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

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 58, Issue 3, 2009, Pages 285-306

  Sangalli, Laura M ^a   Secchi, Piercesare ^a   Vantini, Simone ^a   Veneziani, Alessandro ^b  

^a POLITECNICO DI MILANO   (Italy)

^b EMORY UNIVERSITY   (United States)

Author keywords

Free knot regression splines; Functional data analysis; Local polynomial smoothing; Smooth curve fitting

Indexed keywords

EID: 65949121855     PISSN: 00359254     EISSN: 14679876     Source Type: Journal    
DOI: 10.1111/j.1467-9876.2008.00653.x     Document Type: Article

References (28)

1. Antiga, L., Ene-Iordache, B. Remuzzi, A. (2003) Computational geometry for patient-specific reconstruction and meshing of blood vessels from MR and CT angiography. IEEE Trans. Med. Imgng, 22, 674 684.
2. Berger, S. A., Talbot, L. Yao, L. S. (1983) Flow in curved pipes. A. Rev. Fluid Mech., 15, 461 512.
3. de Boor, C. (1978) A Practical Guide to Splines. New York : Springer.
4. Buja, A., Hastie, T. Tibshirani, R. (1989) Linear smoothers and additive models. Ann. Statist., 17, 453 555.
5. Caro, C. G., Doorly, D. J. Tarnakasky, M. (1996) Non-planar curvature and branching of arteries and non-planar type-flow. Proc. R. Soc. Lond., 452, 185 197.
6. Castro, M. A., Putman, C. M. Cebral, J. R. (2006) Computational fluid dynamics modeling of intracranial aneurysms: effect of parent artery segmentation on intra-aneurysmal hemodynamics. Am. J. Neurradiol., 27, 1703 1709.
7. Chandran, K. (1993) Fluid dynamics in the human aorta. ASME J. Biomech. Engng, 115, 611 616.
8. Dean, W. R. (1927a) Note on the motion of fluid in a curved pipe. Philos. Mag., 4, 208 223.
9. Dean, W. R. (1927b) The streamline motion of fluid in a curved pipe. Philos. Mag., 5, 673 695.
10. Friedman, J. H. (1991) Multivariate adaptive regression splines (with discussion). Ann. Statist., 19, 1 141.
11. Gervini, D. (2006) Free-knot spline smoothing for functional data. J. R. Statist. Soc. B, 68, 671 687.
12. Gluhovsky, I. Gluhovsky, A. (2007) Smooth location-dependent bandwith selection for local polynomial regression. J. Am. Statist. Ass., 102, 718 725.
13. Hassan, T., Timofeev, E. V., Saito, T., Shimizu, H., Ezura, M., Matsumoto, Y., Takayama, K., Tominaga, T. Takahashi, A. (2005) A proposed parent vessel geometry-based categorization of saccular intracranial aneurysms: computational flow dynamics analysis of the risk factors for lesion rupture. J. Neursurg., 103, 662 680.
14. Hastie, T. J. Tibshirani, R. J. (1990) Generalized Additive Models. London : Chapman and Hall.
15. Hoi, Y., Meng, H., Woodward, S. H., Bendok, B. R., Hanel, R. A., Guterman, L. R. Hopkins, L. N. (2004) Effects of arterial geometry on aneurysm growth: three-dimensional computational fluid dynamics study. J. Neursurg., 101, 676 681.
16. Luo, Z. Wahba, G. (1997) Hybrid adaptive splines. J. Am. Statist. Ass., 92, 107 116.
17. Mao, W. Zhao, L. H. (2003) Free-knot polynomial splines with confidence intervals. J. R. Statist. Soc. B, 65, 901 919.
18. Piccinelli, M., Bacigaluppi, S., Boccardi, E., Ene-Iordache, B., Remuzzi, E., Veneziani, A. Antiga, L. (2007) Influence of internal carotid artery geometry on aneurism location and orientation: a computational geometry study. Technical Report. Emory University, Atlanta. (Available from http://www.mathcs.emory.edu.)
19. Ramsay, J. O. Silverman, B. W. (2005) Functional Data Analysis, 2nd edn. New York : Springer.
20. R Development Core Team (2007) R: a Language and Environment for Statistical Computing. Vienna : R Foundation for Statistical Computing.
21. Sangalli, L. M., Secchi, P. Vantini, S. (2008a) Explorative functional data analysis for 3D-geometries of the inner carotid artery. In Functional and Operatorial Statistics (eds S. Dabo-Niang F. Ferraty pp. 289 296. Heidelberg : Physica.
22. Sangalli, L. M., Secchi, P., Vantini, S. Veneziani, A. (2008b) A case study in exploratory functional data analysis: geometrical features of the internal carotid artery. J. Am. Statist. Ass., to be published.
23. Smith, F. T. (1976) Fluid flow into a curved pipe. Proc. R. Soc. Lond. A, 351, 71 87.
24. Stein, C. M. (1981) Estimation of the mean of a multivariate normal distribution. Ann. Statist., 9, 1135 1151.
25. Stone, C. J., Hansen, M. H., Kooperberg, C. Truong, Y. K. (1997) Polynomial splines and their tensor products in extended linear modeling (with discussion). Ann. Statist., 25, 1371 1470.
26. Ustun, C. (2005) Dr. Thomas Willis' famous eponym: the circle of Willis. J. Hist. Neursci., 14, 16 21.
27. Zhang, C. (2003) Calibrating the degrees of freedom for automatic data smoothing and effective curve checking. J. Am. Statist. Ass., 98, 609 628.
28. Zhou, S. Shen, X. (2001) Spatially adaptive regression splines and accurate knot selection schemes. J. Am. Statist. Ass., 96, 247 259.