Multiscale Frame-Based Kernels for Large Deformation Diffeomorphic Metric Mapping

Abstract

We present a set of multiscale frame-based kernels that can be used to construct diffeomorphic transformation in the large deformation diffeomorphic metric mapping (LDDMM) framework. We construct multiscale kernels via compact wavelet frames that are equipped with the hierarchical multiresolution analysis. We show that these kernels under certain conditions can form reproducing kernel Hilbert spaces of smooth velocity fields and hence can be used to generate multiscale diffeomorphic transformation for LDDMM. As a proof of concept, we incorporate these kernels in the LDDMM framework. We show the improvement of whole brain mapping accuracy using the LDDMM with frame-based kernels in comparison to that obtained using the LDDMM with Gaussian kernels. Moreover, we evaluate whole brain mapping accuracy of the LDDMM with frame-based kernels against that obtained from the 14 brain mapping methods given by Klein et al.. Our results suggest that the LDDMM with frame-based kernels has the potential to outperform the 14 brain mapping methods for whole brain mapping.