## Abstract

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, {N_{S}(ε)}_{s∈S}, such that for a given value of s, N_{s}(ε) is the number of edges that contain at least s vertices in Γ^{(epsi;)}. The time complexity for computing the set of functions {N_{s}(ε)}_{s∈S} is almost linear in n, the number of vertices in Γ. In this paper we analyse the N_{s}(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 {N_{s}(ε)}_{s∈S} are a statistical representation of some kind of scale-space image.

Original language | English |
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Pages (from-to) | 1835-1845 |

Number of pages | 11 |

Journal | Pattern Recognition |

Volume | 29 |

Issue number | 11 |

DOIs | |

State | Published - Nov 1996 |

## Keywords

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