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This article presents a new mathematical framework to perform statisticalanalysis on time-indexed sequences of 2D or 3D shapes. At the core of thisstatistical analysis is the task of time interpolation of such data. Currentmodels in use can be compared to linear interpolation for one dimensional data.We develop a spline interpolation method which is directly related to cubicsplines on a Riemannian manifold. Our strategy consists of introducing acontrol variable on the Hamiltonian equations of the geodesics. Motivated bystatistical modeling of spatiotemporal data, we also design a stochastic modelto deal with random shape evolutions. This model is closely related to thespline model since the control variable previously introduced is set as arandom force perturbing the evolution. Although we focus on the finitedimensional case of landmarks, our models can be extended to infinitedimensional shape spaces, and they provide a first step for a non parametricgrowth model for shapes taking advantage of the widely developed framework oflarge deformations by diffeomorphisms.

Shape splines and stochastic shape evolutions: A second order point of view