k-Means Algorithm in Statistical Shape Analysis

In this work it is shown how the k-means method for clustering objects can be applied in the context of statistical shape analysis. Because the choice of the suitable distance measure is a key issue for shape analysis, the Hartigan and Wong k-means algorithm is adapted for this situation. Simulations on controlled artificial data sets demonstrate that distances on the pre-shape spaces are more appropriate than the Euclidean distance on the tangent space. Finally, results are presented of an application to a real problem of oceanography, which in fact motivated the current work.