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A tensor-like representation for averaging, filtering and interpolation of 3D object orientation data
Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA.
Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA.
Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA.
Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).ORCID iD: 0000-0002-9091-4724
2005 (English)In: Image Processing, 2005. ICIP 2005. IEEE International Conference on  (Volume:3 ), 2005, 1092-1095 p.Conference paper, Published paper (Refereed)
Abstract [en]

Averaging, filtering and interpolation of 3-D object orientation data is important in both computer vision and computer graphics, for instance to smooth estimates of object orientation and interpolate between keyframes in computer animation. In this paper we present a novel framework in which the non-linear nature of these problems is avoided by embedding the manifold of 3-D orientations into a 16-dimensional Euclidean space. Linear operations performed in the new representation can be shown to be rotation invariant, and defining a projection back to the orientation manifold results in optimal estimates with respect to the Euclidean metric. In other words, standard linear filters, interpolators and estimators may be applied to orientation data, without the need for an additional machinery to handle the non-linear nature of the problems. This novel representation also provides a way to express uncertainty in 3-D orientation, analogous to the well known tensor representation for lines and hyperplanes.

Place, publisher, year, edition, pages
2005. 1092-1095 p.
National Category
Medical and Health Sciences
Identifiers
URN: urn:nbn:se:liu:diva-28793DOI: 10.1109/ICIP.2005.1530586Local ID: 13978ISBN: 0-7803-9134-9 (print)OAI: oai:DiVA.org:liu-28793DiVA: diva2:249605
Conference
12th IEEE International Conference on Image Processing (ICIP 2005), Genova, Italy, 11 Sep - 14 Sep 2005
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2013-08-28Bibliographically approved

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Brun, AndersWestin, Carl-FredrikKnutsson, Hans

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