A Riemannian scalar measure for diffusion tensor images

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Abstract

We study a well-known scalar quantity in Riemannian geometry, the Ricci scalar, in the context of diffusion tensor imaging (DTI), which is an emerging non-invasive medical imaging modality. We derive a physical interpretation for the Ricci scalar and explore experimentally its significance in DTI. We also extend the definition of the Ricci scalar to the case of high angular resolution diffusion imaging (HARDI) using Finsler geometry. We mention that the Ricci scalar is not only suitable for tensor valued image analysis, but it can be computed for any mapping $ f : \mathbb{R}^n \rightarrow \mathbb{R}^m (m \leq n) $.
Original languageEnglish
Pages (from-to)1885-1891
Number of pages7
JournalPattern Recognition
Volume44
Issue number9
DOIs
Publication statusPublished - 2011

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