On analyzing diffusion tensor images by identifying manifold structure using isomaps.
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.
Section of Biomedical Image Analysis, Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104, USA. ragini.verma@uphs.upenn.edu
Ragini
R
Verma
Parmeshwar
P
Khurd
Christos
C
Davatzikos
D000465:Algorithms; D001185:Artificial Intelligence; D001921:Brain / Q000473:pathology*; D001927:Brain Diseases / Q000175:diagnosis*; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*