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Shortest Paths with Higher-Order Regularization

På svenska

Author

  • Johannes Ulén
  • Petter Strandmark
  • Fredrik Kahl

Summary, in English

This paper describes a new method of finding thin, elongated structures in images and volumes. We use shortest paths to minimize very general functionals of higher-order curve properties, such as curvature and torsion. Our method uses line graphs to find the optimal path on a given discretization, often in the order of seconds on a single computer. The curves are then refined using local optimization making it possible to recover very smooth curves. We are able to place constraints on our curves such as maximum integrated curvature, or a maximum curvature at any point of the curve. To our knowledge, we are the first to perform experiments in three dimensions with curvature and torsion regularization. The largest graphs we process have over a hundred billion arcs. Experiments on medical images and in multi-view reconstruction show the significance and practical usefulness of higher order regularization.

Publishing year

2015

Language

English

Pages

2588-2600

Publication/Series

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volume

37

Issue

12

Document type

Journal article

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Mathematics

Status

Published

ISBN/ISSN/Other

  • ISSN: 1939-3539