Shortest Paths with Curvature and Torsion

Summary, in English

This paper describes a 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 globally optimal method uses line graphs and its runtime is polynomial in the size of the discretization, often in the order of seconds on a single computer. To our knowledge, we are the first to perform experiments in three dimensions with curvature and torsion regularization. The largest graphs we process have almost one hundred billion arcs. Experiments on medical images and in multi-view reconstruction show the significance and practical usefulness of regularization based on curvature while torsion is still only tractable for small-scale problems

• Author: Petter Strandmark; Johannes Ulén; Fredrik Kahl; Leo Grady
• Department/s: Mathematics (Faculty of Engineering); Mathematical Imaging Group; ELLIIT: the Linköping-Lund initiative on IT and mobile communication; eSSENCE: The e-Science Collaboration
• Publishing year: 2013
• Language: English
• Pages: 2024-2031
• Publication/Series: Computer Vision (ICCV), 2013 IEEE International Conference on
• Full text: - 2 MB; Download statistics
• Links: http://www.cv-foundation.org/openaccess/content_iccv_2013/papers/Strandmark_Shortest_Paths_with_2013_ICCV_paper.pdf; http://dx.doi.org/10.1109/ICCV.2013.253
• Document type: Conference paper
• Publisher: IEEE - Institute of Electrical and Electronics Engineers Inc.
• Topic: Computer Vision and Robotics (Autonomous Systems); Mathematics
• Conference name: IEEE International Conference on Computer Vision (ICCV), 2013
• Conference date: 2013-12-01 - 2013-12-08
• Conference place: Sydney, Australia
• Status: Published
• Research group: Mathematical Imaging Group
• ISBN/ISSN/Other: ISSN: 1550-5499