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2012 | OriginalPaper | Chapter

Metric Selection and Diffusion Tensor Swelling

Authors : Ofer Pasternak, Nir Sochen, Peter J. Basser

Published in: New Developments in the Visualization and Processing of Tensor Fields

Publisher: Springer Berlin Heidelberg

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Abstract

The measurement of the distance between diffusion tensors is the foundation on which any subsequent analysis or processing of these quantities, such as registration, regularization, interpolation, or statistical inference is based. Euclidean metrics were first used in the context of diffusion tensors; then geometric metrics, having the practical advantage of reducing the “swelling effect,” were proposed instead. In this chapter we explore the physical roots of the swelling effect and relate it to acquisition noise. We find that Johnson noise causes shrinking of tensors, and suggest that in order to account for this shrinking, a metric should support swelling of tensors while averaging or interpolating. This interpretation of the swelling effect leads us to favor the Euclidean metric for diffusion tensor analysis. This is a surprising result considering the recent increase of interest in the geometric metrics.

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previous chapter Divergence Measures and Means of Symmetric Positive-Definite Matrices

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Title: Metric Selection and Diffusion Tensor Swelling
Authors: Ofer Pasternak
Nir Sochen
Peter J. Basser
Publisher: Springer Berlin Heidelberg
Book: New Developments in the Visualization and Processing of Tensor Fields
Print ISBN: 978-3-642-27342-1

Electronic ISBN: 978-3-642-27343-8

Copyright Year: 2012
DOI: https://doi.org/10.1007/978-3-642-27343-8_17

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