Shape Analysis using Measurement Covariances

Conventional methods for shape analysis, based upon Procrustes and PCA, seem incapable of dealing with ‘non-landmark’ features, meaning measured locations not associated with well defined locations. We argue here that this is due to an assumption of homogenous errors, associated with an attempt to extract linear models with biologically meaningful descriptions. This document contains the mathematical definition of 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 . As this breaks with convention we discuss the properties of this approach and how these covariances can be considered characteristic of the local shape. The idea has been implemented in software and is now being tested on measurements from fly wings. We will use these data to explore possible advantages and disadvantages over the use of Procrustes/PCA.