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Efficient estimation of three-dimensional curves and their derivatives by free-knot regression splines, applied to the analysis of inner carotid artery centrelines

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  • Laura M. Sangalli
  • Piercesare Secchi
  • Simone Vantini
  • Alessandro Veneziani
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    Abstract

    We deal with the problem of efficiently estimating a three-dimensional curve and its derivatives, starting from a discrete and noisy observation of the curve. This problem is now arising in many applicative contexts, thanks to the advent of devices that provide three-dimensional images and measures, such as three-dimensional scanners in medical diagnostics. Our research, in particular, stems from the need for accurate estimation of the curvature of an artery, from image reconstructions of three-dimensional angiographies. This need has emerged within the AneuRisk project, a scientific endeavour which aims to investigate the role of vessel morphology, blood fluid dynamics and biomechanical properties of the vascular wall, on the pathogenesis of cerebral aneurysms. We develop a regression technique that exploits free-knot splines in a novel setting, to estimate three-dimensional curves and their derivatives. We thoroughly compare this technique with a classical regression method, local polynomial smoothing, showing that three-dimensional free-knot regression splines yield more accurate and efficient estimates. Copyright (c) 2009 Royal Statistical Society.

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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9876.2008.00653.x
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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series C (Applied Statistics).

    Volume (Year): 58 (2009)
    Issue (Month): 3 ()
    Pages: 285-306

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    Handle: RePEc:bla:jorssc:v:58:y:2009:i:3:p:285-306

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    Cited by:
    1. Pigoli, Davide & Sangalli, Laura M., 2012. "Wavelets in functional data analysis: Estimation of multidimensional curves and their derivatives," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1482-1498.

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