Indeed the Kanizsa figure itself poses a problem for the two-dimensional BCS / FCS model, because collinear completion is observed for the pac-man figures, which are perceived as complete circles occluded by a triangle, which would suggest a BCS arc through the corner of the triangle. This arc however would block the diffusion of brightness percept, resulting in a different brightness for the part of the triangle overlying the dark circle.
All of these problems can be eliminated by allowing the BCS and FCS to occur through multiple layers, so that the collinear completion of the grid pattern occurs in a layer above the completion of the triangle, which in turn occurs in a layer above the completion of the three circles.
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