%0 Report %1 Alexander2000 %A Alexander, Daniel %D 2000 %K Diffusion, Tensor DTI Imaging, Diffusion %T Note on Indices of Shape and Similarity for Diffusion Tensors %X A novel approach to the problem of finding appropriate similarity measures for DT-MRI data is presented. There are several existing measures in the literature, but there is little indication of which measures are appropriate for particular applications. A mathematical framework is introduced here, based on the physics of the diffusion tensor, which regards the tensor as a real valued function of the unit sphere in 3D. Given two functions of the same domain, their total difference (or similarity) can be expressed as the integral of their difference over their domain. This approach is applied to diffusion tensors and a family of cumulative tensor difference measures is derived. Effectiveness of the resulting measures is validated within an image registration application. Furthermore, this framework can be used to derive and alternative set of DT size and shape indices, which are analogous to existing measures and are presented here.

@techreport{Alexander2000, abstract = {A novel approach to the problem of finding appropriate similarity measures for DT-MRI data is presented. There are several existing measures in the literature, but there is little indication of which measures are appropriate for particular applications. A mathematical framework is introduced here, based on the physics of the diffusion tensor, which regards the tensor as a real valued function of the unit sphere in 3D. Given two functions of the same domain, their total difference (or similarity) can be expressed as the integral of their difference over their domain. This approach is applied to diffusion tensors and a family of cumulative tensor difference measures is derived. Effectiveness of the resulting measures is validated within an image registration application. Furthermore, this framework can be used to derive and alternative set of DT size and shape indices, which are analogous to existing measures and are presented here.}, added-at = {2007-01-10T11:43:56.000+0100}, author = {Alexander, Daniel}, biburl = {https://www.bibsonomy.org/bibtex/2643bee0a7cb87bdc498df7c6082f3168/bmeyer}, description = {Diffusion Tensor Imaging (DTI)}, institution = {Department of Computer Science, UCL (University College London)}, interhash = {1732e92b95a00e4ee7e8c32fd0710c67}, intrahash = {643bee0a7cb87bdc498df7c6082f3168}, keywords = {Diffusion, Tensor DTI Imaging, Diffusion}, month = {October}, pdf = {http://www.cs.ucl.ac.uk/brandnew/research2/Publications/rn14.pdf}, timestamp = {2007-01-10T11:43:56.000+0100}, title = {Note on Indices of Shape and Similarity for Diffusion Tensors}, type = {Research Notes}, year = 2000 }