Diffusion Tensor Analysis with Invariant Gradients and Rotation Tangents

G. Kindlmann, Daniel B. Ennis, Ross T. Whitaker, C.-F. Westin
IEEE Transactions on Medical Imaging
Volume 26, Number 11, Pages 1483-1499
November, 2007

Download full paper            DOI: 10.1109/TMI.2007.907277

Abstract

Guided by empirically established connections between clinically important tissue properties and diffusion tensor parameters, we introduce a framework for decomposing variations in diffusion tensors into changes in shape and orientation. Tensor shape and orientation both have three degrees of freedom, spanned by invariant gradients and rotation tangents, respectively. As an initial demonstration of the framework, we create a tunable measure of tensor difference that can selectively respond to shape and orientation. Second, to analyze the spatial gradient in a tensor volume (a third-order tensor), our framework generates edge strength measures that can discriminate between different neuroanatomical boundaries, as well as creating a novel detector of white matter tracts that are adjacent yet distinctly oriented. Finally, we apply the framework to decompose the fourth-order diffusion covariance tensor into individual and aggregate measures of shape and orientation covariance, including a direct approximation for the variance of tensor invariants such as fractional anisotropy.

covariance tensor visualization
Matrix of images of components Σij of the fourth-order diffusion covariance tensor Σ, measured over local pixel neighborhoods of a synthetic tensor dataset, expressed by contractions with the local tensor basis formed by invariant gradients (Ki) and rotation tangents (Φi). Components are identified by basis tensors across the top and left side. This provides a direct and intuitive visualization of a field of fourth-order tensors, because it highlights all locations of variance and covariance of both shape and orientation.

Reference

Kindlmann G, Ennis DB, Whitaker RT, Westin CF. Diffusion tensor analysis with invariant gradients and rotation tangents. IEEE Transactions on Medical Imaging 2007;26(11):1483-1499.

Bibtex entry

@ARTICLE{kindlmannTMI07,
  author         = {Gordon Kindlmann and Daniel B. Ennis and  Ross T. Whitaker 
                   and Carl-Fredrik Westin},                                   
  title          = {Diffusion Tensor Analysis with Invariant Gradients and     
                   Rotation Tangents},                                         
  journal        = {IEEE Transactions on Medical Imaging},                     
  year           = {2007},                                                     
  volume         = {26},                                                       
  pages          = {1483--1499},                                               
  number         = {11},                                                       
  month          = {November},                                                 
  doi            = "10.1109/TMI.2007.907277"}

Grants

NIH T32-EB002177 NIBIB, NIH K99-HL087614, NIH U41-RR019703, NIH R01-MH074794, NIH P41-RR13218 (NAC), NIH U54-EB005149 (NAMIC)

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