On analyzing diffusion tensor images by identifying manifold structure using isomaps

Ragini Verma, Parmeshwar Khurd, Christos Davatzikos

Research output: Contribution to journalArticle

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 nonlinearity of tensors, which are restricted to lie on a nonlinear submanifold of the space in which they are defined, namely R6. We estimate this submanifold using the Isomap manifold learning technique and perform tensor calculations using geodesic distances along this manifold. Multivariate statistics used in group analyses also use geodesic distances between tensors, thereby warranting that proper estimates of means and covariances are obtained via calculations restricted to the proper subspace of R6. 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 languageEnglish (US)
Pages (from-to)772-778
Number of pages7
JournalIEEE Transactions on Medical Imaging
Volume26
Issue number6
DOIs
StatePublished - Jun 2007
Externally publishedYes

Fingerprint

Tensors
Magnetic Resonance Spectroscopy
Learning
Magnetic resonance
Statistical methods
Statistics

Keywords

  • Diffusion tensor imaging
  • Geodesics
  • Isomaps
  • Manifold learning
  • Tensor statistics

ASJC Scopus subject areas

  • Biomedical Engineering
  • Radiology Nuclear Medicine and imaging
  • Radiological and Ultrasound Technology
  • Electrical and Electronic Engineering
  • Computer Science Applications
  • Computational Theory and Mathematics

Cite this

On analyzing diffusion tensor images by identifying manifold structure using isomaps. / Verma, Ragini; Khurd, Parmeshwar; Davatzikos, Christos.

In: IEEE Transactions on Medical Imaging, Vol. 26, No. 6, 06.2007, p. 772-778.

Research output: Contribution to journalArticle

Verma, Ragini ; Khurd, Parmeshwar ; Davatzikos, Christos. / On analyzing diffusion tensor images by identifying manifold structure using isomaps. In: IEEE Transactions on Medical Imaging. 2007 ; Vol. 26, No. 6. pp. 772-778.
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