On automatic threshold selection for polygonal approximations of digital curves

Arie Pikaz*, Amir Averbuch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Polygonal approximation is a very common representation of digital curves. A polygonal approximation depends on a parameter ε, which is the error value. In this paper we present a method for an automatic selection of the error value, ε. Let Γ(ε) be a polygonal approximation of the original curve Γ, with an error value ε. We define a set of function, {NS(ε)}s∈S, such that for a given value of s, Ns(ε) is the number of edges that contain at least s vertices in Γ(epsi;). The time complexity for computing the set of functions {Ns(ε)}s∈S is almost linear in n, the number of vertices in Γ. In this paper we analyse the Ns(ε) graph, and show that for adequate values of s a wide plateau is expected to appear at the top of the graph. This plateau corresponds to a stable state in the multi-scale representation of {Γ(ε)}ε∈E. We show that the functions {Ns(ε)}s∈S are a statistical representation of some kind of scale-space image.

Original languageEnglish
Pages (from-to)1835-1845
Number of pages11
JournalPattern Recognition
Issue number11
StatePublished - Nov 1996


  • Automatic threshold selection
  • Digital curves
  • Image analysis
  • Percolation theory
  • Polygonal approximations
  • Scale-space analysis
  • Set Disjoint datastructure


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