Multiscale Frame-based Kernels for LDDMM Brain Mapping

Large Deformation Diffeomorphic Metric Mapping (LDDMM) [1] has been recognized as a powerful approach for whole brain mapping. Its deformation is diffeomorphic and is constructed through a smooth vector field in a reproducing kernel Hilbert space with diffeomorphic metric. Nevertheless, existing diffeomorphic metric is defined largely based on a Gaussian kernel that cannot often adapt to multi-scale brain features. This LDDMM with multiscale frame-based kernel uses alternative diffeomorphic metric through frame-based kernels with multiscale nature.

 

This new LDDMM with frame-based kernels employ multiscale frame-based kernels for constructing diffeomorphic metrics in the LDDMM framework. We consider multiscale kernels constructed via compact wavelet frames that are equipped with hierarchical multiresolution analysis (MRA) structures. Importantly, these reproducing kernels model velocity fields with sufficient smoothness to guarantee diffeomorphisms. Compared with the LDDMM algorithm [1], this new LDDMM with frame-based kernels improves whole brain mapping accuracy.

 

This toolbox also provides examples for brain image mapping (see readme.pdf).

 

Reference

[1] Jia Du, Laurent Younes, Anqi Qiu, “Whole Brain Diffeomorphic Metric Mapping via Integration of Sulcal and Gyral Curves, Cortical Surfaces, and Images”, Neuroimage, 56(1):162-173, 2011.

[2] Mingzhen Tan, Anqi Qiu*, “Large Deformation Multiresolution Diffeomorphic Metric Mapping for Multiresolution Cortical Surfaces: A Coarse-to-Fine Approach”, IEEE transactions on image processing, 25(9):4061-4074, 2016.

[3] Mingzhen Tan, Anqi Qiu, “Multiresolution Diffeomorphic Mapping for Cortical Surface”, Information Process Med Imaging, 2015, 315-326.