DTI Segmentation by Statistical Surface Evolution - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2006

DTI Segmentation by Statistical Surface Evolution


We address the problem of the segmentation of cerebral white matter structures from diffusion tensor images (DTI). DTI produces, from a set of diffusion-weighted MR images, tensor-valued images where each voxel is assigned with a $3 \times3$ symmetric, positive-definite matrix. This second order tensor is simply the covariance matrix of a local Gaussian process, with zero mean, modeling the average motion of water molecules. As we will show in this article, the definition of a dissimilarity measure and statistics between such quantities is a non trivial task which must be tackled carefully. We claim and demonstrate that, by using the theoretically well-founded differential geometrical properties of the manifold of multivariate normal distributions, it is possible to improve the quality of the segmentation results obtained with other dissimilarity measures such as the Euclidean distance or the Kullback-Leibler divergence. The main goal of this work is to prove that the choice of the probability metric, i.e. the dissimilarity measure, has a deep impact on the tensor statistics and, hence, on the achieved results. We introduce a variational formulation, in the level-set framework, to estimate the optimal segmentation of a diffusion tensor image according to the following hypothesis: Diffusion tensors exhibit a Gaussian distribution in the different partitions. We must also respect the geometric constraints imposed by the interfaces existing among the cerebral structures and detected by the gradient of the diffusion tensor image. We show how to express all the statistical quantities for the different probability metrics. We validate and compare the results obtained on various synthetic data-sets, a biological rat spinal cord phantom and human brain DT images.
Fichier principal
Vignette du fichier
RR-5843.pdf (33.45 Mo) Télécharger le fichier

Dates and versions

inria-00070183 , version 1 (19-05-2006)


  • HAL Id : inria-00070183 , version 1


Christophe Lenglet, Mikaël Rousson, Rachid Deriche. DTI Segmentation by Statistical Surface Evolution. [Research Report] RR-5843, INRIA. 2006, pp.45. ⟨inria-00070183⟩
188 View
17146 Download


Gmail Facebook Twitter LinkedIn More