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A New Algorithm for Computing Riemannian Geodesic Distance in Rectangular 2-D and 3-D Grids
Linköping University. (Department of Science and Technology)
University of Oslo. (Department of Informatics)
Linköping University. (Department of Science and Technology)
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.ORCID iD: 0000-0002-4405-6888
2013 (English)In: International journal on artificial intelligence tools, ISSN 0218-2130, Vol. 22, no 6, 1360020- p.Article in journal (Refereed) Published
Abstract [en]

We present a novel way to efficiently compute Riemannian geodesic distance over a two- or three-dimensional domain. It is based on a previously presented method for computation of geodesic distances on surface meshes. Our method is adapted for rectangular grids, equipped with a variable anisotropic metric tensor. Processing and visualization of such tensor fields is common in certain applications, for instance structure tensor fields in image analysis and diffusion tensor fields in medical imaging.

The included benchmark study shows that our method provides significantly better results in anisotropic regions in 2-D and 3-D and is faster than current stat-of-the- art solvers in 2-D grids. Additionally, our method is straightforward to code; the test implementation is less than 150 lines of C++ code. The paper is an extension of a previously presented conference paper and includes new sections on 3-D grids in particular. 

Place, publisher, year, edition, pages
World Scientific, 2013. Vol. 22, no 6, 1360020- p.
Keyword [en]
geodesic distance, distance transform
National Category
Computer Vision and Robotics (Autonomous Systems)
Research subject
Computerized Image Analysis
Identifiers
URN: urn:nbn:se:uu:diva-212534DOI: 10.1142/S0218213013600208ISI: 000329050600009OAI: oai:DiVA.org:uu-212534DiVA: diva2:678230
Available from: 2013-12-11 Created: 2013-12-11 Last updated: 2017-12-06Bibliographically approved

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Brun, Anders

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