Edge Integration and Image Segmentation in Lightness and Color: Computational and Neural Theory

A dark disk surrounded by a wide white annulus appears darker than a physically identical disk surrounded by a narrow white annulus (left figure). In previous work, I modeled this phenomenon with a computational neural theory in which the disk color is computed from a sum of contributions from the inner and outer annulus borders (Rudd & Zemach, 2004, Vision Res.; Rudd, 2010, J. Vision). According to the model, the inner border signals to the brain that the region on the inside of this border is darker than the region on the outside, while the outer border signals that the region on the inside of that border is lighter than the region on the outside. The overall disk lightness is computed from a weighted sum of these two influences (indicated by the light and dark arrows in the figure). The disk on the left looks darker because the weights associated with edges are assumed to decrease with the distance of an edge from the disk. Thus, the outer annulus edge on the left side of the figure produces a weaker lightness-inducing influence on the disk color that the outer annulus edge on the right. In the full computational model, a contrast gain control mechanism also acts between nearby edges to further amplify the weight associated with the outer edge relative to the weight associated with the inner edge when the annulus is narrow. In the full model, the disk color is computed from the following equation: Φ D = ω 1 (D − A) 1− ν in z A − B # $ % & + + ω 2 (z)(A − B) 1+ ν out z D − A # $ % & + , (1) where Φ D is the disk lightness; D, A, and B are the luminances of the disk, annulus, and background field (in log units); z is the annulus width, ν in and ν out are the strengths of the inwardly-and outwardly-directed contrast gain controls acting between the inner and outer annulus edges; and ω 1 and ω 2 are the weights associated with the inner and outer edges, which are assumed to decrease monotonically as a function of distance from the disk. Here, I discuss how this can be extended to model lightness and color computation in more complex spatial stimuli. The figure at left shows a 2016 election map in which hatched yellow …