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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. Linköping University, The Institute of Technology.
University of Oslo, Norway .
Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
Uppsala University, Sweden .
2013 (English)In: International journal on artificial intelligence tools, ISSN 0218-2130, Vol. 22, no 6Article 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 Publishing , 2013. Vol. 22, no 6
Keyword [en]
Geodesic distance; the eikonal equation; manifold
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-103725DOI: 10.1142/S0218213013600208ISI: 000329050600009OAI: oai:DiVA.org:liu-103725DiVA: diva2:690690
Available from: 2014-01-24 Created: 2014-01-24 Last updated: 2017-12-06

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Nilsson, OlaMuseth, Ken

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