Principal Warps: Thin-Plate Splines and the Decomposition of Deformations

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 11, Issue 6, 1989, Pages 567-585

  Bookstein, Fred L ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Affine transformations; biharmonic equation; biomedical image analysis; deformation; principal warps; quadratic variation; shape; thin plate splines; warping

Indexed keywords

EID: 79957563017     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/34.24792     Document Type: Article

References (21)

1. R. Bajcsy, R. Lieberson, and M. Reivich, “A computerized system for the elastic matching of deformed radiographic images to idealized atlas images,” J. Comput. Assisted Tomography, vol. 7. pp. 618-625. 1983.
2. R. Bajcsy and F. Solina. “Three-dimensional object representation revisited,” in Proc. First Int. Conf. Computer Vision. IEEE Comput. Soc., Catalog No. 87CH2465-3. 1987. pp. 231-240.
3. F. L. Bookstein, The Measurement of Biological Shape and Shape Change (Lecture Notes in Biomathematics, vol. 24). New York: Springer-Verlag. 1978.
4. M. L. Riolo, R. E. Moyers, J. S. McNamara, and W. S. Hunter, “An atlas of craniofacial growth,” Center for Human Growth and Development, Univ. Michigan, 1974.
5. D. Terzopoulos. “Multilevel computational processes for visual surface reconstruction,” Comput. Vision, Graphics, Image Processing. vol. 24, pp. 52-96, 1983.
6. “Regularization of inverse visual problems involving discontinuities,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 413-424, 1986.
7. A. Witkin, D. Terzopoulos, and M. Kass, “Signal matching through scale space,” Int. J. Comput. Vision, vol. 1, pp. 133-144, 1987.
8. “Transformations of quadrilaterals, tensor fields, and morphogenesis,” in Mathematical Essays on Growth and the Emergence of Form, P. L. Antonelli, Ed. Edmonton, Alta.: University of Alberta Press, 1985.
9. “Size and shape spaces for landmark data in two dimensions,” Stat. Sci., vol. 1, pp. 181-242, 1986.
10. “Morphometries for functional imaging studies,” J. Cerebral Blood Flow and Metabolism (Assessment of Goals and Obstacles in Data Acquisition and Analysis from Emission Tomography), J. C. Mazziotta and S. H. Koslow, Eds., vol. 7, pp. S23-S27, 1987.
11. “Toward a notion of feature extraction for plane mappings,” in Proc. Tenth Int. Conf. Information Processing in Medical Imaging, C. de Graaf and M. Viergever, Eds. New York: Plenum, 1988, pp. 23-44.
12. Comment on D. G. Kendall, “A survey of the statistical theory of shape,” Stat. Sci., May 1989.
13. F. L. Bookstein, B. Chernoff, R. Elder, J. Humphries, G. Smith, and R. Strauss. Morphometries in Evolutionary Biology: The Geometry of Size and Shape Change, with Examples from Fishes. Philadelphia, PA: Acad. Natural Sci., 1985.
14. C. Broit, “Optimal registration of deformed images,” unpublished doctoral dissertation, Univ. Pennsylvania, 1981.
15. J. Duchon, “Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces,” RAIRO Analyse Numérique, vol. 10, pp. 5-12, 1976.
16. J. M. Fitzpatrick and M. R. Leuze, “A class of one-to-one two-dimensional transformations,” Comput. Vision, Graphics, Image Processing, vol. 39, pp. 369-382, 1987.
17. R. Franke, “Scattered data interpolation: Tests of some methods,” Math. Computat., vol. 38, pp. 181-200, 1982.
18. M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active contour models,” Int. J. Comput. Vision, vol. 1, pp. 321-331, 1987.
19. J. Meinguet, “Multivariate interpolation at arbitrary points made simple,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), vol. 30, pp. 292-304, 1979.
20. “An intrinsic approach to multivariate spline interpolation at arbitrary points,” in Polynomial and Spline Approximation, B. Sahney, Ed. Dordrecht, The Netherlands: Reidel, 1979, pp. 163-190.
21. “Surface spline interpolation: Basic theory and computational aspects,” in Approximation Theory and Spline Functions, S. P. Singh et al., Eds. Dordrecht, The Netherlands: Reidel, 1984, pp. 127-142.