Curvilinear Three-Dimensional Modeling of Spinal Curves with Dual Kriging

References

• Kralky , V. , ( 1975 ). Analytical Photogrammetry in Scoliosis. In Photogrammetria , 31 , 195 – 210 .
   Google Scholar
• McNeice , G. , Korseka , J. and Raso , J. , ( 1975 ). Spatial Description of the Spine in Scoliosis. Advance in Engineering. ASME Winter Annual Meeting , Houston , pp. 76 – 86 .
   Google Scholar
• Brown , R. H. , Bursyein , A. H. , Nash , C. L. and Schock , C. C. , ( 1976 ). Spinal Analysis Using a Three-Dimensional Radiographs Technique. In Journal of Biomechanics , 9 , 355 – 365 .
   PubMed Web of Science ®Google Scholar
• Hindmarsh , J. , Larsson , J. and Mattsson , O. , ( 1980 ). Analysis of Changes in the Scoliotic Spine Using a Three-Dimensional Radiographic Technique. In Journal of Biomechanics , 12 , 279 – 290 .
   Google Scholar
• DeSmet , A. A. , Tarlton , M. A. , Cook , L. T. , Berridge , A. S. and Asher , M. A. , ( 1983 ). The Top View for Analysis of Scoliosis Progression. In Radiology , 147 , 369 – 372 .
   PubMedGoogle Scholar
• Stokes , I. A. F. , ( 1985 ). Biplanar Radiography for Measurement of Spinal Shape and Motion. In Automedica , 6 , 37 – 49 .
   Google Scholar
• Dansereau , J. , Papillon , B. and Labelle , H. , ( 1990 ). Development of a Personalized Parametric Model of Three-Dimensional Reconstructed Scoliotic Spine . In Proceedings of the Canadian Society for Biomechanics Sixth Biennial Conference , Qudbéc , Canada , pp. 717 – 72 .
   Google Scholar
• Hecquet , J. , Leg aye , J. and Sanlin , J.-J. , ( 1992 ). Logiciel Rachis 91tm . In International Symposium on 3-D Scoliotic Deformities ( ed. J. Dansereau ), Gustav Fisher Verlag Publishers , pp. 26 – 33 .
   Google Scholar
• André , B. , Danscrcau , J. and Labellc , H. , ( 1992 ). Effect of Radiographic Landmark Identification Errors on the Accuracy of Threc-Dimcnsional Reconstruction of the Human Spine. In Medical and Biological Engineering and Computing , 30 , 569 – 575 .
   PubMedGoogle Scholar
• Stokes , I. A. F. and Gardner-Morse , M. , ( 1993 ). Cross-Sectional and Longitudinal Study of Spinal Curvature and Rotation. In International Symposium on 3-D Scoliotic Deformities (ed. J. Dansereau ), Gustav Fisher Verlag Publishers. pp. 206 – 210 .
   Google Scholar
• Drcrup , B. and Hierholzer , E. , ( 1992 ). Evaluation of Frontal Radiographs of Scoliotic Spines —Part I Measurement of position and orientation of vertebrae and assessment of clinical shape parameters. In Journal of Biomechanics , 25 , 1357 – 1362 .
   PubMedGoogle Scholar
• Drerup , B. and Hierholzer , E. , ( 1992 ). Evaluation of Frontal Radiographs of Scoliotic Spines —Part II Relation between lateral deviation, lateral tilt and axial rotation of vertebrae. In |jtJournal of Biomechanics|t, 25 , 1443 – 1450 .
   Google Scholar
• Stokes , I. A. F. , Bigalow , L. C. and Morelan , M. S. ,( 1987 ). Three-Dimensional Spinal Curvature in Idiopathic Scoliosis. In Journal of Orthopaedic Research , 5, , p102–113. p
   Google Scholar
• Danscrcau , J. , ( 1983 ). Détermination des paramétres intrin-se´ques de courbure et de torsion d'un modéle tridimen-sionncl de la colonne vertébrate scoliotique. In Mémoire dc maîtrisc es science appliquées , École Polytechnique de Montréal , Canada.
   Google Scholar
• Andre , B. , Trochu , F. and Dansereau , J. , ( 1996 ). Approach for the Smoothing of Three-Dimensional reconstructions of the Human Spine using Dual Kriging Interpolation. In Medical and Biological Engineering and Computing , 34 , 185 – 191 .
   PubMed Web of Science ®Google Scholar
• Krige , D. G. , ( 1951 ). |atA Statistical Approach to Some Basic Mine Evaluation Problems on the Witwatersrand. In Journal of Chemical and Metallic Mining of the Society of South Africa , 52 , 119 – 139 .
   Google Scholar
• Matheron , G. , ( 1980 ). Splines et krigeage leur équivalence formelle. Report N-667 , Centre de géostatistiques, École des Mines de Paris , France.
   Google Scholar
• Trochu , F. , ( 1993 ). A Contouring Program Based on Dual Kriging Interpolation. In Engineering with Computers , 9, , 160 – 177 .
   Web of Science ®Google Scholar
• Perdriolle , R. , La scoliose , ( 1979 ). son étude tridimension-nelle ( Maloine , Paris ).
   Google Scholar
• Pope , M. , Stokes , I. A. F. and Moreiand , M. , ( 1984 ). The Biomechanics of Scoliosis in Critical Reviews. In Biomedical Engineering , 11 , 157 – 188 .
   Google Scholar
• Scoles , P. V. , Linton , A. E. , Latimer , B. , Levy , M. E. and Digiovanni , B. F. , ( 1988 ). Vertebral Body and Posterior Element Morphology The normal spine in middle life. In Spine , 13 , 1082 – 1086 .
   PubMed Web of Science ®Google Scholar
• Lipschutz , M. M. , ( 1969 ). Schaum's outline of theory and problems of differential geometry ( McGraw-Hill , New-York ), pp. 61 – 79 .
   Google Scholar
• Kreyszig , E. , ( 1983 ). Advanced engineering mathematics ( John Wiley and Sons , New York ), 5th ed., Chap. 8, , pp. 375 – 378 .
   Google Scholar