Statistical properties of Jacobian maps and the realization of unbiased large-deformation nonlinear image registration.

Published

Journal Article

Maps of local tissue compression or expansion are often computed by comparing magnetic resonance imaging (MRI) scans using nonlinear image registration. The resulting changes are commonly analyzed using tensor-based morphometry to make inferences about anatomical differences, often based on the Jacobian map, which estimates local tissue gain or loss. Here, we provide rigorous mathematical analyses of the Jacobian maps, and use themto motivate a new numerical method to construct unbiased nonlinear image registration. First, we argue that logarithmic transformation is crucial for analyzing Jacobian values representing morphometric differences. We then examine the statistical distributions of log-Jacobian maps by defining the Kullback-Leibler (KL) distance on material density functions arising in continuum-mechanical models. With this framework, unbiased image registration can be constructed by quantifying the symmetric KL-distance between the identity map and the resulting deformation. Implementation details, addressing the proposed unbiased registration as well as the minimization of symmetric image matching functionals, are then discussed and shown to be applicable to other registration methods, such as inverse consistent registration. In the results section, we test the proposed framework, as well as present an illustrative application mapping detailed 3-D brain changes in sequential magnetic resonance imaging scans of a patient diagnosed with semantic dementia. Using permutation tests, we show that the symmetrization of image registration statistically reduces skewness in the log-Jacobian map.

Full Text

Duke Authors

Cited Authors

  • Leow, AD; Yanovsky, I; Chiang, M-C; Lee, AD; Klunder, AD; Lu, A; Becker, JT; Davis, SW; Toga, AW; Thompson, PM

Published Date

  • June 2007

Published In

Volume / Issue

  • 26 / 6

Start / End Page

  • 822 - 832

PubMed ID

  • 17679333

Pubmed Central ID

  • 17679333

Electronic International Standard Serial Number (EISSN)

  • 1558-254X

International Standard Serial Number (ISSN)

  • 0278-0062

Digital Object Identifier (DOI)

  • 10.1109/tmi.2007.892646

Language

  • eng