The Large Deformation Diffeomorphic Metric Mapping
framework constitutes a widely used and mathematically well-founded
setup for registration in medical imaging. At its heart lies the notion
of the regularization kernel, and the choice of kernel greatly affects the
results of registrations. This paper presents an extension of the LDDMM
framework allowing multiple kernels at multiple scales to be incorporated
in each registration while preserving many of the mathematical properties
of standard LDDMM. On a dataset of landmarks from lung CT
images, we show by example the influence of the kernel size in standard
LDDMM, and we demonstrate how our framework, LDDKBM, automatically
incorporates the advantages of each scale to reach the same
accuracy as the standard method optimally tuned with respect to scale.
The framework, which is not limited to landmark data, thus removes the
need for classical scale selection. Moreover, by decoupling the momentum
across scales, it promises to provide better interpolation properties, to
allow sparse descriptions of the total deformation, to remove the tradeoff
between match quality and regularity, and to allow for momentum
based statistics using scale information.