Testing the role of luminance edges in White's illusion with contour adaptation

White's illusion is the perceptual effect that two equiluminant gray patches superimposed on a black-and-white square-wave grating appear different in lightness: A test patch placed on a dark stripe of the grating looks lighter than one placed on a light stripe. Although the effect does not depend on the aspect ratio of the test patches, and thus on the amount of border that is shared with either the dark or the light stripe, the context of each patch must, in a yet to be specified way, influence their lightness. We employed a contour adaptation paradigm (Anstis, 2013) to test the contribution of each of the test patches' edges to the perceived lightness of the test patches. We found that adapting to the edges that are oriented parallel to the grating slightly increased the lightness illusion, whereas adapting to the orthogonal edges abolished, or for some observers even reversed, the lightness illusion. We implemented a temporal adaptation mechanism in three spatial filtering models of lightness perception, and show that the models cannot account for the observed adaptation effects. We conclude that White's illusion is largely determined by edge contrast across the edge orthogonal to the grating, whereas the parallel edge has little or no influence. We suggest mechanisms that could explain this asymmetry.