Journal
IEEE TRANSACTIONS ON MEDICAL IMAGING
Volume 30, Issue 3, Pages 849-858Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TMI.2010.2099130
Keywords
Attention deficit hyperactivity disorder (ADHD) classification; parameterization invariance; Riemannian distances; shape analysis
Categories
Funding
- Air Force Office of Scientific Research [FA9550-06-1-0324]
- Office of Naval Research [N00014-09-1-0664]
- National Science Foundation [DMS-0915003]
- National Institutes of Health/National Institute on Drug Abuse [R21-DA021034]
- National Institutes of Health/National Institute on Alcohol Abuse and Alcoholism [R01-AA06966, R01-AA09524]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0915003] Funding Source: National Science Foundation
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We consider 3-D brain structures as continuous parameterized surfaces and present a metric for their comparisons that is invariant to the way they are parameterized. Past comparisons of such surfaces involve either volume deformations or non-rigid matching under fixed parameterizations of surfaces. We propose a new mathematical representation of surfaces, called-maps, such that L-2 distances between such maps are invariant to re-parameterizations. This property allows for removing the parameterization variability by optimizing over the re-parameterization group, resulting in a proper parameterization-invariant distance between shapes of surfaces. We demonstrate this method in shape analysis of multiple brain structures, for 34 subjects in the Detroit Fetal Alcohol and Drug Exposure Cohort study, which results in a 91% classification rate for attention deficit hyperactivity disorder cases and controls. This method outperforms some existing techniques such as spherical harmonic point distribution model (SPHARM-PDM) or iterative closest point (ICP).
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