Visual completion is a ubiquitous phenomenon: Human vision often constructs contours and surfaces in regions that have no sharp gradients in any image property. When does human vision interpolate a contour between a given pair of luminance-defined edges? Two difference answers have been proposed: relatability and minimizing inflections. We state and prove a proposition that links these two proposals by showing that, under appropriate conditions, relatability is mathematically equivalent to the existence of a smooth curse with no inflection points that interpolates between the two edges. the proposition thus provides a set of necessary and sufficient conditions for two edges to be relatable. Based on these conditions, we suggest possible ways to extend the notion of relatability.
It has been shown that the relatability law is equivalent to the existence of a smooth curve with no inflection points connecting the two inducers REF .