### Abstract

This paper addresses the problem of statistical analysis of diffusion tensor magnetic resonance images (DT-MRI)., DT-MRI cannot be analyzed by commonly used linear methods, due to the inherent non-linearity of tensors, which are restricted to lie on a non-linear sub-manifold of the space in which they are defined, namely IR ^{6}. We perform statistical analysis on tensors by identifying the underlying manifold of the set of tensors under consideration using the Isomap manifold learning technique. Multivariate statistics are then performed on this estimated manifold using geodesic distances between tensors, thereby warranting that the analysis is restricted to the proper subspace of R ^{6}. Experimental results on data with known ground truth show that the proposed statistical analysis method properly captures statistical relationships among tensor image data, and it identifies group differences. Comparisons, with standard statistical analyses that rely on Euclidean, rather than geodesic distances, are also discussed.

Original language | English (US) |
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Title of host publication | 2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings |

Pages | 790-793 |

Number of pages | 4 |

Volume | 2006 |

State | Published - 2006 |

Externally published | Yes |

Event | 2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Arlington, VA, United States Duration: Apr 6 2006 → Apr 9 2006 |

### Other

Other | 2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro |
---|---|

Country | United States |

City | Arlington, VA |

Period | 4/6/06 → 4/9/06 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings*(Vol. 2006, pp. 790-793). [162535]

**Manifold based analysis of diffusion tensor images using isomaps.** / Verma, Ragini; Davatzikos, Christos.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings.*vol. 2006, 162535, pp. 790-793, 2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Arlington, VA, United States, 4/6/06.

}

TY - GEN

T1 - Manifold based analysis of diffusion tensor images using isomaps

AU - Verma, Ragini

AU - Davatzikos, Christos

PY - 2006

Y1 - 2006

N2 - This paper addresses the problem of statistical analysis of diffusion tensor magnetic resonance images (DT-MRI)., DT-MRI cannot be analyzed by commonly used linear methods, due to the inherent non-linearity of tensors, which are restricted to lie on a non-linear sub-manifold of the space in which they are defined, namely IR 6. We perform statistical analysis on tensors by identifying the underlying manifold of the set of tensors under consideration using the Isomap manifold learning technique. Multivariate statistics are then performed on this estimated manifold using geodesic distances between tensors, thereby warranting that the analysis is restricted to the proper subspace of R 6. Experimental results on data with known ground truth show that the proposed statistical analysis method properly captures statistical relationships among tensor image data, and it identifies group differences. Comparisons, with standard statistical analyses that rely on Euclidean, rather than geodesic distances, are also discussed.

AB - This paper addresses the problem of statistical analysis of diffusion tensor magnetic resonance images (DT-MRI)., DT-MRI cannot be analyzed by commonly used linear methods, due to the inherent non-linearity of tensors, which are restricted to lie on a non-linear sub-manifold of the space in which they are defined, namely IR 6. We perform statistical analysis on tensors by identifying the underlying manifold of the set of tensors under consideration using the Isomap manifold learning technique. Multivariate statistics are then performed on this estimated manifold using geodesic distances between tensors, thereby warranting that the analysis is restricted to the proper subspace of R 6. Experimental results on data with known ground truth show that the proposed statistical analysis method properly captures statistical relationships among tensor image data, and it identifies group differences. Comparisons, with standard statistical analyses that rely on Euclidean, rather than geodesic distances, are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=33750954186&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750954186&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33750954186

SN - 0780395778

SN - 9780780395770

VL - 2006

SP - 790

EP - 793

BT - 2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings

ER -