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Alan L. Gilchrist, Ana Radonjic; Computing lightness at a slant: Taking light source direction into account versus a relaxed coplanar ratio model. Journal of Vision 2006;6(6):393. doi: https://doi.org/10.1167/6.6.393.
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According to several recent reports, lightness constancy under target rotation (relative to light source) is achieved by taking target slant and light source direction into account. In fact there is a simpler explanation: a relaxed version of the coplanar ratio principle (Gilchrist, 1980); The strength of a ratio between two surfaces weakens as their coplanarity weakens, either when the surfaces are displaced away from each other while remaining parallel, or when one surface rotates away from the plane of the other. We pitted these accounts against one another using an actual scene containing blocks resting on the floor, spheres floating in midair, attached shadows, cast shadows, glossy highlights and luminance gradients. The target square, always attached to the middle of the right-facing side of a large cube, appeared in different orientations. The general light source was located to the upper left, except that the cube was shadowed from this light source and illuminated by a hidden projector located off to the right. This gave the right face of the cube a higher luminance than the left face. Thus, as a target of fixed luminance is rotated successively away from the general light source, the high-level taking into account theory predicts lower lightness values, while the relaxed coplanar ratio principle predicts darker values. We found that the target appeared about two Munsell steps darker in the extreme rotated position, compared to a position normal to the general light source. Our results support a mid-level, relaxed coplanar account over a high-level account.
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