Undetected gray strips displace perceived edges nonlinearly

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Abstract
The luminance profile of a contour affects its perceived location. We measured the relationship between luminance profile and perceived location of an edge by interposing a thin uniform strip of variable luminance between the black and the white sides of a sharp edge and having observers make Vernier adjustments of an uncomplicated sharp edge so that the two edges appeared to be aligned. The perceived location of the contour depended on the luminance of the strip even when the strip itself was too thin to be seen. The largest visual angle at which a strip was still invisible was approximately 1.4′. Although the relation between perceived location and luminance was nonlinear, the relation approached linearity as the strip thickness decreased. A model with no free parameters, involving three stages of spatial filtering and an interposed nonlinearity, described the data from strips that could not be seen. With a strip thickness of 1.4′, the model halved both errors of prediction and residual variance over those based on the assumption of linearity.