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Principal Warps: Thin-Plate Splines and the Decomposition of Deformations
June 1989 (vol. 11 no. 6)
pp. 567-585

The decomposition of deformations by principal warps is demonstrated. The method is extended to deal with curving edges between landmarks. This formulation is related to other applications of splines current in computer vision. How they might aid in the extraction of features for analysis, comparison, and diagnosis of biological and medical images in indicated.

[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," inProc. 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] F. L. Bookstein, "Transformations of quadrilaterals, tensor fields, and morphogenesis," inMathematical Essays on Growth and the Emergence of From, P. L. Antonelli, Ed. Edmonton, Alta.: University of Alberta Press, 1985.
[5] F. L. Bookstein, "Size and shape spaces for landmark data in two dimensions,"Stat. Sci., vol. 1, pp. 181-242, 1986.
[6] F. L. Bookstein, "Morphometrics 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.
[7] F. L. Bookstein, "Toward a notion of feature extraction for plane mappings," inProc. Tenth Int. Conf. Information Processing in Medical Imaging, C. de Graaf and M. Viergever, Eds. New York: Plenum, 1988, pp. 23-44.
[8] F. L. Bookstein,, "Comment on D. G. Kendall, 'A survey of the statistical theory of shape,'"Stat. Sci., May 1989.
[9] F. L. Bookstein, B. Chernoff, R. Elder, J. Humphries, G. Smith, and R. Strauss,Morphometrics in Evolutionary Biology: The Geometry of Size and Shape Change, with Examples from Fishes. Philadelphia, PA: Acad. Natural Sci., 1985.
[10] C. Broit, "Optimal registration of deformed images," Ph.D. thesis, Comput. Inform. Sci. Dept., Univ. Pennsylvania, Philadelphia, 1981.
[11] 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.
[12] 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.
[13] R. Franke, "Scattered data interpolation: Tests of some methods,"Math. Computat., vol. 38, pp. 181-200, 1982.
[14] M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active contour models,"Int. J. Comput. Vision, vol. 1, pp. 321-331, 1987.
[15] J. Meinguet, "Multivariate interpolation at arbitrary points made simple,"Zeitschrift für Angewandte Mathematik und Physik (ZAMP), vol. 30, pp. 292-304, 1979.
[16] J. Meinguet, "An intrinsic approach to multivariate spline interpolation at arbitrary points," inPolynomial and Spline Approximation, B. Sahney, Ed. Dordrecht, The Netherlands: Reidel, 1979, pp. 163-190.
[17] J. Meinguet, "Surface spline interpolation: Basic theory and computational aspects," inApproximation Theory and Spline Functions, S. P. Singhet al., Eds. Dordrecht, The Netherlands: Reidel, 1984, pp. 127- 142.
[18] 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.
[19] D. Terzopoulos, "Multilevel computational processes for visual surface reconstruction,"Comput. Vision, Graphics, Image Processing, vol. 24, pp. 52-96, 1983.
[20] D. Terzopoulos, "Regularization of inverse visual problems involving discontinuities,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 4, pp. 413-424, July 1986.
[21] A. Witkin, D. Terzopoulos, and M. Kass, "Signal matching through scale space,"Int. J. Comput. Vision, vol. 1, pp. 133-144, 1987.

Index Terms:
biomedical images; feature extraction; pattern recognition; thin-plate splines; decomposition; deformations; principal warps; curving edges; computer vision; biomedical engineering; computer vision; computerised pattern recognition
Citation:
F.L. Bookstein, "Principal Warps: Thin-Plate Splines and the Decomposition of Deformations," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 6, pp. 567-585, June 1989, doi:10.1109/34.24792
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