Locally affine registration of free-form surfaces

In this paper, we are concentrating on the problem of nonrigid matching of two surfaces described by points. We deform the first surface by attaching to each point a local affine transformation. We ensure that the variation of these affine transformations along the surface is smooth, that the curvature of the deformed surface tends to be preserved and that the corresponding points on the two surfaces tend to be brought nearer. We call this deformation a locally affine deformation. Our framework does not require either a prior parametrization or the knowledge of the topology of the surfaces. It is illustrated with experiments on real biomedical surfaces: faces, brains and hearts