Completing visual contours: The relationship between relatability and
Manish Singh and Donald D. Hoffman
Perception & Psychophysics, 61: 943-951 (1999).
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 different 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 curve 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 a way to extend the definition of relatability: