Human Systems Integration Division @ NASA Ames

X-junctions are image features that occur when a linear reflectance edge is crossed by a linear illumination edge. In a monochromatic world, the luminances in the four quadrants about the X-junction satisfy a precise numerical relation; namely, that the products of the luminances of opposite quadrants will be equal. In the real world, where the reflectances and illuminants differ in color, the same relationship holds on a wavelength-by-wavelength basis, but in general no precise relationship holds between the resulting color sensations. A relationship will be obeyed when the spectra can be described by low-dimensional linear models, as is often assumed in current theories of color constancy. In this situation, a vector analog of the cross-product statistic can distinguish valid transparent junctions from randomly colored junctions. This study sought to assess the usefulness of this calculation and compare its results to human judgments. Computer simulation was used to generate all possible X-junctions formed from a pair of reflectances drawn from 16 possible Munsell chip reflectances and a pair of black illuminants drawn from a set of 16 spanning the range of color temperatures from 4000-9000. A control set was formed by randomly selecting groups of four colors from the same set. The STEPIT procedure was used to adjust the parameters in the calculation to provide maximum discriminability between the two sets of junctions, resulting in a final d' of about 6. These calculations may also be used to identify which of the two limbs corresponds to the shadow boundary, and which to the reflectance boundary. Since humans do not seem to have this ability, it is argued that the human perceptual system does not use different representations for perceived illuminants and perceived surfaces.