Support vector machine for elastic planar shape on the linearized space

In this paper, we consider a classification model based on support vector machines (SVM) for shape data, which is utilized in various application areas such as computer vision, medical imaging, and so on.When shape is represented as a function, we need a shape distance invariant to translation, scaling, rotation, and reparameterization.We adopt the elastic shape analysis framework based on the square-root velocity function (SRVF) representation.The framework enables us to analyze shape data on a unit hypersphere instead of a Riemannian manifold, the original representation space.The data could be even linearized using a tangent space at the mean of the transformed sample shapes.We apply the SVM to the tangent Euclidean vectors after projection.We design simulation studies for shape classification by generating planar curves from a mixture of von Mises-Fisher distributions.We analyze real data of algal shapes, and compare its performance with other statistical classification methods.