Learning Shape Metrics for Inferring the Nature of Allometry and Shape Classification

We extend the classical Procrustes metric to a new family of shape metrics and introduce a generalized Procrustes shape model. Furthermore, we propose learning models and numerical algorithms for learning metrics by using, guided by the suggestion from biologists that the spreads of landmarks should be concentrated in relatively small regions, optimization of some measurements of sparseness to select the appropriate shape metric for gene data. We apply the generalized Procrustes shape model to the shape classification problem as well and propose a selection criterion to pick out the most qualified metric for distinguishing different shape species. The experiment results illustrate the power of our shape framework.