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Removing phase variability to extract a mean shape for juggling trajectories

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Removing phase variability to extract a mean shape for juggling trajectories. / Brunel, Nicolas; Park, Juhyun.

In: Electronic Journal of Statistics, Vol. 8, No. 2, 29.10.2014, p. 1848-1855.

Research output: Contribution to journalJournal articlepeer-review

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Brunel, N & Park, J 2014, 'Removing phase variability to extract a mean shape for juggling trajectories', Electronic Journal of Statistics, vol. 8, no. 2, pp. 1848-1855. https://doi.org/10.1214/14-EJS937E

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Brunel, Nicolas ; Park, Juhyun. / Removing phase variability to extract a mean shape for juggling trajectories. In: Electronic Journal of Statistics. 2014 ; Vol. 8, No. 2. pp. 1848-1855.

Bibtex

@article{344b9c911e374b4e895fa08a3bd63389,
title = "Removing phase variability to extract a mean shape for juggling trajectories",
abstract = "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.",
keywords = "Curve alignment , multi-dimensional curves, Frenet-Serret frame , Fr{\'e}chet mean",
author = "Nicolas Brunel and Juhyun Park",
year = "2014",
month = oct,
day = "29",
doi = "10.1214/14-EJS937E",
language = "English",
volume = "8",
pages = "1848--1855",
journal = "Electronic Journal of Statistics",
issn = "1935-7524",
publisher = "Institute of Mathematical Statistics",
number = "2",

}

RIS

TY - JOUR

T1 - Removing phase variability to extract a mean shape for juggling trajectories

AU - Brunel, Nicolas

AU - Park, Juhyun

PY - 2014/10/29

Y1 - 2014/10/29

N2 - 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.

AB - 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.

KW - Curve alignment

KW - multi-dimensional curves

KW - Frenet-Serret frame

KW - Fréchet mean

U2 - 10.1214/14-EJS937E

DO - 10.1214/14-EJS937E

M3 - Journal article

VL - 8

SP - 1848

EP - 1855

JO - Electronic Journal of Statistics

JF - Electronic Journal of Statistics

SN - 1935-7524

IS - 2

ER -