Geodesic-Loxodromes for Diffusion Tensor Interpolation and Difference Measurement

G. Kindlmann, R. San Jose Estepar, M. Niethammer, Steven Haker, C.-F. Westin
Tenth International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI'07)
Pages 1-9
October, 2007

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Abstract

In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.

anisotropy creases with tractography
Interpolations between two cylindrical tensors. Trace is linearly interplated in (a), and determinant (K) is monotonically interpolated in (b) and (c). Geodesic-loxodromes (d) monotonically interpolate all Ki as well as (in this case) the determinant. Constancy of mode (K3) wholly avoids planar anisotropy at intermediate values.

Reference

Kindlmann G, Estepar RSJ, Niethammer M, Haker S, Westin CF. Geodesic-loxodromes for diffusion tensor interpolation and difference measurement. In Tenth International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI'07), Lecture Notes in Computer Science 4791. Brisbane, Australia, 2007;1-9.

Bibtex entry

@InProceedings{kindlmannMICCAI07,
  author         = "Gordon Kindlmann and Raul San Jose Estepar and  Marc       
                   Niethammer and Steven Haker and Carl-Fredrik Westin",       
  title          = "Geodesic-Loxodromes for Diffusion Tensor Interpolation and 
                   Difference Measurement",                                    
  booktitle      = "Tenth International Conference on Medical Image Computing  
                   and Computer-Assisted Intervention (MICCAI'07)",            
  month          = "October",                                                  
  year           = "2007",                                                     
  pages          = "1--9",                                                     
  series         = "Lecture Notes in Computer Science 4791",                   
  address        = "Brisbane, Australia"}

Grants

NIH U41-RR019703, NIH P41-RR13218 (NAC), NIH R01-MH050740, NIH R01-MH074794, NIH R01-AG20012, NIH P41-RR15241