Summary
Many different measures have been proposed to compute similarities and distances between diffusion tensors. These measures are commonly used for algorithms such as segmentation, registration, and quantitative analysis of Diffusion Tensor Imaging data sets. The results obtained from these algorithms are extremely dependent on the chosen measure. The measures presented in literature can be of complete different nature, and it is often difficult to predict the behavior of a given measure for a specific application. In this chapter, we classify and summarize the different measures that have been presented in literature. We also present a framework to analyze and compare the behavior of the measures according to several selected properties. We expect that this framework will help in the initial selection of a measure for a given application and to identify when the generation of a new measure is needed. This framework will also allow the comparison of new measures with existing ones.
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Acknowledgments
We thank Laura Astola for her insights in statistics and Riemannian geometry. This work was supported by the Dutch BSIK program entitled Molecular Imaging of Ischemic heart disease (project number BSIK 03033), Fundação para a Ciência e a Tecnologia (FCT, Portugal) under grant SFRH/BD/24467/ 2005, and the Netherlands Organization for Scientific Research (NWO-VENI grant 639.021.407).
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Peeters, T.H.J.M., Rodrigues, P.R., Vilanova, A., ter Haar Romeny, B.M. (2009). Analysis of Distance/Similarity Measures for Diffusion Tensor Imaging. In: Laidlaw, D., Weickert, J. (eds) Visualization and Processing of Tensor Fields. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88378-4_6
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DOI: https://doi.org/10.1007/978-3-540-88378-4_6
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