Visual contours often result from the integration or interpolation of fragmented edges. The strength of the completion increases when the edges share the same contrast polarity (CP). Here we demonstrate that the appearance in the perceptual field of this integrated unit, or contour of invariant CP, is concomitant with a vivid brightness alteration of the surfaces at its opposite sides. To observe this effect requires some stratagems because the formation in the visual field of a contour of invariant CP normally engenders the formation of a second contour and then the rise of two streams of induction signals that interfere in different ways. Particular configurations have been introduced that allow us to observe the induction effects of one contour taken in isolation. I documented these effects by phenomenological observations and psychophysical measurement of the brightness alteration in relation to luminance contrast. When the edges of the same CP complete to form a contour, the background of homogeneous luminance appears to dim at one side and to brighten at the opposite side (in accord with the CP). The strength of the phenomenon is proportional to the local luminance contrast. This effect weakens or nulls when the contour of the invariant CP separates surfaces filled with different gray shades. These conflicting results stimulate a deeper exploration of the induction phenomena and their role in the computation of brightness contrast. An alternative perspective is offered to account for some brightness illusions and their relation to the phenomenal transparency. The main assumption asserts that, when in the same region induction signals of opposite CP overlap, the filling-in is blocked unless the image is stratified into different layers, one for each signal of the same polarity. Phenomenological observations document this "solution" by the visual system.