luminance sequence was not
changed by mutual illumination, and those were the difference with the lightness sequence
was increased and decreased. Separate calculations of these groups revealed that
the effect of local scattering light makes it more difficult to detect the correct lightness.
Mutual illuminations increasing the difficulty resulted in less constancy (τR smaller),
whereas mutual illumination resulting in greater similarity of the lightness and luminance
sequences (thus reducing the difficulty) yielded better constancy (τR greater).
The effect of light scattered locally at three-dimensional objects is not taken into account
in the process leading to lightness constancy of perception.
