Size and shape spaces for landmark data in two dimensions

Statistical Science

Volumn 1, Issue 2, 1986, Pages 181-222

  Bookstein, Fred L ^a  

^a UNIVERSITY OF MICHIGAN SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Allometry; Biorthogonal grids; Craniofacial growth; Landmark data; Morphometrics; Shape variables; Size variables; Statistics of deformations; Tensor biometrics

Indexed keywords

EID: 84972512610     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/ss/1177013696     Document Type: Article

References (30)

1. Benson, R. H., Chapman, R. E. and Siegel, A. F. (1982). On the measurement of morphology and its change. Paleobiology 8 328-339.
2. Bookstein, F. L. (1978a). The Measurement of Biological Shape and Shape Change. Lecture Notes in Biomathematics 24. Springer, New York.
3. Bookstein, F. L. (1978b). Linear machinery for morphological distortion. Comput. Biomed. Res. 11 435-458.
4. Bookstein, F. L. (1982a). Foundations of morphometries. Annu. Rev. Ecology Systemat. 13 451-470.
5. Bookstein, F. L. (1982b). On the cephalometrics of skeletal change. Amer. J. Orthodont. 82 177-198.
6. Bookstein, F. L. (1983). The geometry of craniofacial growth invariants. Amer. J. Orthodont. 83 221-234.
7. Bookstein, F. L. (1984a). A statistical method for biological shape comparisons. J. Theoret. Biol. 107 475-520.
8. Bookstein, F. L. (1984b). Tensor biometrics for changes in cranial shape. Ann. Human Biol. 11 413-437.
9. Bookstein, F. L. (1985). Transformations of quadrilaterals, tensor fields, and morphogenesis. In Mathematical Essays on Growth and the Emergence of Form (P. L. Antonelli, ed.) 221-265. Univ. of Alberta Press, Edmonton.
10. Bookstein, F. L. (1986). Soft modeling and the measurement of biological shape. In Theoretical Empiricism: a General Rationale for Scientific Model-Building (H. Wold, ed.). Paragon Press, in press.
11. Bookstein, F. L, Chernoff, B., Elder, R., Humphries, J., Smith, G. and Strauss, R. (1985). Morphometries in Evolutionary Biology. The Geometry of Size and Shape Change, with Examples from Fishes. Philadelphia, Academy of Natural Sciences of Philadelphia.
12. Bookstein, F. L., Lohmann, G. P. and Schweitzer, P. (1986). Landmarks from eigenshapes: Ecophenotypy in Globorotalia truncatulinoides, revisited. Unpublished manuscript.
13. Chayes, F. (1971). Ratio Correlation. Univ. of Chicago Press.
14. Goodall, C. R. (1983). The statistical analysis of growth in two dimensions. Doctoral dissertation, Department of Statistics, Harvard Univ.
15. Hofer, H. (1954). Die cranio-cerebrale Topographie bei den Affen und ihrer Bedeutung für die menschliche Schädelform. Homo 5 52-72.
16. Hofer, H. (1965). Die morphologische Analyse des Schädels des Menschen. Menschliche Abstammungslehre (G. Heberer, ed.) 145-226. Gustav Fischer, Stuttgart.
17. Lohmann, G. P. (1983). Eigenshape analysis of microfossils: A general morphometric procedure for describing changes in shape. Math. Geol. 15 659-672.
18. Mosimann, J. E. (1970). Size allometry: Size and shape variables with characterizations of the lognormal and generalized gamma distributions. J. Amer. Statist. Assoc. 65 930-948.
19. Mosimann, J. E. and James, F. C. (1979). New statistical methods for allometry with application to Florida red-winged blackbirds. Evolution 33 444-459.
20. Oxnard, C. (1984). The Order of Man. Yale Univ. Press, New Haven, Conn.
21. Reyment, R. A., Blackith, R. E. and Campbell, N. A. (1984). Multivariate Morphometries. 2nd ed. Academic, New York.
22. Riolo, M. L., Moyers, R. E., Mcnamara, J. A. and Hunter, W. S. (1974). An Atlas of Craniofacial Growth. Monograph No 2, Craniofacial Growth Series, Center for Human Growth and Development, Univ. of Michigan.
23. Sampson, P. D. (1981). Dental arch shape: a statistical analysis using conic sections. Amer. J. Orthodont. 79 535-548.
24. Serra, J. P. (1982). Image Analysis and Mathematical Morphology. Academic, New York.
25. Siegel, A. F. and Benson, R. H. (1982). A robust comparison of biological shapes. Biometrics 38 341-350.
26. Sneath, P. H. A. (1967). Trend-surface analysis of transformation grids. J. Zool (London) 151 65-88.
27. Sprent, P. (1972). The mathematics of size and shape. Biometrics 28 23-37.
28. Strauss, R. E. and Bookstein, F. L. (1982). The truss: body form reconstruction in morphometries. Systematic Zool. 31 113-135.
29. Thompson, D’A. W. (1961 [1917, 1942]). On Growth and Form (J. T. Bonner, ed. ab.). University Press, Cambridge.
30. Tobler, W. R. (1978). The comparison of plane forms. Geograph. Anal. 10 154-162.