Spatial transformer spectral kernels for deformable image registration

Recent advances in kernel methods have made them more attractive tools for spatial transformation models. In this work, Spatial Transformer Spectral Kernels are introduced as a framework for Deformable Image Registration. The transformation is restricted to live in a Reproducing Kernel Hilbert Space, and Generalized Spectral Mixture kernels are used as the reproducing kernels. This combination results in a powerful but simple regularization model that can adapt to many deformation scenarios with nonstationary and possibly long range nonmonotonic relations across the pixels. Our formulation leads to a Kernel Ridge Regression transform that is pre-computed once before optimization, and unlike most developments in image registration the loss function explicitly pairs this transform with a specific interpolation function. We derive a closed-form gradient of the loss function with respect to the spatial transformation and interpolation function which enhances registration results. Based on our evaluation, while being simpler our method can perform comparably to more complex Large Deformation Diffeomorphic Metric Mapping models in terms of reducing the intensity sum of squared differences, and can provide a more accurate estimate of the underlying displacement field.