Brunel, Nicolas and Park, Juhyun (2014) Removing phase variability to extract a mean shape for juggling trajectories. Electronic Journal of Statistics, 8 (2). pp. 1848-1855. ISSN 1935-7524
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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.