Rubin's face-vase display is a famous example of figure-ground perception and the multi-stability of human vision.
Here's an analysis of how the percept can switch from a pair of black faces on a white ground to a central face on a black ground.
The main ingredients of the analysis are that either the black or white regions can "own" the border but not both.
The region that owns the border adds a "contrast boost" to the luminance-defined point representing each region.
This boost breaks the symmetry between the black and white regions to allow grouping into occluding figure and occluded ground layers.
The grouping rule is simple: given a point formed by the intersection of the projections of the black and white regions, this will be closer to the un-boosted black or white point, meaning the region defined as ground. Hence the ground will be represented as an opaque occluded surface (the origin of the decomposition being the point itself.)
The bi-stability of the display is then explained by the "decision" of whether the black or white regions "own" the contrast defined at the boundary between regions.
(We can model the integration of the differential signal at the boundary over the enclosed regions as a PDE problem, namely, as a solution to the Laplace equation with Neumann boundary conditions.)
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