## Abstract

An active contour model for parametric curve and surface approximation is presented. The active curve or surface adapts to the model shape to be approximated in an optimization algorithm. The quasi-Newton optimization procedure in each iteration step minimizes a quadratic function which is built up with the help of local quadratic approximants of the squared distance function of the model shape and an internal energy which has a smoothing and regularization effect. The approach completely avoids the parametrization problem. We also show how to use a similar strategy for the solution of variational problems for curves on surfaces. Examples are the geodesic path connecting two points on a surface and interpolating or approximating spline curves on surfaces. Finally we indicate how the latter topic leads to the variational design of smooth motions which interpolate or approximate given positions.

Original language | English (US) |
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Title of host publication | Proceedings - 10th Pacific Conference on Computer Graphics and Applications, PG 2002 |

Publisher | IEEE Computer Society |

Pages | 8-25 |

Number of pages | 18 |

Volume | 2002-January |

ISBN (Electronic) | 0769517846 |

DOIs | |

State | Published - 2002 |

Externally published | Yes |

Event | 10th Pacific Conference on Computer Graphics and Applications, PG 2002 - Beijing, China Duration: Oct 9 2002 → Oct 11 2002 |

### Other

Other | 10th Pacific Conference on Computer Graphics and Applications, PG 2002 |
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Country | China |

City | Beijing |

Period | 10/9/02 → 10/11/02 |

## Keywords

- Active contours
- Application software
- Character generation
- Computer vision
- Geometry
- Least squares approximation
- Parameter estimation
- Polynomials
- Smoothing methods
- Spline

## ASJC Scopus subject areas

- Software
- Computer Graphics and Computer-Aided Design
- Modeling and Simulation