Final published version, 167 KB, PDF document
Available under license: CC BY
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
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 -