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Probabilistic Modeling of Anatomical Variability using a Low Dimensional Parameterization of Diffeomorphisms

Institution:
1Computer Science and Artificial Intelligence Laboratory, MIT, Cambridge, MA, USA. Electronic address: miao86@mit.edu.
2Surgical Planning Laboratory, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
Publisher:
Elsevier Science
Publication Date:
Oct-2017
Journal:
Med Image Anal
Volume Number:
41
Pages:
55-62
Citation:
Med Image Anal. 2017 Oct;41:55-62.
PubMed ID:
28732595
PMCID:
PMC5578831
Keywords:
Bandlimited space, Diffeomorphic shape variability, Principal geodesic analysis, Probabilistic modeling
Appears in Collections:
NAC, NCIGT, SPL
Sponsors:
U01 AG024904/AG/NIA NIH HHS/United States
P41 EB015898/EB/NIBIB NIH HHS/United States
R01 NS086905/NS/NINDS NIH HHS/United States
U01 HD087211/HD/NICHD NIH HHS/United States
P41 EB015902/EB/NIBIB NIH HHS/United States
Generated Citation:
Zhang M., Wells III W.M., Golland P. Probabilistic Modeling of Anatomical Variability using a Low Dimensional Parameterization of Diffeomorphisms. Med Image Anal. 2017 Oct;41:55-62. PMID: 28732595. PMCID: PMC5578831.
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We present an efficient probabilistic model of anatomical variability in a linear space of initial velocities of diffeomorphic transformations and demonstrate its benefits in clinical studies of brain anatomy. To overcome the computational challenges of the high dimensional deformation-based descriptors, we develop a latent variable model for principal geodesic analysis (PGA) based on a low dimensional shape descriptor that effectively captures the intrinsic variability in a population. We define a novel shape prior that explicitly represents principal modes as a multivariate complex Gaussian distribution on the initial velocities in a bandlimited space. We demonstrate the performance of our model on a set of 3D brain MRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Our model yields a more compact representation of group variation at substantially lower computational cost than the state-of-the-art method such as tangent space PCA (TPCA) and probabilistic principal geodesic analysis (PPGA) that operate in the high dimensional image space.