Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups
This work provides a theoretical framework for multi-scale diffeomorphic image analysis, but it is largely an extension of existing methods.
The paper develops a multi-scale theory for diffeomorphism groups within LDDMM, providing a variational approach and semidirect product representation for multi-scale analysis, and demonstrates equivalence with mixture of kernels. Results are illustrated on synthetic and real images.
In the framework of large deformation diffeomorphic metric mapping (LDDMM), we develop a multi-scale theory for the diffeomorphism group based on previous works. The purpose of the paper is (1) to develop in details a variational approach for multi-scale analysis of diffeomorphisms, (2) to generalise to several scales the semidirect product representation and (3) to illustrate the resulting diffeomorphic decomposition on synthetic and real images. We also show that the approaches presented in other papers and the mixture of kernels are equivalent.