Logistic regression models for elastic shape of curves based on tangent representations

Shape analysis is widely used in many application areas such as computer vision, medical and biological studies. One challenge to analyze the shape of an object in an image is its invariant property to shape-preserving transformations. To measure the distance or dissimilarity between two different shapes, we worked with the square-root velocity function (SRVF) representation and the elastic metric. Since shapes are inherently high-dimensional in a nonlinear space, we adopted a tangent space at the mean shape and a few principal components (PCs) on the linearized space. We proposed classification methods based on logistic regression using these PCs and tangent vectors with the elastic net penalty. We then compared its performance with other model-based methods for shape classification in application to shape of algae in watersheds as well as simulated data generated by the mixture of von Mises-Fisher distributions.