AGGREGATED PAIRWISE CLASSIFICATION OF ELASTIC PLANAR SHAPES

The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to early formulations of the problem with an object to be classified described as a vector in a relatively low-dimensional Euclidean space. Statistical shape data have two main properties that suggest a need for a novel approach: (i) shapes are inherently infinite-dimensional with strong dependence among the positions of nearby points, and (ii) shape space is not Euclidean but is fundamentally curved. To accommodate these features of the data, we work with the square-root velocity function of the curves to provide a useful formal description of the shape, pass to tangent spaces of the manifold of shapes at projection points (which effectively separate shapes for pairwise classification in the training data) and use principal components within these tangent spaces to reduce dimensionality. We illustrate the impact of the projection point and choice of subspace on the misclassification rate with a novel method of combining pairwise classifiers.

Automated summary

Shape classification is a key task in various fields, but the inherently infinite-dimensional and curved nature of shape data may require novel approaches. Therefore, methods such as using the square-root velocity function of curves for shape description, working with tangent spaces of shape manifolds to reduce dimensionality, and combining pairwise classifiers to improve misclassification rates may be necessary.