Extending the Full Procrustes Distance to Anisotropic Scale in Shape Analysis

The full Procrustes distance between the configuration matrices of landmarks is the most fundamental landmark-based distance in shape analysis. To summarize, it is obtained by matching landmarks on a shape with those on another shape as closely as possible over the similarity transformations that consist of translation, rotation, and isotropic scaling. Thus, it considers similarity transformations only. Accordingly, it often does not work well for shapes skewed by non-similarity transformations. In this paper, we provide an efficient solution to this problem by extending the full Procrustes distance to anisotropic scale. With several shape datasets, we demonstrate that the extended full Procrustes distance is more effective in shape retrieval than typical distances, including the original full Procrustes distance.