On automatic threshold selection for polygonal approximations of digital curves

摘要

Polygonal approximation is a very common representation of digital curves. A polygonal approximation depends on a parameter e, which is the error value. In this paper we present a method for an automatic selection of the error value, e. Let Γ(ε) be a polygonal approximation of the original curve Γ, with an error value e. We define a set of function, {Ns(ε)}sϵS s, such that for a given value of s, Ns(ε) is the number of edges that contain at least s vertices in Γ(ε.. The time complexity for computing the set of functions Ns(ε)}sϵSsϵS 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 {Г(ϵ)}ϵ∈E We show that the functions Ns(ϵ)sϵS are a statistical representation of some kind of scale-space image.