Identifying Skeleton Curves in Noisy Data

References

• Banfield , J. , Raftery , A. ( 1992 ). Ice flow identification in satellite images using mathematical morphology and clustering about principal curves . Journal of American Statistical Association 87 : 7 – 16 .
   Web of Science ®Google Scholar
• Blake , A. , Isard , M. ( 1998 ). Active Contours: The Application of Techniques from Graphics, Vision, Control Theory and Statistics to Visual Tracking of Shapes in Motion . New York : Springer-Verlag .
   Google Scholar
• Bouix , S. , Pruessner , J. , Collins , L. , Siddiqi , K. ( 2005 ). Hippocampal shape analysis using medial surfaces . NeuroImage 25 : 1077 – 1089 .
   PubMed Web of Science ®Google Scholar
• Caffo , B. , Crainiceanu , C. , Deng , L. , Hendrix , C. W. ( 2008 ). A case study of pharmacological colon imaging using principal curves in single photon emission computed tomography . Journal of the American Statistical Association 103 ( 484 ): 1470 – 1480 .
   PubMed Web of Science ®Google Scholar
• Chaudhuri , P. , Khandekar , R. , Sethi , D. , Kalra , P. ( 2004 ). An efficient central path algorithm for virtual navigation. Computer Graphics International Conference, Crete, Greece, pp. 188–195 .
   Google Scholar
• Cohen , L. , Kimmel , R. ( 1996 ). Fast marching the global minimum of active contours. Proc. IEEE International Conference on Image Processing (ICIP'96), Lausanne, Switzerland, pp. 473–476 .
   Google Scholar
• Delfour , M. , Zolésio , J.-P. ( 2001 ). Shapes and Geometries, Vol. 4 of Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM). Philadelphia, PA .
   Google Scholar
• Deschamps , T. , Cohen , L. ( 2000 ). Fast extraction of minimal paths in 3D images and applications to virtual endoscopy . Medical Image Analysis 5 ( 4 ): 281 – 299 .
   Web of Science ®Google Scholar
• Green , P. ( 1995 ). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination . Biometrika 82 ( 4 ): 711 – 732 .
   Web of Science ®Google Scholar
• Green. , P. J. , Silverman , B. W. ( 1994 ). Nonparametric Regression and Generalized Linear Models . Volume 58 of Monographs on Statistics and Applied Probability. London : Chapman & Hall .
   Google Scholar
• Hastie , T. ( 1984 ). Principal Curves and Surfaces. PhD thesis, Department of Statistics, Stanford University, Stanford, California .
   Google Scholar
• Hastie , T. , Stuetzle , W. ( 1989 ). Principal curves . Journal of the American Statistical Association 84 : 502 – 516 .
   Web of Science ®Google Scholar
• Kass , M. , Witkin , A. P. , Terzopoulos , D. ( 1988 ). Snakes: Active contour models . International Journal of Computer Vision 1 ( 4 ): 321 – 331 .
   Web of Science ®Google Scholar
• Kreyszig , E. ( 1968 ). Introduction to Differential Geometry and Riemannian Geometry . Toronto : University of Toronto Press, Toronto .
   Google Scholar
• Ma , W. , Wu , F. , Ouhyoung , M. ( 2003 ). Skeleton extraction of 3D objects with radial basis functions. Proc. Shape Modeling International 2003, Seoul, South Korea, pp. 207–215 .
   Google Scholar
• Piegl , L. , Tiller , W. ( 1997 ). The NURBS Book. , 2nd ed. New York : Springer-Verlag .
   Google Scholar
• Pievatolo , A. , Green , P. ( 1998 ). Boundary detection through dynamic polygons . Journal of the Royal Statistical Society, Series B, Statistical Methodology 60 ( 3 ): 609 – 626 .
   Web of Science ®Google Scholar
• Ramsay , J. O. , Silverman , B. W. (2005). Functional Data Analysis. , 2nd ed. Springer Series in Statistics. New York : Springer.
   Google Scholar
• Reinhard , K. , Niranjan , M. ( 1998 ). Subspace models for speech transitions using principal curves. Proc. Institute of Acoustics, pp. 53–60 .
   Google Scholar
• Rueckert , D. , Burger , P. ( 1997 ). Geometrically deformable templates for shape-based segmentation and tracking in cardiac MR images. EMMCVPR '97: Proceedings of the First International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, London, UK: Springer-Verlag, pp. 83–98 .
   Google Scholar
• Sadleir , R. , Whelan , P. ( 2002 ). Colon centreline calculation for CT colonography using optimised 3D topological thinning. 3DPVT 2002 – First International Symposium on 3D Data Processing Visualization and Transmission, Padova, Italy, June 19–21 .
   Google Scholar
• Stanberry , L. I. , Besag , J. Boundary reconstruction in binary images using splines. (unpublished)
   Google Scholar
• Stanford , D. , Raftery , A. E. ( 1997 ). Principal curve clustering with noise. Technical Report, University of Washington, Seattle, WA .
   Google Scholar
• Styner , M. , Lieberman , J. A. , Pantazis , D. , Gerig , G. ( 2004 ). Boundry and medial shape analysis of the hippocampus in schizophrenia . Med. Image Anal. 8 : 197 – 203 .
   PubMed Web of Science ®Google Scholar
• Tauber , C. , Batatia , H. , Morin , G. , Ayache , A. ( 2004 ). Robust B-spline snakes for ultrasound image segmentation. IEEE Computers in Cardiology, Chicago 325–328 .
   Google Scholar
• Terzopoulos , D. , Witkin , A. , Kass , M. ( 1987 ). Snakes: Active contour models. IEEE International Conference on Computer Vision, London, pp. 259–268 .
   Google Scholar