Intrinsic sample mean in the space of planar shapes

• We propose an algorithm to obtain the intrinsic mean of sample data (planar shapes).
• Shape space is identified with a Grassmann manifold of infinite dimension.
• The Fréchet mean for manifolds and the gradient descent algorithm are used.
• A simulation study is carried out to check the performance of the methodology.

In this paper we consider the shape space as the set of smooth simple closed curves in R2R2 (parameterized curves), modulo translations, rotations and scale changes. An algorithm to obtain the intrinsic average of a sample data (set of planar shape realizations), from the identification of the shape space with an infinite dimensional Grassmannian is proposed using a gradient descent type algorithm. A simulation study is carried out to check the performance of the algorithm.