English, Article edition: Efficient estimation of three-dimensional curves and their derivatives by free-knot regression splines, applied to the analysis of inner carotid artery centrelines Laura M. Sangalli; Piercesare Secchi; Simone Vantini; ...

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Bookmark: http://trove.nla.gov.au/version/156129
Physical Description
  • article
Language
  • English

Edition details

Title
  • Efficient estimation of three-dimensional curves and their derivatives by free-knot regression splines, applied to the analysis of inner carotid artery centrelines
Author
  • Laura M. Sangalli
  • Piercesare Secchi
  • Simone Vantini
  • Alessandro Veneziani
Physical Description
  • article
Notes
  • 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.
  • RePEc:bla:jorssc:v:58:y:2009:i:3:p:285-306
Language
  • English
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