title: Anatomical curve identification.
abstract: Methods for capturing images in three dimensions are now widely available, with stereo-photogrammetry and laser scanning being two common approaches. In anatomical studies, a number of landmarks are usually identified manually from each of these images and these form the basis of subsequent statistical analysis. However, landmarks express only a very small proportion of the information available from the images. Anatomically defined curves have the advantage of providing a much richer expression of shape. This is explored in the context of identifying the boundary of breasts from an image of the female torso and the boundary of the lips from a facial image. The curves of interest are characterised by ridges or valleys. Key issues in estimation are the ability to navigate across the anatomical surface in three-dimensions, the ability to recognise the relevant boundary and the need to assess the evidence for the presence of the surface feature of interest. The first issue is addressed by the use of principal curves, as an extension of principal components, the second by suitable assessment of curvature and the third by change-point detection. P-spline smoothing is used as an integral part of the methods but adaptations are made to the specific anatomical features of interest. After estimation of the boundary curves, the intermediate surfaces of the anatomical feature of interest can be characterised by surface interpolation. This allows shape variation to be explored using standard methods such as principal components. These tools are applied to a collection of images of women where one breast has been reconstructed after mastectomy and where interest lies in shape differences between the reconstructed and unreconstructed breasts. They are also applied to a collection of lip images where possible differences in shape between males and females are of interest.
authors.affiliation: School of Mathematics & Statistics, The University of Glasgow, UK.
authors.forename: Adrian W
authors.initials: AW
authors.lastname: Bowman
authors.affiliation: Institute of Mathematics and Statistics, Masaryk University, Brno, Czech Republic.
authors.forename: Stanislav
authors.initials: S
authors.lastname: Katina
authors.affiliation: School of Mathematics & Statistics, The University of Glasgow, UK.
authors.forename: Joanna
authors.initials: J
authors.lastname: Smith
authors.affiliation: MRC/CSO Social & Public Health Sciences Unit, The University of Glasgow, UK.
authors.forename: Denise
authors.initials: D
authors.lastname: Brown
keywords: Anatomy; Change-point; P-splines; Principal components; Principal curves; Shape analysis; Smoothing