Statistical Properties of Jacobian Maps and the Realization of Unbiased Large-Deformation Nonlinear Image Registration.
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| Title: | Statistical Properties of Jacobian Maps and the Realization of Unbiased Large-Deformation Nonlinear Image Registration. |
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| Authors: | Leow, Alex D.1 feuillet@ucla.edu, Yanovsky, Igor2 yanovsky@ucla.edu, Ming-Chang Chiang3, Lee, Agatha D.3, Kiunder, Andrea D.3, Lu, Allen3, Becker, James T.4, Davis, Simon W.4, Toga, Arthur W.3, Thompson, Paul M.3 |
| Source: | IEEE Transactions on Medical Imaging. Jun2007, Vol. 26 Issue 6, p822-832. 11p. 1 Chart, 11 Graphs. |
| Subjects: | Magnetic resonance imaging, Diagnostic imaging, Mathematical continuum, Jacobian matrices, Functions of several complex variables, Mathematical analysis |
| Abstract: | 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 them to 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. [ABSTRACT FROM AUTHOR] |
| Copyright of IEEE Transactions on Medical Imaging is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 25351634 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Statistical Properties of Jacobian Maps and the Realization of Unbiased Large-Deformation Nonlinear Image Registration. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Leow%2C+Alex+D%2E%22">Leow, Alex D.</searchLink><relatesTo>1</relatesTo><i> feuillet@ucla.edu</i><br /><searchLink fieldCode="AR" term="%22Yanovsky%2C+Igor%22">Yanovsky, Igor</searchLink><relatesTo>2</relatesTo><i> yanovsky@ucla.edu</i><br /><searchLink fieldCode="AR" term="%22Ming-Chang+Chiang%22">Ming-Chang Chiang</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22Lee%2C+Agatha+D%2E%22">Lee, Agatha D.</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22Kiunder%2C+Andrea+D%2E%22">Kiunder, Andrea D.</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22Lu%2C+Allen%22">Lu, Allen</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22Becker%2C+James+T%2E%22">Becker, James T.</searchLink><relatesTo>4</relatesTo><br /><searchLink fieldCode="AR" term="%22Davis%2C+Simon+W%2E%22">Davis, Simon W.</searchLink><relatesTo>4</relatesTo><br /><searchLink fieldCode="AR" term="%22Toga%2C+Arthur+W%2E%22">Toga, Arthur W.</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22Thompson%2C+Paul+M%2E%22">Thompson, Paul M.</searchLink><relatesTo>3</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IEEE+Transactions+on+Medical+Imaging%22">IEEE Transactions on Medical Imaging</searchLink>. Jun2007, Vol. 26 Issue 6, p822-832. 11p. 1 Chart, 11 Graphs. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Magnetic+resonance+imaging%22">Magnetic resonance imaging</searchLink><br /><searchLink fieldCode="DE" term="%22Diagnostic+imaging%22">Diagnostic imaging</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+continuum%22">Mathematical continuum</searchLink><br /><searchLink fieldCode="DE" term="%22Jacobian+matrices%22">Jacobian matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Functions+of+several+complex+variables%22">Functions of several complex variables</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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 them to 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IEEE Transactions on Medical Imaging is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1109/TMI.2007.892646 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 11 StartPage: 822 Subjects: – SubjectFull: Magnetic resonance imaging Type: general – SubjectFull: Diagnostic imaging Type: general – SubjectFull: Mathematical continuum Type: general – SubjectFull: Jacobian matrices Type: general – SubjectFull: Functions of several complex variables Type: general – SubjectFull: Mathematical analysis Type: general Titles: – TitleFull: Statistical Properties of Jacobian Maps and the Realization of Unbiased Large-Deformation Nonlinear Image Registration. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Leow, Alex D. – PersonEntity: Name: NameFull: Yanovsky, Igor – PersonEntity: Name: NameFull: Ming-Chang Chiang – PersonEntity: Name: NameFull: Lee, Agatha D. – PersonEntity: Name: NameFull: Kiunder, Andrea D. – PersonEntity: Name: NameFull: Lu, Allen – PersonEntity: Name: NameFull: Becker, James T. – PersonEntity: Name: NameFull: Davis, Simon W. – PersonEntity: Name: NameFull: Toga, Arthur W. – PersonEntity: Name: NameFull: Thompson, Paul M. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2007 Type: published Y: 2007 Identifiers: – Type: issn-print Value: 02780062 Numbering: – Type: volume Value: 26 – Type: issue Value: 6 Titles: – TitleFull: IEEE Transactions on Medical Imaging Type: main |
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