Electronic Journal of Statistics

Removing phase variability to extract a mean shape for juggling trajectories

Nicolas J.-B. Brunel and Juhyun Park

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One of the purposes of the curve alignment has been to recover a structural mean of the curves by taking into account the common structural information or shape. Borrowing ideas from shape analysis, we introduce the Frenet-Serret framework to remove phase variation and to define a mean shape for three dimensional curves. Our method effectively regularizes the estimation of the geometry through curvature and torsion, and does not require curve alignment to define a mean. The method is demonstrated with the juggling data set.

Article information

Electron. J. Statist., Volume 8, Number 2 (2014), 1848-1855.

First available in Project Euclid: 29 October 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 65D10: Smoothing, curve fitting
Secondary: 49K15: Problems involving ordinary differential equations

Curve alignment multi-dimensional curves Frenet-Serret frame Fréchet mean


Brunel, Nicolas J.-B.; Park, Juhyun. Removing phase variability to extract a mean shape for juggling trajectories. Electron. J. Statist. 8 (2014), no. 2, 1848--1855. doi:10.1214/14-EJS937E. https://projecteuclid.org/euclid.ejs/1414588172

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See also

  • Related item: Ramsay, J. O., Gribble, P., and Kurtek, S. (2014). Description and processing of functional data arising from juggling trajectories. Electron. J. Statist. 8 1811–1816.