Abstract

An important goal of early vision is to determine which edges in the image correspond to boundaries between different materials. When there is a “spectral cross-point” at a luminance edge, it can be reliably inferred that, regardless of illuminant color, the edge is due to a material change.¹ [If L and S denote two spectral samples of image intensity, there is a cross-point when (L_x − L_y)(S_x − S_y) < 0, where subscripts x and y denote the two regions on either side of the edge.] There will almost never be a cross-point at a nonmaterial edge, such as a shadow, highlight, or surface orientation discontinuity. Another simple condition at an edge is opposite slope sign or (L_x − S_x)(L_y − S_y) < 0. When the illuminant is white (or equivalently, after the image has been spectrally normalized), the opposite slope sign condition also reliably indicates material changes²; this condition also does not arise at nonmaterial edges. The cross-point and opposite slope sign conditions are independent. Detecting these two conditions requires two distinct kinds of double-opponent operators. Biological double-opponent cells may detect material changes. It can be tested whether there are two varieties of such cells, one computing the cross-point condition, the other, the opposite slope sign.

© 1985 Optical Society of America