## Abstract

We present a mathematical airway tree-shape framework

where airway trees are compared using geodesic distances. The framework

consists of a rigorously dened shape space for treelike shapes,

endowed with a metric such that the shape space is a geodesic metric

space. This means that the distance between two tree-shapes can be realized

as the length of the geodesic, or shortest deformation, connecting

the two shapes. By computing geodesics between airway trees, as well as

the corresponding airway deformation, we generate airway branch correspondences.

Correspondences between an unlabeled airway tree and a set

of labeled airway trees are combined with a voting scheme to perform

automatic branch labeling of segmented airways from the challenging

EXACT'09 test set. In spite of the varying quality of the data, we obtain

robust labeling results.

where airway trees are compared using geodesic distances. The framework

consists of a rigorously dened shape space for treelike shapes,

endowed with a metric such that the shape space is a geodesic metric

space. This means that the distance between two tree-shapes can be realized

as the length of the geodesic, or shortest deformation, connecting

the two shapes. By computing geodesics between airway trees, as well as

the corresponding airway deformation, we generate airway branch correspondences.

Correspondences between an unlabeled airway tree and a set

of labeled airway trees are combined with a voting scheme to perform

automatic branch labeling of segmented airways from the challenging

EXACT'09 test set. In spite of the varying quality of the data, we obtain

robust labeling results.

Original language | English |
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Title of host publication | MFCA 2011 : 3rd MICCAI Workshop on Mathematical Foundations of Computational Anatomy |

Editors | Xavier Pennec, Sarang Joshi, Mads Nielsen |

Number of pages | 12 |

Publication date | 2011 |

Pages | 123-134 |

Publication status | Published - 2011 |

Event | 3rd MICCAI Workshop on Mathematical Foundations of Computational Anatomy - Westin Harbour Castle, Toronto, Canada Duration: 22 Sep 2011 → 22 Sep 2011 Conference number: 3 |

### Conference

Conference | 3rd MICCAI Workshop on Mathematical Foundations of Computational Anatomy |
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Number | 3 |

Location | Westin Harbour Castle |

Country/Territory | Canada |

City | Toronto |

Period | 22/09/2011 → 22/09/2011 |