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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 isdoi:10.1214/14-ejs937e fatcat:lks7zbacp5f3jfumkxmznr2z7u