Measurement-Based Shape Analysis

Conventional methods for shape analysis, based upon Procrustes and PCA, seem incapable of dealing with ‘non-landmark’ features, meaning measured positions not associated with well defined locations. This is due to an assumption of homogeneous errors, associated with an attempt to extract linear models with biologically meaningful descriptions. We propose a shape analysis system based upon the description of landmarks with measurement covariance which will extend the modelling process to ‘pseudo-landmarks’ such as boundaries and surfaces. We discuss the properties of our approach and how these covariances can be considered characteristic of the local shape. The method has been implemented and tested on measurements from fly wing, hand and face data. We use these data to explore possible advantages and disadvantages over the use of Procrustes/PCA.