On analyzing diffusion tensor images by identifying manifold structure using isomaps

Ragini Verma, Parmeshwar Khurd, Christos Davatzikos

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


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
Issue number6
StatePublished - Jun 2007
Externally publishedYes


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

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering


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