Robust statistical shape analysis based on the tangent shape space

In this paper, we propose and develop a robust formulation for statistical shape analysis based on an elastic metric between closed planar curves. The proposed solution is founded on robustifying the inverse exponential map that links the preshape space to the tangent shape space relatively to a reference point. Applying this robust transition map, we obtain a rectified version of the shape database cleaned from aberrant points and more adequate for statistical analysis. Hence, we derive a new tangent PCA which we call a Robust Tangent PCA (RTPCA) where the main modes reflect the variability of the data with a resistance to outliers that may affect a classical analysis. We illustrate the capability of our approach with an application on the Kimia-HAND database.