Principal component analysis of landmarks from reversible images

C. M. Theobald, C. A. Glasbey, G. W. Horgan and C. D. Robinson

Journal of the Royal Statistical Society Series C, 2004, vol. 53, issue 1, 163-175

Abstract: Summary. We consider the use of principal component analysis to summarize the variation in labelled landmark data for images which are reversible in the sense that a mirror image may be defined for each image and the original and mirror images may be regarded as equally representative of the population. We examine the effect of including the original and mirror images on a principal component analysis based on the landmark co‐ordinates. The inclusion of mirror images is found to lead to a simplified interpretation in which some components measure asymmetry in the images and the remainder depend symmetrically on pairs of co‐ordinates. This is illustrated on shape variation in carrots. A second application is to the segmentation of X‐ray computed tomography images of sheep to locate the inner boundary of the carcass. It is found that image boundaries can be identified more accurately by modelling them with principal components, and that including mirror images can offer a further improvement in accuracy. Similar arguments apply when a population of images is thought to be invariant under a rotation and may also be relevant when a principal component analysis is applied to descriptive statistics such as Fourier sums.

Date: 2004
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