On Minimal Perimeter Polyminoes

  • Yaniv Altshuler
  • Vladimir Yanovsky
  • Daniel Vainsencher
  • Israel A. Wagner
  • Alfred M. Bruckstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)

Abstract

This paper explores proofs of the isoperimetric inequality for 4-connected shapes on the integer grid ℤ2, and its geometric meaning. Pictorially, we discuss ways to place a maximal number unit square tiles on a chess board so that the shape they form has a minimal number of unit square neighbors. Previous works have shown that “digital spheres” have a minimum of neighbors for their area. We here characterize all shapes that are optimal and show that they are all close to being digital spheres. In addition, we show a similar result when the 8-connectivity metric is assumed (i.e. connectivity through vertices or edges, instead of edge connectivity as in 4-connectivity).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yaniv Altshuler
    • 1
  • Vladimir Yanovsky
    • 1
  • Daniel Vainsencher
    • 1
  • Israel A. Wagner
    • 1
    • 2
  • Alfred M. Bruckstein
    • 1
  1. 1.Computer Science DepartmentTechnionHaifaIsrael
  2. 2.MATAMIBM Haifa LabsHaifaIsrael

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