Is Pinocchio's nose long or his head small? Learning shape distances for classification

This work presents a new approach to analysis of shapes represented by finite set of landmarks, that generalizes the notion of Procrustes distance - an invariant metric under translation, scaling, and rotation. In many shape classification tasks there is a large variability in certain landmarks due to intra-class and/or inter-class variations. Such variations cause poor shape alignment needed for Procrustes distance computation, and lead to poor classification performance. We apply a general framework to the task of supervised classification of shapes that naturally deals with landmark distributions exhibiting large intra class or inter-class variabilty. The incorporation of Procrustes metric and of a learnt general quadratic distance inspired by Fisher linear discriminant objective function, produces a generalized Procrustes distance. The learnt distance retains the invariance properties and emphasizes the discriminative shape features. In addition, we show how the learnt metric can be useful for kernel machines design and demonstrate a performance enhancement accomplished by the learnt distances on a variety of classification tasks of organismal forms datasets.