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Numerical Inversion of SRNFs for Efficient Elastic Shape Analysis of Star-Shaped Objects
Qian Xie1, Ian Jermyn2, Sebastian Kurtek3, and Anuj Srivastava1
1Florida State University, Tallahassee, Florida, United States
qxie@stat.fsu.edu
anuj@fsu.edu
2Durham University, Durham, County Durham DH1, United Kingdom
ian.jermyn@inria.fr
3Ohio State University, Columbus, Ohio, United States
kurtek.1@stat.osu.edu
Abstract. The elastic shape analysis of surfaces has proven useful in several application areas, including medical image analysis, vision, and graphics.
This approach is based on defining new mathematical representations of parameterized surfaces, including the square root normal field (SRNF), and then using the 
norm to compare their shapes. Past work is based on using the pullback of the 
metric to the space of surfaces, performing statistical analysis under this induced Riemannian metric. However, if one can estimate the inverse of the SRNF mapping, even approximately, a very efficient framework results: the surfaces, represented by their SRNFs, can be efficiently analyzed using standard Euclidean tools, and only the final results need be mapped back to the surface space. Here we describe a procedure for inverting SRNF maps of star-shaped surfaces, a special case for which analytic results can be obtained. We test our method via the classification of 34 cases of ADHD (Attention Deficit Hyperactivity Disorder), plus controls, in the Detroit Fetal Alcohol and Drug Exposure Cohort study. We obtain state-of-the-art results.
Keywords: Statistical shape analysis, elastic shape analysis, parameterized surface, geodesic computation, deformation analysis
LNCS 8693, p. 485 ff.
lncs@springer.com
© Springer International Publishing Switzerland 2014