The Specification of Edge Penalties for Regular and Irregular Pixel Images

Bernard W. Silverman, Christopher Jennison, Julian Stander, Timothy C. Brown

Research output: Contribution to journalArticlepeer-review


One of the ingredients of recent methodology in statistical image reconstruction is the idea of introducing a system of “edges” between pixels in the image. If an edge is present between two contiguous pixels, then they are not considered as neighbors in the reconstruction procedure. In penalized maximum likelihood estimation of the image, the number and configuration of the edges is controlled by a penalty term. In this correspondence, we show how some geometrical insights can be used to provide penalties for the various edge configurations in a way that is roughly independent of the pixel discretization. The penalties obtained are consistent over pixels of different sizes, shapes, and orientations, even if these occur in the same pattern. The cases of square, rectangular, hexagonal, and irregular pixels are considered. In an experiment, our penalties perform substantially better than those previously proposed.

Original languageEnglish
Pages (from-to)1017-1024
Number of pages8
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number10
Publication statusPublished - 1 Oct 1990


  • Discretization
  • edge process
  • Euler-Poincare characteristic
  • hexagonal pixels
  • irregular pixels
  • line length
  • Markov random field
  • penalized likelihood
  • statistical image reconstruction
  • stochastic geometry
  • tessellations

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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