Completing visual contours: The relationship between relatability and minimizing inflections

Manish Singh, Donald D. Hoffman

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


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. On the basis of these conditions, we suggest a way to extend the definition of relatability (1) to include the role of genericity, and (2) to extend the current all-or-none character of relatability to a graded measure that can track the gradedness in psychophysical data.

Original languageEnglish (US)
Pages (from-to)943-951
Number of pages9
JournalPerception and Psychophysics
Issue number5
StatePublished - Jul 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Experimental and Cognitive Psychology
  • Sensory Systems
  • General Psychology


Dive into the research topics of 'Completing visual contours: The relationship between relatability and minimizing inflections'. Together they form a unique fingerprint.

Cite this