Shape splines and stochastic shape evolutions: a second order point of view (Q2892167)

This paper proposes a second-order method for the shape evolution analysis. For this purpose the authors introduce the Hamiltonian equations of geodesics for landmark matching. Then an external force is added to the landmark configuration. Assuming a random distribution of this additional term, the authors derive a stochastic differential equation as model and use it to obtain a new minimization problem for the growth estimation to obtain a corresponding spline as description of the shape evolution. After proving existence results for this new model and further theoretical properties, the authors present several numerical studies also considering noisy data as input for the reconstruction of the shape evolution. Throughout, the authors concentrate on the finite-dimensional case but discuss the extension to the infinite-dimensional setting.