The tilt aftereffect in plaids and gratings: channel codes, local signs and "patchwise" transforms

The perceived structure of a suprathreshold plaid made from two sinusoidal gratings tilted +/- 45 deg from vertical usually resembles a blurred checkerboard. Physically increasing the tilt of the components away from vertical elongates the pattern horizontally, yielding rectangular checks. We asked whether illusory tilt of the components induced by adaptation to a vertical grating would also give apparent elongation of the checks. Using a staircase method, we found that after adaptation the component orientations had to be set 3-4 deg closer to vertical to maintain a square, checkerboard-like appearance, implying that the +/- 45 deg plaid did appear elongated. This result suggests that the tilt aftereffect adaptation not only distorts the orientation of 1-D patterns but can also change the relative location of features, even when their orientation is not altered. This is not easy to explain within filter models that (often implicitly) assume each receptive field carries a fixed "local sign" indicating its position within the retinal array. We consider a representation in which localized patches of the image are encoded by the coefficients of a 2-D Fourier-like transform. With a simple subtractive model of adaptation, we show that the spatial information carried by each patch would be distorted in just the way observed for plaids and gratings. The fact that perceived structure is both distorted and coherent, not fragmented, after adaptation suggests an additional, more global process whereby local patches are combined to form a coherent, composite "neural image". We offer a simple principle that could establish this coherence. If the positions of local patches are adjusted so as to maximize the contrast energy of the composite image, then the spatial distortions of the patches (induced by selective adaptation) are carried through to the global structure of the composite. Thus, the conflict between channel codes and local signs is resolved, but perceptual distortion is the result.