In the context of shape analysis and computational anatomy, the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework was introduced to tackle the image matching problem. Given two images, it uses tools from sub-Riemmannian geometry on Lie groups to find a diffeomorphism sending the source image to the target and characterize shape variations through diffeomorphic deformations. In this setting, the diffeomorphisms have only finite regularity, hence the deformation group is in general not a Lie group but a half-Lie group. In this talk, we will discuss a recent work with Alain Trouvé on a natural extension of this setting to more general half-Lie groups to capture new motions. We will give the particular example of multi-scale registration