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Shortest Paths with Higher-Order Regularization

Ulén, Johannes LU ; Strandmark, Petter LU and Kahl, Fredrik LU (2015) In IEEE Transactions on Pattern Analysis and Machine Intelligence 37(12). p.2588-2600
Abstract
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... (More)
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. (Less)
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
IEEE Transactions on Pattern Analysis and Machine Intelligence
volume
37
issue
12
pages
2588 - 2600
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000364831700018
  • scopus:84960943376
  • pmid:26539860
ISSN
1939-3539
DOI
10.1109/TPAMI.2015.2409869
language
English
LU publication?
yes
id
2e3f7fc4-c7da-4f30-a3b5-e014123415d7 (old id 5149781)
date added to LUP
2016-04-01 12:55:42
date last changed
2022-05-07 06:26:58
@article{2e3f7fc4-c7da-4f30-a3b5-e014123415d7,
  abstract     = {{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.}},
  author       = {{Ulén, Johannes and Strandmark, Petter and Kahl, Fredrik}},
  issn         = {{1939-3539}},
  language     = {{eng}},
  number       = {{12}},
  pages        = {{2588--2600}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Pattern Analysis and Machine Intelligence}},
  title        = {{Shortest Paths with Higher-Order Regularization}},
  url          = {{http://dx.doi.org/10.1109/TPAMI.2015.2409869}},
  doi          = {{10.1109/TPAMI.2015.2409869}},
  volume       = {{37}},
  year         = {{2015}},
}