Shape Analysis
Stereolithographic models of human skulls (supported by grant from Wellcome Trust, LASR 2001 Proceedings). Image © K.V. Mardia.
Fractal shapes: a
ceiling panel (4’ x 4’) at
Image © K.V. Mardia.
A definition of “shape” is the information about an object that is not affected by size, location, or orientation of the object. Shapes are everywhere: fractals provides one very popular example.
For centuries, one of the major techniques in biology for separating similar animals and plants into different groups has involved the comparison of the shapes of the specimens. This field is known as morphometrics.
In modern times this task has been facilitated by the ability to record easily the positions of “landmarks” on the specimens in two or three dimensions, and new methods of statistical analysis have been developed to deal with this type of data.
See also:
http://en.wikipedia.com/wiki/Statistical_shape_analysis
Some key contributions: Mardia-Dryden model, Goodall-Mardia multivariate shape models, complex Bingham quartic distributions, bilateral symmetry and projective invariants.
Book:
1998 Statistical Shape Analysis (with
Edited Volume:
1995 Current Issues in Statistical Shape Analysis, co-editor C. A.
Gill. LASR Proceedings:
Papers in Journals:
1989 Shape analysis of triangles through directional techniques. J. Roy. Statist. Soc. Ser. B 51, 449-458.
1989 The statistical analysis of shape data (with I. L. Dryden). Biometrika 76, 271-281.
1989 On multimodality of the likelihood in the spatial linear model (with A. J. Watkins). Biometrika 76, 289-295.
1989 Shape distribution for landmark data (with I. L. Dryden). Adv. Appl. Probab. 21, 742-755.
1991 General shape distributions in a plane (with I. L. Dryden). Adv. Appl. Probab. 23, 259-276.
1991 A geometrical derivation of the shape density (with C.R. Goodall). Adv. Appl. Probab. 23, 496-514.
1992 On shape and size analysis of palmar interdigital areas (with P. D. L. Constable). J. Appl. Statist. 19, 285-292.
1992 The noncentral
1992 Size and shape analysis of landmark data (with I.L. Dryden). Biometrika 79, 57-86.
1993 Shape averages and bias (with I. Dryden). Adv. Probab. 26, 334-340.
1993 Familial Spinal Shape (with Q. Li, I.L. Dryden, P. A. Millner, R. A.Dickson and M. A. Hurn). J. Appl. Stat. 21,623-642.
1993 Multivariate aspects of shape theory (with C. Goodall). Ann. Statist. 21, 848-866.
1994 Shape analysis of paired landmark data (with A. N. Walder). Biometrika 81, 185-196.
1994 Size-shape distributions for paired landmark data (with A. N. Walder). J. Appl. Prob. 26, 894-905.
1995 Shape changes in the plane for landmark data (with M. J. Prentice). Ann. Statist. 23, 1960-1974.
1997 Consistency of Procrustes estimators (with J. T. Kent). J.
Roy. Statist. Soc. Ser. B 59,
281-290.
1999 Projective shape analysis (with C. R. Goodall). J. Comput. Graph. Statist. 8, 143-168.
1999 The complex Watson distribution and shape analysis (with I. L. Dryden). J. Roy. Statist. Soc. Ser. B 61, 913-926.
2000 Statistical assessment of bilateral symmetry (with F. L. Bookstein and I. J. Moreton). Biometrika 87, 285-300.
2001 Shape, Procrustes tangent projections and bilateral symmetry (with J. T. Kent). Biometrika 88, 469-485.
2003 A wavelet approach to shape analysis for spine curves (with R. G. Aykroyd). J. Appl. Statist 30 (6) 605-623.
2004 A shape-based Glaucoma index for images (with G. Derado, V. Patrangenaru, and H. W. Thompson). J. Appl. Statist. 31, 95-102.
2005 Directions and projective shapes (with V. Patrangenaru). Ann. Statist. 33, 1666-1699.
2006 Complex elliptical distributions with application to shape analysis (with A. C. Micheas and D. K. Dey). J. Statist. Plan. Inf. 136, 2961-2982.
2006 The complex Bingham quartic distribution and shape analysis (with J. T. Kent, and P. McDonnell) J. Roy. Statist. Soc. Ser. B 68, 747-765.
Papers in Edited Volumes:
1999 Analysing growth in faces
(with R. J. Morris, J. T. Kent, M. Fidrich, R. G.
Aykroyd, and A. Linney). In Proc. Conf. Imaging Science, Systems and Technology,
2000 Procrustes growth models
for shape (with J.T. Kent, R. J. Morris, and R. G. Aykroyd). In First Joint
Statistical Meeting, IISA
2001 Assessing the accuracy of stereolithographic models (with K.M.A. de Souza, A.L. Jackson, J.T. Kent and R.W. Soames). In LASR2001 Proceedings. (Editors: K.V. Mardia and R.G. Aykroyd), Leeds University Press, pp155-156.
2006 A new representation for projective shape (with J. T. Kent). In LASR2006 Proceedings. (Editors: S. Barber, P.D. Baxter, K.V. Mardia and R.E. Walls), Leeds University Press, pp75-78.