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Abstract:
Background: The introduction and statistical formalisation of landmark-based methods for analysing biological
shape has made a major impact on comparative morphometric analyses. However, a satisfactory solution for
including information from 2D/3D shapes represented by ‘semi-landmarks’ alongside well-defined landmarks into the
analyses is still missing. Also, there has not been an integration of a statistical treatment of measurement error in the
current approaches.
Results: We propose a procedure based upon the description of landmarks with measurement covariance, which
extends statistical linear modelling processes to semi-landmarks for further analysis. Our formulation is based upon a
self consistent approach to the construction of likelihood-based parameter estimation and includes corrections for
parameter bias, induced by the degrees of freedom within the linear model. The method has been implemented and
tested on measurements from 2D fly wing, 2D mouse mandible and 3D mouse skull data. We use these data to
explore possible advantages and disadvantages over the use of standard Procrustes/PCA analysis via a combination of
Monte-Carlo studies and quantitative statistical tests. In the process we show how appropriate weighting provides
not only greater stability but also more efficient use of the available landmark data. The set of new landmarks
generated in our procedure (‘ghost points’) can then be used in any further downstream statistical analysis.
Conclusions: Our approach provides a consistent way of including different forms of landmarks into an analysis and
reduces instabilities due to poorly defined points. Our results suggest that the method has the potential to be utilised
for the analysis of 2D/3D data, and in particular, for the inclusion of information from surfaces represented by multiple
landmark points.
