Contemporary shape analysis procedures are limited at present in their ability to represent, quantify, and summarize patterns of variation in any aspect of variation that cannot be represented by a set of landmarks or semilandmarks and/or features that are not present in every specimen across a population or sample. Yet, the problems presented to shape analysts for resolution fail to respect these rather stringent conceptual boundaries. An often-overlooked aspect of quantitative shape data inherent to all digital images is the pixel grid itself. For sets of images scaled to comparable pixel resolutions, this collection of quantitated brightness and colour values can be regarded as a set of semilandmarks that contain both spatial and feature-representational information. As such, the pixel grid can be considered to specify a 'shape' in the manner of a complex 3D (grayscale images) or as a 5D (colour images) surface and subjected to geometric morphometric analysis. Data analytic procedures necessary to implement the direct analysis of such digital image 'shapes' using standard geometric morphometric procedures are presented and discussed via reference to a hypothetical ladybird beetle dataset whose modes of variation are not well suited to traditional forms of shape analysis. Results indicate that all the formalisms associated with traditional shape analysis (e.g., summarisation of major patterns of form variation, visual portrayal of shape-based comparisons in an ordination space, empirical modelling of various locations within ordination spaces to inform either geometric and biological interpretation, a priori group discrimination, statistical testing of putative group differences) can be realised for the direct analysis of digital images. In addition, recent concerns that have been raised regarding the appropriateness of canonical variates analysis (CVA) as a useful procedure for shape data, and the proposal of between-groups principal components (BG-PCA) as an adequate alternative, are considered in light of the empirical results generated by the ladybird beetle dataset. So long as the ordination results of a CVA are tested statistically against expectations of reasonable null hypotheses (e.g., datasets drawn randomly from the same parent population), and so long as shape models are used to interpret the geometries of CVA ordination spaces, there seems no practical reason to prefer BG-PCA to CVA for the purpose of assessing group-structured shape variation hypotheses. When BG-PCA and CVA produce very different ordination patterns, the CVA result is likely to be the more useful especially insofar as it (1) utilises more information directly related to the group-discrimination problem (2) creates an ordination space more closely tied to the logic of the group-discrimination problem, (3) exhibits no insurmountable interpretive or statistical testing issues, and (4) usually achieves better group-discrimination results, than the former. Indeed, many of the same practical criticisms levelled at CVA are also true of BG-PCA, standard PCA, Procrustes PCA (=relative warps analysis), principal/partial warps analysis, and other geometric morphometric procedures when these are used to portray distinctions between a priori-defined groups. Precisely the same statistical procedures need to be implemented to assess and interpret the significance of the group-specific ordinations produced by these, alternative (and usually suboptimal), group-level data analysis procedures as are necessary for CVA.
展开▼
