Exploring Variation in Three-Dimensional Shape Data

• Published in: Journal of computational and graphical statistics 2006-09, Vol.15 (3), p.524-541
• Main Authors: Bowman, Adrian W, Bock, Mitchum T
• Format: Article
• Language: English
• Subjects: Children; Computer software; Coordinate systems; Covariance matrices; Curve data; Dimensionality; Facial modeling; Geometric shapes; Landmark data; Landmarks; Longitudinal studies; Mathematical vectors; Permutation tests; Principal components; Principal components analysis; Procrustes analysis; Shape analysis; Software; Statistical analysis; Studies; Tangents; Three dimensional imaging
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1198/106186006X136679

A variety of very useful methods of statistical shape analysis are available for landmark data. In particular, standard methods of multivariate analysis can often be applied after suitable alignment and transformation of the data. An important example is the use of principal components analysis to provide a convenient route to graphical exploration of the main modes of variation in a sample. Where there are many landmarks or shape information is extracted in the form of curves or surfaces, the dimensionality of the resulting data can be very high and it is unlikely that substantial proportions of variability will be captured in one or two principal components. Issues of graphical exploration are explored in this setting, including random tours of a suitable low-dimensional subspace, the comparison of different groups of data, longitudinal changes and the identification of the features which distinguish individual cases from a group of controls. A suitable software environment for handling these methods with three-dimensional data is outlined. Issues of comparing principal components across time are also tackled through appropriately constructed permutation tests. All of these techniques are illustrated on a longitudinal study of facial development in young children, with particular interest in the identification of differences in facial shape between control children and those who have undergone surgical repair of a cleft lip and/or palate.