Lightness models, gradient illusions, and curl

Gradient illusions require that models of suprathreshold appearance include a spatial integration that fills areas between edges. We describe a structural problem inherent in such models; for many scenes there are inconsistencies (nonzero curl) in thresholded derivatives that prevent simple spatial integration. Our experiments show that the human visual system does encounter curl problems and that it uses two different types of perceptual solution: field segmentation and lightness-gradient manipulation. The latter occurs under conditions where field segmentation is impossible. At least two such conditions can occur: failure to form a segmenting contour and topological problems in potential segmenting contours.

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