Résumé en anglais

This article presents a mathematical framework recently developed to perform deterministic interpolation on time-indexed sequences of 2D or 3D shapes. Most of current models in use can be compared to linear interpolation for one dimensional data. We develop a spline interpolation method which is the equivalent of splines interpolation in the Euclidean space, but in the widely developed framework of large deformations by diffeomorphisms. We open some preliminary statistical perspectives for the study of cross-evolution data.