Splines for diffeomorphisms

Splines for diffeomorphisms

This paper develops a method for higher order parametric regression on diffeomorphisms for image regression. We present a principled way to define curves with nonzero acceleration and nonzero jerk. This work extends methods based on geodesics which have been developed during the last decade for computational anatomy in the large deformation diffeomorphic image analysis framework. In contrast to...

Clamped-Plate Splines and the Optimal Flow of Bounded Diffeomorphisms

Circle Diffeomorphisms: Quasi-reducibility and Commuting Diffeomorphisms

In this article, we show two related results on circle diffeomorphisms. The first result is on quasi-reducibility: for a Baire-dense set of α, for any diffeomorphism f of rotation number α, it is possible to accumulate Rα with a sequence hn f h−1 n , hn being a diffeomorphism. The second result is: for a Baire-dense set of α, given two commuting diffeomorphisms f and g, such that f has α for ro...

Frequency Diffeomorphisms for Efficient Image

This paper presents an e cient algorithm for large deformation di eomorphic metric mapping (LDDMM) with geodesic shooting for image registration. We introduce a novel nite dimensional Fourier representation of di eomorphic deformations based on the key fact that the high frequency components of a di eomorphism remain stationary throughout the integration process when computing the deformation a...

Equilibrium States for Mañé Diffeomorphisms

We study thermodynamic formalism for the family of robustly transitive diffeomorphisms introduced by Mañé, establishing existence and uniqueness of equilibrium states for natural classes of potential functions. In particular, we characterize the SRB measures for these diffeomorphisms as unique equilibrium states for a suitable geometric potential. We also obtain large deviations and multifracta...