Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics.
Practical statistical analysis of diffusion tensor images is considered, and we focus primarily on methods that use metrics based on Euclidean distances between powers of diffusion tensors. First we describe a family of anisotropy measures based on a scale invariant power-Euclidean metric, which are...
| Main Authors: | , , , , |
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| Format: | Article |
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Taylor & Francis (Routledge)
2016
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| Online Access: | https://eprints.nottingham.ac.uk/41115/ |
| _version_ | 1848796199685980160 |
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| author | Zhou, Diwei Dryden, Ian L. Koloydenko, Alexey A. Audenaert, Koenraad M.R. Bai, Li |
| author_facet | Zhou, Diwei Dryden, Ian L. Koloydenko, Alexey A. Audenaert, Koenraad M.R. Bai, Li |
| author_sort | Zhou, Diwei |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Practical statistical analysis of diffusion tensor images is considered, and we focus primarily on methods that use metrics based on Euclidean distances between powers of diffusion tensors. First we describe a family of anisotropy measures based on a scale invariant power-Euclidean metric, which are useful for visualisation. Some properties of the measures are derived and practical considerations are discussed, with some examples. Second we discuss weighted Procrustes methods for diffusion tensor interpolation and smoothing, and we compare methods based on different metrics on a set of examples as well as analytically. We establish a key relationship between the principal-square-root-Euclidean metric and the size-and-shape Procrustes metric on the space of symmetric positive semi-definite tensors. We explain, both analytically and by experiments, why the size-and-shape Procrustes metric may be preferred in practical tasks of interpolation, extrapolation, and smoothing, especially when observed tensors are degenerate or when a moderate degree of tensor swelling is desirable. Third we introduce regularisation methodology, which is demonstrated to be useful for highlighting features of prior interest and potentially for segmentation. Finally, we compare several metrics in a dataset of human brain diffusion-weighted MRI, and point out similarities between several of the non-Euclidean metrics but important differences with the commonly used Euclidean metric. |
| first_indexed | 2025-11-14T19:44:11Z |
| format | Article |
| id | nottingham-41115 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:44:11Z |
| publishDate | 2016 |
| publisher | Taylor & Francis (Routledge) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-411152020-05-04T20:05:48Z https://eprints.nottingham.ac.uk/41115/ Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics. Zhou, Diwei Dryden, Ian L. Koloydenko, Alexey A. Audenaert, Koenraad M.R. Bai, Li Practical statistical analysis of diffusion tensor images is considered, and we focus primarily on methods that use metrics based on Euclidean distances between powers of diffusion tensors. First we describe a family of anisotropy measures based on a scale invariant power-Euclidean metric, which are useful for visualisation. Some properties of the measures are derived and practical considerations are discussed, with some examples. Second we discuss weighted Procrustes methods for diffusion tensor interpolation and smoothing, and we compare methods based on different metrics on a set of examples as well as analytically. We establish a key relationship between the principal-square-root-Euclidean metric and the size-and-shape Procrustes metric on the space of symmetric positive semi-definite tensors. We explain, both analytically and by experiments, why the size-and-shape Procrustes metric may be preferred in practical tasks of interpolation, extrapolation, and smoothing, especially when observed tensors are degenerate or when a moderate degree of tensor swelling is desirable. Third we introduce regularisation methodology, which is demonstrated to be useful for highlighting features of prior interest and potentially for segmentation. Finally, we compare several metrics in a dataset of human brain diffusion-weighted MRI, and point out similarities between several of the non-Euclidean metrics but important differences with the commonly used Euclidean metric. Taylor & Francis (Routledge) 2016 Article PeerReviewed Zhou, Diwei, Dryden, Ian L., Koloydenko, Alexey A., Audenaert, Koenraad M.R. and Bai, Li (2016) Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics. Journal of Applied Statistics, 43 (5). pp. 943-978. ISSN 1360-0532 Anisotropy; Metric; Positive definite; Power; Procrustes; Riemannian; Smoothing; Weighted Frechet mean http://www.tandfonline.com/doi/full/10.1080/02664763.2015.1080671 doi:10.1080/02664763.2015.1080671 doi:10.1080/02664763.2015.1080671 |
| spellingShingle | Anisotropy; Metric; Positive definite; Power; Procrustes; Riemannian; Smoothing; Weighted Frechet mean Zhou, Diwei Dryden, Ian L. Koloydenko, Alexey A. Audenaert, Koenraad M.R. Bai, Li Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics. |
| title | Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics. |
| title_full | Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics. |
| title_fullStr | Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics. |
| title_full_unstemmed | Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics. |
| title_short | Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics. |
| title_sort | regularisation, interpolation and visualisation of diffusion tensor images using non-euclidean statistics. |
| topic | Anisotropy; Metric; Positive definite; Power; Procrustes; Riemannian; Smoothing; Weighted Frechet mean |
| url | https://eprints.nottingham.ac.uk/41115/ https://eprints.nottingham.ac.uk/41115/ https://eprints.nottingham.ac.uk/41115/ |