Dr Laura Sangalli, Politecnico di Milano

Title : Efficient estimation of curves in more than one dimension by free-knot regression splines, with applications to the analysis of 3D cerebral vascular geometries.

Abstract : We deal with the problem of efficiently estimating a 3D curve and its derivatives, starting from a discrete and noisy observation of the curve.  We develop a regression technique based on free-knot splines, ie. regression splines where the number and position of knots are not fixed in advance but chosen in a way to minimize a penalized sum of squared errors criterion.  We thoroughly compare this technique to a classical regression method, local polynomial smoothing, via simulation studies and application to the analysis of inner carotid artery centerlines (AneuRisk Project dataset).  We show that 3D free-knot regression splines yield more accurate and efficient estimates.

 Joint work with Piercesare Secchi and Simone Vantini.