Piecewise Approximation of Pictures Using Maximal Neighborhoods

Narendra Ahuja, Larry S. Davis, David L. Milgram, Azriel Rosenfeld

Research output: Contribution to journalArticlepeer-review


Suppose that we are given a picture having approximately piecewise constant gray level. Each point P has a largest neighborhood N(P) that is entirely contained in one of the constant regions, and the set of maximal N(P)‘s (ie., N(P)‘s not contained in other N(P)‘s) constitutes an economical description of the picture, generalizing the Blum “skeleton” or medial axis transformation. This description can be used to construct approximations to the picture (eg., by discarding small N(P)‘s). The picture can be smoothed, without excessive blurring, by averaging over each N(P). By taking differences between pairs of touching maximal N(P)‘s, the edges between the regions can be detected; since this edge detection scheme is not based on symmetrical detection operators, it is not handicapped when two adjacent regions differ greatly in size.

Original languageEnglish (US)
Pages (from-to)375-379
Number of pages5
JournalIEEE Transactions on Computers
Issue number4
StatePublished - Apr 1978
Externally publishedYes


  • Edge detection
  • image processing
  • medial axis transformation
  • picture processing
  • piecewise approximation
  • smoothing

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computational Theory and Mathematics


Dive into the research topics of 'Piecewise Approximation of Pictures Using Maximal Neighborhoods'. Together they form a unique fingerprint.

Cite this