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Numerical inversion of SRNFs for efficient elastic shape analysis of star-shaped objects.

Xie, Qian and Jermyn, Ian and Kurtek, Sebastian and Srivastava, Anuj (2014) 'Numerical inversion of SRNFs for efficient elastic shape analysis of star-shaped objects.', in Computer vision - ECCV 2014 : 13th European Conference Zurich, Switzerland, September 6-12, 2014 ; proceedings, part V. Cham: Springer, pp. 485-499. Lecture notes in computer science. (8693).

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 L2 norm to compare their shapes. Past work is based on using the pullback of the L2 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.

Item Type:Book chapter
Keywords:Statistical shape analysis, Elastic shape analysis, Parameterized surface, Geodesic computation, Deformation analysis.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/978-3-319-10602-1_32
Publisher statement:The final publication is available at Springer via https://doi.org/10.1007/978-3-319-10602-1_32.
Date accepted:No date available
Date deposited:30 July 2015
Date of first online publication:September 2014
Date first made open access:No date available

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