A Fraser illusion without local cues?

In the well-known Fraser illusion, a line composed of tilted elements itself appears tilted. The standard explanation of this illusion has been that the global orientation of the line is in some way influenced by the local orientation of the elements. The illusion was recreated using a texture composed of collinear Gabor stimuli, which were vertical. There was no local tilt. The illusory tilt was produced by gradually shifting the phase of the successive Gabors along each line. Although the 2D Fourier transform of this global pattern peaks at off-vertical orientations, the local energy of the patches is predominantly vertical. How does the visual system nevertheless pick up this global information? This can be explained by elongated linear filters, or a phase-tuned second-stage mechanism. We examined the first theory using a stereoscopic demonstration. When lines of opposite tilt are presented in the two eyes, they combine binocularly to produce stereoscopic slant. We tested whether the illusory tilts in the phase-shifted Gabors texture give stereoscopic slant, when opposite tilts are presented to the two eyes. They do not. Instead, stereoscopic depth is dominated by the local phase-disparity of the individual patches. This indicates that the illusion is not present at the stage of linear filters, which are input to stereo, but must involve second-stage interactions or collators.