### 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 Ricci scalar is not only suitable for tensor valued image analysis, but it can be computed for any mapping f : Rn ¿ Rm (m = n), for example when an original image changes in time.
Keywords: Riemann Geometry, Diffusion Tensor Imaging, Ricci Scalar, Finsler geometry, High Angular Resolution Diffusion Imaging.

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Technische Universiteit Eindhoven |

Number of pages | 18 |

Publication status | Published - 2010 |

### Publication series

Name | CASA-report |
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Volume | 1057 |

ISSN (Print) | 0926-4507 |

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## Cite this

Astola, L. J., Fuster, A., & Florack, L. M. J. (2010).

*A Riemannian scalar measure for diffusion tensor images*. (CASA-report; Vol. 1057). Technische Universiteit Eindhoven.