Parameterization-Invariant Shape Comparisons of Anatomical Surfaces

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....

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Bibliographic Details
Published in:IEEE transactions on medical imaging 2011-03, Vol.30 (3), p.849-858
Main Authors: Kurtek, S, Klassen, E, Zhaohua Ding, Jacobson, S W, Jacobson, J L, Avison, M J, Srivastava, A
Format: Article
Language:English
Subjects:
Algorithms
Attention Deficit Hyperactivity Disorder
Attention deficit hyperactivity disorder (ADHD) classification
Brain
Brain - anatomy & histology
Diseases
Humans
Hyperactivity
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Imaging, Three-Dimensional - methods
Jacobian matrices
Magnetic Resonance Imaging - methods
Measurement
Orbits
parameterization invariance
Pattern Recognition, Automated - methods
Reproducibility of Results
Riemannian distances
Sensitivity and Specificity
Shape
shape analysis
Three dimensional displays
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Summary: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 q-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).
ISSN:0278-0062
1558-254X
DOI:10.1109/TMI.2010.2099130