### Abstract

We present a unified scheme for detecting digital components of various planar curves in a binary edge image. A digital component of a curve is the set of input edge points from each of which the horizontal or vertical distance to the curve is at most 0.5. Our algorithm outputs all curve components containing at least k points (k is a given threshold) in O(n^{d}) time (if d≥2) and linear space, where n is the number of points, and d is a measure that reflects the complexity of a family of curves; for example, d=2,3 and 5 for lines, circles and ellipses, respectively. For most of the popular families of curves, our only primitive operations are algebraic operations of bounded degree and comparisons. We also propose an approximate algorithm for computing an approximation solution with error ratio ε=1-α (called an α-sensitive solution), whose time complexity is O((t/ε)^{d-1}n), which is very efficient if the threshold-ratio t=n/k is small.

Original language | English |
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Pages (from-to) | 73-93 |

Number of pages | 21 |

Journal | Computational Geometry: Theory and Applications |

Volume | 18 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2001 Mar 1 |

### Keywords

- Algorithm
- Arrangement
- Digital curve
- Image recognition

### ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics

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## Cite this

*Computational Geometry: Theory and Applications*,

*18*(2), 73-93. https://doi.org/10.1016/S0925-7721(01)00002-5